Wetting - Knowledge (XXG)

4857:

triple line. The triple line, which is in contact with the heterogeneous surface, cannot rest on the heterogeneous surface like the rest of the drop. In theory, it should follow the surface imperfection. This bending in the triple line is unfavorable and is not seen in real-world situations. A theory that preserves the Cassie–Baxter equation while at the same time explaining the presence of the minimized energy state of the triple line hinges on the idea of a precursor film. This film of submicrometer thickness advances ahead of the motion of the droplet and is found around the triple line. Furthermore, this precursor film allows the triple line to bend and take different conformations that were originally considered unfavorable. This precursor fluid has been observed using

6186: 4848:). Therefore, the Cassie equation can be easily derived from the Cassie–Baxter equation. Experimental results regarding the surface properties of Wenzel versus Cassie–Baxter systems showed the effect of pinning for a Young angle of 180 to 90°, a region classified under the Cassie–Baxter model. This liquid/air composite system is largely hydrophobic. After that point, a sharp transition to the Wenzel regime was found where the drop wets the surface, but no further than the edges of the drop. Actually, the Young, Wenzel and Cassie-Baxter equations represent the transversality conditions of the variational problem of wetting. 52: 4189:

wetting regime, though, is where the surface is a composite of two types of patches. An important example of such a composite surface is one composed of patches of both air and solid. Such surfaces have varied effects on the contact angles of wetting liquids. Cassie–Baxter and Wenzel are the two main models that attempt to describe the wetting of textured surfaces. However, these equations only apply when the drop size is sufficiently large compared with the surface roughness scale. When the droplet size is comparable to that of the underlying pillars, the effect of line tension should be considered.

801: 4153:. When these values are exceeded, the displacement of the contact line, such as the one in Figure 3, will take place by either expansion or retraction of the droplet. Figure 6 depicts the advancing and receding contact angles. The advancing contact angle is the maximum stable angle, whereas the receding contact angle is the minimum stable angle. Contact angle hysteresis occurs because many different thermodynamically stable contact angles are found on a nonideal solid. These varying thermodynamically stable contact angles are known as metastable states. 2652: 4185:, When a contact line advances, covering more of the surface with liquid, the contact angle is increased and is generally related to the velocity of the contact line. If the velocity of a contact line is increased without bound, the contact angle increases, and as it approaches 180°, the gas phase will become entrained in a thin layer between the liquid and solid. This is a kinetic nonequilibrium effect which results from the contact line moving at such a high speed that complete wetting cannot occur. 506: 2334: 135: 3616: 796:{\displaystyle {\begin{aligned}\gamma _{\alpha \theta }+\gamma _{\theta \beta }\cos \left(\theta \right)+\gamma _{\alpha \beta }\cos \left(\alpha \right)&=0\\\gamma _{\alpha \theta }\cos \left(\theta \right)+\gamma _{\theta \beta }+\gamma _{\alpha \beta }\cos \left(\beta \right)&=0\\\gamma _{\alpha \theta }\cos \left(\alpha \right)+\gamma _{\theta \beta }\cos \left(\beta \right)+\gamma _{\alpha \beta }&=0\end{aligned}}} 3607: 477: 2647:{\displaystyle r_{\mathrm {A} }=\left({\frac {\sin ^{3}\left(\theta _{\mathrm {A} }\right)}{2-3\cos \left(\theta _{\mathrm {A} }\right)+\cos ^{3}\left(\theta _{\mathrm {A} }\right)}}\right)^{\frac {1}{3}}~;~~r_{\mathrm {R} }=\left({\frac {\sin ^{3}\left(\theta _{\mathrm {R} }\right)}{2-3\cos \left(\theta _{\mathrm {R} }\right)+\cos ^{3}\left(\theta _{\mathrm {R} }\right)}}\right)^{\frac {1}{3}}} 4921:

impregnating wetting regime. Since the liquid can wet the larger-scale grooves, the adhesive force between the water and solid is very high. This explains why the water droplet will not fall off even if the petal is tilted at an angle or turned upside down. This effect will fail if the droplet has a volume larger than 10 μL because the balance between weight and surface tension is surpassed.

4930: 485: 265: 4074: 881: 4320: 296:(θ), as seen in Figure 1, is the angle at which the liquid–vapor interface meets the solid–liquid interface. The contact angle is determined by the balance between adhesive and cohesive forces. As the tendency of a drop to spread out over a flat, solid surface increases, the contact angle decreases. Thus, the contact angle provides an inverse measure of wettability. 4894:" describes the fact that a water droplet on the surface of a rose petal is spherical in shape, but cannot roll off even if the petal is turned upside down. The water drops maintain their spherical shape due to the superhydrophobicity of the petal (contact angle of about 152.4°), but do not roll off because the petal surface has a high adhesive force with water. 8405: 2323: 5051: 4870: 4033: 6142: 3292: 3269: 2017:. In many cases, surfaces are far from this ideal situation, and two are considered here: the case of rough surfaces and the case of smooth surfaces that are still real (finitely rigid). Even in a perfectly smooth surface, a drop will assume a wide spectrum of contact angles ranging from the so-called advancing contact angle, 4198: 5072:, the penetration front spreads beyond the drop and a liquid film forms over the surface. Figure 11 depicts the transition from the Wenzel state to the surface film state. The film smoothes the surface roughness and the Wenzel model no longer applies. In this state, the equilibrium condition and Young's relation yields: 315:". The table describes varying contact angles and their corresponding solid/liquid and liquid/liquid interactions. For nonwater liquids, the term lyophilic is used for low contact angle conditions and lyophobic is used when higher contact angles result. Similarly, the terms omniphobic and omniphilic apply to both 6247:

are oxidised to produce positively charged groups, as illustrated at right. The contact angle with water on the PFcMA-coated wafers was 70° smaller following oxidation, while in the case of PVFc the decrease was 30°, and the switching of wettability has been shown to be reversible. In the PFcMA case,

4912:

hysteresis, which means the water droplet is not able to wet the microstructure spaces between the spikes. This allows air to remain inside the texture, causing a heterogeneous surface composed of both air and solid. As a result, the adhesive force between the water and the solid surface is extremely

4188:

A well-known departure from ideal conditions is when the surface of interest has a rough texture. The rough texture of a surface can fall into one of two categories: homogeneous or heterogeneous. A homogeneous wetting regime is where the liquid fills in the grooves of a rough surface. A heterogeneous

446:

Knowing the critical surface tension of a solid, it is possible to predict the wettability of the surface. The wettability of a surface is determined by the outermost chemical groups of the solid. Differences in wettability between surfaces that are similar in structure are due to differences in the

5175:

If a drop is placed on a smooth, horizontal surface, it is generally not in the equilibrium state. Hence, it spreads until an equilibrium contact radius is reached (partial wetting). While taking into account capillary, gravitational, and viscous contributions, the drop radius as a function of time

4920:

The rose petal's micro- and nanostructures are larger in scale than those of the lotus leaf, which allows the liquid film to impregnate the texture. However, as seen in Figure 9, the liquid can enter the larger-scale grooves, but it cannot enter into the smaller grooves. This is known as the Cassie

4843:

Here the key difference to notice is that there is no surface tension between the solid and the vapor for the second surface tension component. This is because of the assumption that the surface of air that is exposed is under the droplet and is the only other substrate in the system. Subsequently,

4298:

is the apparent contact angle which corresponds to the stable equilibrium state (i.e. minimum free energy state for the system). The roughness ratio, r, is a measure of how surface roughness affects a homogeneous surface. The roughness ratio is defined as the ratio of true area of the solid surface

467:

implies the advancing and receding contact angles are equal. In other words, only one thermodynamically stable contact angle exists. When a drop of liquid is placed on such a surface, the characteristic contact angle is formed as depicted in Figure 1. Furthermore, on an ideal surface, the drop will

299:

A contact angle less than 90° (low contact angle) usually indicates that wetting of the surface is very favorable, and the fluid will spread over a large area of the surface. Contact angles greater than 90° (high contact angle) generally mean that wetting of the surface is unfavorable, so the fluid

5974:

increases. Surfactants are absorbed onto the liquid–vapor, solid–liquid, and solid–vapor interfaces, which modify the wetting behavior of hydrophobic materials to reduce the free energy. When surfactants are absorbed onto a hydrophobic surface, the polar head groups face into the solution with the

4327:

When dealing with a heterogeneous surface, the Wenzel model is not sufficient. A more complex model is needed to measure how the apparent contact angle changes when various materials are involved. This heterogeneous surface, like that seen in Figure 8, is explained using the Cassie–Baxter equation

5058:

The penetration front propagates to minimize the surface energy until it reaches the edges of the drop, thus arriving at the Wenzel state. Since the solid can be considered an absorptive material due to its surface roughness, this phenomenon of spreading and imbibition is called hemiwicking. The

4856:

With the advent of high resolution imaging, researchers have started to obtain experimental data which have led them to question the assumptions of the Cassie–Baxter equation when calculating the apparent contact angle. These groups believe the apparent contact angle is largely dependent on the

2883:

With improvements in measuring techniques such as AFM, confocal microscopy and SEM, researchers were able to produce and image droplets at ever smaller scales. With the reduction in droplet size came new experimental observations of wetting. These observations confirm that the modified Young's

4047:

For many surface/adsorbate configurations, surface energy data and experimental observations are unavailable. As wetting interactions are of great importance in various applications, it is often desired to predict and compare the wetting behavior of various material surfaces with particular

355:) are very strong. Thus, it takes a large amount of energy to break these solids (alternatively, a large amount of energy is required to cut the bulk and make two separate surfaces), so they are termed "high-energy". Most molecular liquids achieve complete wetting with high-energy surfaces. 2168: 4838: 4889:

takes advantage of this by using a hierarchy of micro- and nanostructures on each petal to provide sufficient roughness for superhydrophobicity. More specifically, each rose petal has a collection of micropapillae on the surface and each papilla, in turn, has many nanofolds. The term

3814: 5981: 5975:

tail pointing outward. In more hydrophobic surfaces, surfactants may form a bilayer on the solid, causing it to become more hydrophilic. The dynamic drop radius can be characterized as the drop begins to spread. Thus, the contact angle changes based on the following equation:

4619: 3602:{\displaystyle \cos(\theta \mp \alpha )=A+B{\frac {\cos(\alpha )}{a}}\pm C\sin(\theta \mp \alpha )(\cos(\theta )+1)^{2}{\biggl (}{\frac {\sin(\alpha )(\cos(\alpha )+2)}{(\cos(\alpha )+1)^{2}}}\mp {\frac {\sin(\theta )(\cos(\theta )+2)}{(\cos(\theta )+1)^{2}}}{\biggr )}} 4038:

The first two terms are the modified Young's equation, while the third term is due to the Laplace pressure. This nonlinear equation correctly predicts the sign and magnitude of κ, the flattening of the contact angle at very small scales, and contact angle hysteresis.

1532: 3054: 1244: 1785: 374:). Since these solids are held together by weak forces, a very low amount of energy is required to break them, thus they are termed "low-energy". Depending on the type of liquid chosen, low-energy surfaces can permit either complete or partial wetting. 6841:

Chen, Kuang-Yen; Ivashenko, Oleksii; Carroll, Gregory T.; Robertus, Jort; Kistemaker, Jos C. M.; London, Gábor; Browne, Wesley R.; Rudolf, Petra; Feringa, Ben L. (2014). "Control of Surface Wettability Using Tripodal Light-Activated Molecular Motors".

871:

meaning that not one of the surface tensions can exceed the sum of the other two. If three fluids with surface energies that do not follow these inequalities are brought into contact, no equilibrium configuration consistent with Figure 3 will exist.

5162: 4945:

from the Cassie state to the Wenzel state, the air pockets are no longer thermodynamically stable and liquid begins to nucleate from the middle of the drop, creating a "mushroom state" as seen in Figure 10. The penetration condition is given by:

3043: 4424: 5917: 4306:

for a system in thermodynamic equilibrium, defined for a perfectly flat surface. Although Wenzel's equation demonstrates the contact angle of a rough surface is different from the intrinsic contact angle, it does not describe contact angle

810:

is the surface energy between the two indicated phases. These relations can also be expressed by an analog to a triangle known as Neumann's triangle, shown in Figure 4. Neumann's triangle is consistent with the geometrical restriction that

4716:

is the solid liquid surface tension of every component. A case that is worth mentioning is when the liquid drop is placed on the substrate and creates small air pockets underneath it. This case for a two-component system is denoted by:

468:

return to its original shape if it is disturbed. The following derivations apply only to ideal solid surfaces; they are only valid for the state in which the interfaces are not moving and the phase boundary line exists in equilibrium.

4060:

approaches such as DFT, ice is commonly substituted for water. This is because DFT calculations are generally conducted assuming conditions of zero thermal movement of atoms, essentially meaning the simulation is conducted at

5015: 3808:, a geometric property of a sessile droplet to the bulk thermodynamics, the energy at the three phase contact boundary, and the curvature of the surface α. For the special case of a sessile droplet on a flat surface (α=0), 4861:(ESEM) in surfaces with pores formed in the bulk. With the introduction of the precursor film concept, the triple line can follow energetically feasible conformations, thereby correctly explaining the Cassie–Baxter model. 968: 5823:

Many technological processes require control of liquid spreading over solid surfaces. When a drop is placed on a surface, it can completely wet, partially wet, or not wet the surface. By reducing the surface tension with

4266: 2318:{\displaystyle \theta _{\mathrm {c} }=\arccos \left({\frac {r_{\mathrm {A} }\cos \left(\theta _{\mathrm {A} }\right)+r_{\mathrm {R} }\cos \left(\theta _{\mathrm {R} }\right)}{r_{\mathrm {A} }+r_{\mathrm {R} }}}\right)} 4723: 4028:{\displaystyle \cos(\theta )={\frac {\gamma _{SG}-\gamma _{SL}}{\gamma _{LG}}}+{\frac {\kappa }{\gamma _{LG}}}{\frac {1}{a}}-{\frac {\gamma }{3\gamma _{LG}}}(2+\cos(\theta )-2\cos ^{2}(\theta )-\cos ^{3}(\theta ))} 1891: 2870: 2784: 6137:{\displaystyle \cos \,\left(\theta (t)\right)=\cos \,\left(\theta _{0}\right)+\left(\cos \,\left(\theta _{\infty }\right)-\cos \,\left(\theta _{0}\right)\right)\left(1-\mathrm {e} ^{-{\frac {t}{\tau }}}\right)} 3692: 447:

packing of the atoms. For instance, if a surface has branched chains, it will have poorer packing than a surface with straight chains. Lower critical surface tension means a less wettable material surface.

5167:

By fine-tuning the surface roughness, it is possible to achieve a transition between both superhydrophobic and superhydrophilic regions. Generally, the rougher the surface, the more hydrophobic it is.

4515: 4065:. This simplification nevertheless yields results that are relevant for the adsorption of water under realistic conditions and the use of ice for the theoretical simulation of wetting is commonplace. 7651:

de Gennes, Pierre-Gilles; Brochard-Wyart, Françoise; Quéré, David (2004). Capillarity and Wetting Phenomena. Springer New York. doi:10.1007/978-0-387-21656-0. ISBN 978-1-4419-1833-8. S2CID 137894832

6264:

and other applications involving high-temperature hydrophobicity. The presence of oxygen vacancies at surfaces of ceria or other rare earth oxides is instrumental in governing surface wettability.

4144: 4452:, the Cassie–Baxter equations becomes the Wenzel equation. On the other hand, when there are many different fractions of surface roughness, each fraction of the total surface area is denoted by 3264:{\displaystyle 0={\frac {dA_{LG}}{dA_{SL}}}+{\frac {\gamma _{SL}-\gamma _{SG}}{\gamma _{LG}}}-{\frac {\kappa }{\gamma _{LG}}}{\frac {dL}{dA_{SL}}}-{\frac {V}{\gamma _{LG}}}{\frac {dP}{dA_{SL}}}} 2003: 511: 3783: 8298:

Saini, C. P.; Barman, A.; Das, D.; Satpati, B.; Bhattacharyya, S. R.; Kanjilal, D.; Ponomaryov, A.; Zvyagin, S.; Kanjilal, A. (2017). "Role of Oxygen Vacancy on the Hydrophobic Behavior of TiO

3735: 4156:

Such motion of a phase boundary, involving advancing and receding contact angles, is known as dynamic wetting. The difference between dynamic and static wetting angles is proportional to the

5414: 1607: 1655: 850: 5723: 4905:", it is important to note some striking differences. The surface structure of the lotus leaf and the rose petal, as seen in Figure 9, can be used to explain the two different effects. 7851:

Muzammil, I.; Li, Y.P.; Li, X.Y.; Lei, M.K. (2018). "Duty cycle dependent chemical structure and wettability of RF pulsed plasma copolymers of acrylic acid and octafluorocyclobutane".

1397: 1100: 6276:, in which OH and H are adsorbed separately at solid surfaces. The presence of oxygen vacancies is generally found to enhance hydrophobicity while promoting dissociative adsorption. 2160: 2131: 2102: 2073: 2044: 1663: 1344: 5078: 2698:. The lack of a solution to the Young–Dupré equation is an indicator that there is no equilibrium configuration with a contact angle between 0 and 180° for those situations. 500:

per unit length acting along the boundary line between the three phases must be zero. The components of net force in the direction along each of the interfaces are given by:

4714: 4678: 1386: 2893: 311:. Superhydrophobic surfaces have contact angles greater than 150°, showing almost no contact between the liquid drop and the surface. This is sometimes referred to as the " 1562: 4338: 4296: 1297: 6677:

Sharfrin, E.; Zisman, William A. (1960). "Constitutive relations in the wetting of low energy surfaces and the theory of the retraction method of preparing monolayers".

5834: 4642: 3806: 1072: 1929: 8241:

Fronzi, Marco; Assadi, M. Hussein N.; Hanaor, Dorian A.H.; Hanaor, Dorian A. H.; Gan, Yixiang (2019). "Theoretical insights into the hydrophobicity of low index CeO

4507: 4477: 4205:

The Wenzel model describes the homogeneous wetting regime, as seen in Figure 7, and is defined by the following equation for the contact angle on a rough surface:

1028: 8116: 4081:

Unlike ideal surfaces, real surfaces do not have perfect smoothness, rigidity, or chemical homogeneity. Such deviations from ideality result in phenomenon called

488:

Figure 4: Neumann's triangle relating the surface energies and contact angles of three fluid phases coexisting in static equilibrium, as depicted in Figure 3

4182: 4149:

When the contact angle is between the advancing and receding cases, the contact line is considered to be pinned and hysteretic behaviour can be observed, namely

1828: 1808: 1092: 6793: 852:, and applying the law of sines and law of cosines to it produce relations that describe how the interfacial angles depend on the ratios of surface energies. 7576: 6185: 888:

If the β phase is replaced by a flat rigid surface, as shown in Figure 5, then β = π, and the second net force equation simplifies to the Young equation,

8191:

Elbert, J.; Gallei, M.; Rüttiger, C.; Brunsen, A.; Didzoleit, H.; Stühn, B.; Rehahn, M. (2013). "Ferrocene Polymers for Switchable Surface Wettability".

4858: 114:

Wetting is a focus of research attention in nanotechnology and nanoscience studies due to the advent of many nanomaterials in the past two decades (e.g.

6177:

As the surfactants are absorbed, the solid–vapor surface tension increases and the edges of the drop become hydrophilic. As a result, the drop spreads.

4952: 3286:, which is proportional to the mean curvature of the droplet, and is non zero. Solving the above equation for both convex and concave surfaces yields: 894: 6553: 2884:

equation does not hold at the micro-nano scales. In addition the sign of the line tension is not maintained through the modified Young's equation.

4211: 7890: 4833:{\displaystyle \gamma \cos \,\left(\theta ^{*}\right)=f_{1}\left(\gamma _{\text{1,sv}}-\gamma _{\text{1,sl}}\right)-\left(1-f_{1}\right)\gamma } 4048:

crystallographic orientations, with relation to water or other adsorbates. This can be done from an atomistic perspective with tools including

2674:

can be larger than the sum of the other two surface energies. The consequence of this restriction is the prediction of complete wetting when γ

8382: 8349: 7529: 6919: 6776: 6751: 1836: 8032:

Lee, K. S.; Ivanova, N.; Starov, V. M.; Hilal, N.; Dutschk, V. (2008). "Kinetics of wetting and spreading by aqueous surfactant solutions".

2806: 8164:

Liu, W.-Y.; Xu, Q.-H.; Ma, Y.-X.; Liang, Y.-M.; Dong, N.-L.; Guan, D.-P. (2001). "Solvent-free synthesis of ferrocenylethene derivatives".

6979: 5828:, a nonwetting material can be made to become partially or completely wetting. The excess free energy (σ) of a drop on a solid surface is: 2711: 989:

on a solid surface from knowledge of the three surface energies involved. This equation also applies if the "gas" phase is another liquid,

3626: 7816:

Lin, F.; Zhang, Y; Xi, J; Zhu, Y; Wang, N; Xia, F; Jiang, L (2008). "Petal Effect: A Superhydrophobic State with High Adhesive Force".

3282:

work becomes significant at small scales. The variation in pressure at constant volume at the free liquid-vapor boundary is due to the

7705:"Young, Boruvka–Neumann, Wenzel and Cassie–Baxter equations as the transversality conditions for the variational problem of wetting" 6898: 6536: 4614:{\displaystyle \gamma \cos \,\left(\theta ^{*}\right)=\sum _{n=1}^{N}f_{i}\left(\gamma _{\text{i,sv}}-\gamma _{\text{i,sl}}\right)} 7666:"The rigorous derivation of Young, Cassie–Baxter and Wenzel equations and the analysis of the contact angle hysteresis phenomenon" 7639:

Wenzel, Robert N. "Resistance of solid surfaces to wetting by water." Industrial & engineering chemistry 28.8 (1936): 988-994.

480:

Figure 3: Coexistence of three fluid phases in mutual contact; here, α, β, and θ each indicate both a phase and its contact angle.

7575:

Chen, Xuemei; Ma, Ruiyuan; Li, Jintao; Hao, Chonglei; Guo, Wei; Luk, B. L.; Li, Shuai Cheng; Yao, Shuhuai; Wang, Zuankai (2012).

6609:

Mertens, Stijn F. L.; Hemmi, Adrian; Muff, Stefan; Gröning, Oliver; De Feyter, Steven; Osterwalder, Jürg; Greber, Thomas (2016).

331:

and low-energy solids. The relative energy of a solid has to do with the bulk nature of the solid itself. Solids such as metals,

103:

of two materials. Wetting and the surface forces that control wetting are also responsible for other related effects, including

7303:"Relationship between contact angle and contact line radius for micro to atto [10−6 to 10−18] liter size oil droplets" 6610: 6471: 443:) of that surface. This critical surface tension is an important parameter because it is a characteristic of only the solid. 7339:"A generalized variational approach for predicting contact angles of sessile nano-droplets on both flat and curved surfaces" 4099: 7405:

Costa, D (2017). "Edge wetting effects of γ-Al2O3 and anatase-TiO2 supports by MoS2 and CoMoS active phases: A DFT study".

6936: 7378: 7955: 7742:

Bormashenko, Edward (2020-01-17). "Variational framework for defining contact angles: a general thermodynamic approach".

3740: 77:

interactions when the two are brought together. This happens in presence of a gaseous phase or another liquid phase not

8147: 3697: 327:

Liquids can interact with two main types of solid surfaces. Traditionally, solid surfaces have been divided into high-

5182: 6824: 6252:) has been investigated, and it was found that longer chains produce significantly larger contact angle reductions. 1934: 8219: 7152:"Evaluation of three methods of static contact angle measurements for TiO 2 nanofluid droplets during evaporation" 6421: 1527:{\displaystyle {\cal {L}}=\gamma _{LG}{\sqrt {1+y'^{2}}}+(\gamma _{SL}-\gamma _{SG})-\lambda _{1}y'-\lambda _{2}y} 814: 7623: 4053: 1239:{\displaystyle {\cal {F}}=\int _{0}^{L}\left(\gamma _{LG}{\sqrt {1+y'^{2}}}+(\gamma _{SL}-\gamma _{SG})\right)dx} 493: 5425: 1567: 51: 8432: 8427: 6552:

Rafiee, J.; Mi, X.; Gullapalli, H.; Thomas, A. V.; Yavari, F.; Shi, Y.; Ajayan, P. M.; Koratkar, N. A. (2012).

2663: 1780:{\displaystyle {\cal {H}}=-\gamma _{LG}{\frac {1}{\sqrt {1+y'^{2}}}}-(\gamma _{SL}-\gamma _{SG})+\lambda _{2}y} 1612: 38: 8368: 436: 7022:

Tadmor, Rafael (2004). "Line energy and the relation between advancing, receding and Young contact angles".

6273: 2136: 2107: 2078: 2049: 2020: 6361: 6323: 5777: 4914: 6528:

Bio-aggregates Based Building Materials: State-of-the-Art Report of the RILEM Technical Committee 236-BBM

5419:

For the complete wetting situation, the drop radius at any time during the spreading process is given by

5157:{\displaystyle \cos \,\left(\theta ^{*}\right)=\phi \cos \,\left(\theta _{C}\right)+\left(1-\phi \right)} 8002:

Härth, Michael; Schubert, Dirk W. (2012). "Simple Approach for Spreading Dynamics of Polymeric Fluids".

7577:"Evaporation of Droplets on Superhydrophobic Surfaces: Surface Roughness and Small Droplet Size Effects" 6592: 6356: 7786: 3038:{\displaystyle \delta w=\gamma _{LV}dA_{LV}+\gamma _{SL}dA_{SL}+\gamma _{SV}dA_{SV}-\kappa dL-PdV-VdP} 2800:

Combining the spreading parameter definition with the Young relation yields the Young–Dupré equation:

8264: 7937: 7905: 7860: 7704: 7677: 7591: 7220: 7163: 6988: 6808: 6625: 6568: 6483: 6436: 6314: 1302: 154: 86: 45: 31: 4683: 4647: 4419:{\displaystyle \cos \,\left(\theta ^{*}\right)=r_{f}\,f\,\cos \,\left(\theta _{\text{Y}}\right)+f-1} 1349: 8437: 8409: 6383:"Photochemical Immobilization of Polymers on a Surface: Controlling Film Thickness and Wettability" 5912:{\displaystyle \sigma =\gamma S+PV+\pi \,R^{2}\left(\gamma _{\text{SL}}-\gamma _{\text{SV}}\right)} 398: 367: 7548:

Abraham Marmur (2003). "Wetting of Hydrophobic Rough Surfaces: To be heterogeneous or not to be".

1540: 8355: 8280: 8254: 7929: 7767: 7615: 7502: 7484: 7432: 7358: 7338: 7302: 7208: 7189: 7004: 6959: 6867: 6649: 6507: 6452: 6244: 6243:

wafers and the wettability measured when the polymer chains are uncharged and when the ferrocene

4942: 4274: 4049: 1252: 386: 81:

with the first one. The degree of wetting (wettability) is determined by a force balance between

381:

upon the application of an appropriate stimuli. For example, a surface presenting photon-driven

6350: – Minimum electric current through a contact to break through the surface film resistance 6344: – Minimum electric current through a contact to break through the surface film resistance 8378: 8345: 8139: 8097: 8049: 7921: 7833: 7759: 7724: 7607: 7525: 7376:

Sun, Xuegui (2017). "Molecular dynamics simulation of wetting behaviors of Li on W surfaces".

7283: 7275: 7236: 7181: 7039: 6915: 6894: 6859: 6772: 6747: 6721: 6641: 6584: 6532: 6499: 6402: 6260:

Rare earth oxides exhibit intrinsic hydrophobicity, and hence can be used in thermally stable

6228: 316: 6526: 6200:

surface due to electrostatic attractions between the resulting charges and the polar solvent.

4627: 3791: 1033: 8337: 8311: 8272: 8200: 8173: 8131: 8087: 8041: 8011: 7970: 7913: 7868: 7825: 7798: 7751: 7716: 7685: 7599: 7557: 7494: 7454: 7414: 7387: 7350: 7314: 7267: 7228: 7171: 7066: 7031: 6996: 6951: 6851: 6816: 6713: 6686: 6633: 6576: 6491: 6444: 6394: 4157: 3283: 1899: 425: 352: 119: 104: 4509:

equals 1 or the total surface. Cassie–Baxter can also be recast in the following equation:

4485: 4455: 6347: 6341: 6261: 6224: 5741: 1004: 417: 409: 382: 70: 6381:

Carroll, Gregory T.; Turro, Nicholas J.; Mammana, Angela; Koberstein, Jeffrey T. (2017).

4938: 4329: 8398: 8268: 7909: 7864: 7681: 7595: 7224: 7167: 7085: 6992: 6812: 6629: 6572: 6487: 6440: 6382: 4164: 997:

Simplification to planar geometry, Young's relation derived from variational computation

134: 7102: 6309: 6300: – Chemicals that prevent the condensation of water as small droplets on a surface 6220: 4941:, the drop sits on top of the textured surface with trapped air underneath. During the 1813: 1793: 1077: 402: 378: 157:

forces within the liquid cause the drop to ball up and avoid contact with the surface.

74: 8177: 7974: 7000: 2887:

For a sessile droplet, the free energy of the three phase system can be expressed as:

2013:

The Young equation assumes a perfectly flat and rigid surface often referred to as an

8421: 8359: 8284: 7771: 7665: 7362: 7193: 7008: 6963: 6871: 6653: 6511: 4909: 4303: 4150: 4082: 4062: 2014: 460: 456: 371: 348: 344: 340: 293: 96: 7933: 7619: 7506: 7391: 7256:"Line Energy and the Relation between Advancing, Receding, and Young Contact Angles" 366:, etc.) where the molecules are held together essentially by physical forces (e.g., 7802: 7720: 7603: 7498: 7475:

Shi, Z.; et al. (2018). "Dynamic contact angle hysteresis in liquid bridges".

6456: 6335: 4902: 4898: 4891: 359: 312: 7755: 7445:

Robert J. Good (1992). "Contact angle, wetting, and adhesion: a critical review".

6657: 4073: 8372: 8276: 7917: 7872: 7689: 7354: 7318: 5010:{\displaystyle \cos \,\left(\theta _{\text{C}}\right)={\frac {\phi -1}{r-\phi }}} 2879:

A generalized model for the contact angle of droplets on flat and curved surfaces

7132: 6474:(2013). "The effect of oxygen vacancies on water wettability of a ZnO surface". 6329: 6232: 6197: 6190: 5825: 4929: 476: 363: 308: 304: 7978: 7418: 5966:

Based on this equation, the excess free energy is minimized when γ decreases, γ

5038:

is the fraction of solid/liquid interface where drop is in contact with surface

4881:

of a surface can be enhanced by being textured with different length scales of

3619:

Schematic Diagrams for droplets on flat (a) concave (b) and convex (c) surfaces

3615: 963:{\displaystyle \gamma _{SG}=\gamma _{SL}+\gamma _{LG}\cos \left(\theta \right)} 435:

and θ is low. Zisman termed the intercept of these lines when cos θ = 1 as the

8341: 8045: 6820: 6448: 6292: 6286: 6265: 6249: 4878: 4308: 990: 484: 464: 264: 108: 8315: 7763: 7728: 7279: 7255: 7185: 6725: 6406: 92:. There are two types of wetting: non-reactive wetting and reactive wetting. 7458: 7209:"Line Tension and the Intrinsic Contact Angle in Solid–Liquid–Fluid Systems" 6303: 6204: 5757: 4261:{\displaystyle \cos \,\left(\theta ^{*}\right)=r\cos \,\left(\theta \right)} 55:

Water bead on a fabric that has been made non-wetting by chemical treatment.

8143: 8101: 8053: 8015: 7925: 7837: 7611: 7287: 7232: 7043: 6955: 6863: 6645: 6588: 6503: 6317: – Upward force that opposes the weight of an object immersed in fluid 5059:

contact angles at which spreading/imbibition occurs are between 0 and π/2.

4319: 884:

Figure 5: Contact angle of a liquid droplet wetted to a rigid solid surface

880: 8404: 8332:

de Gennes, Pierre-Gilles; Brochard-Wyart, Françoise; Quéré, David (2004).

7240: 6239:

ferrocenecarboxylate), PFcMA. Both PVFc and PFcMA have been tethered onto

1391:

The modified Lagrangian, taking into account the constraints is therefore

385:

was shown to undergo changes in water contact angle when switched between

300:

will minimize contact with the surface and form a compact liquid droplet.

6297: 6248:

the effect of longer chains with more ferrocene groups (and also greater

4882: 856: 142: 123: 115: 100: 82: 78: 7070: 6690: 6637: 6268:

of water at oxide surfaces can occur as molecular adsorption, in which H

6189:

Strands of an uncharged ferrocene-substituted polymer are tethered to a

5050: 4869: 2793:> 0, the liquid wets the surface completely (complete wetting). When 397:

Low-energy surfaces primarily interact with liquids through dispersive (

8092: 8075: 6717: 6495: 6216: 6212: 6211:-active organometallic compound which can be incorporated into various 5767: 1886:{\displaystyle {\frac {\partial {\cal {F}}}{\partial L}}=-{\cal {H}}=0} 986: 459:

is flat, rigid, perfectly smooth, chemically homogeneous, and has zero

336: 17: 8204: 8135: 7829: 7561: 7271: 7176: 7151: 7035: 6855: 6398: 2865:{\displaystyle S=\gamma _{LG}\left(\cos \left(\theta \right)-1\right)} 6580: 6240: 6193: 2779:{\displaystyle S=\gamma _{SG}-\left(\gamma _{SL}+\gamma _{LG}\right)} 978: 328: 146: 63: 8259: 7489: 6306: – Retraction of a fluid from a surface it was forced to cover 3687:{\displaystyle A={\frac {\gamma _{SG}-\gamma _{SL}}{\gamma _{LG}}}} 6208: 6184: 5049: 4928: 4868: 4318: 4197: 4196: 4072: 3614: 3048:

At constant volume in thermodynamic equilibrium, this reduces to:

2666:

1805; Anthanase Dupré and Paul Dupré 1869) dictates that neither γ

974: 879: 497: 483: 475: 332: 273: 263: 150: 133: 111:

can be used to increase the wetting power of a liquid like water.

89: 67: 50: 7709:

Colloids and Surfaces A: Physicochemical and Engineering Aspects

4886: 4644:

is the Cassie–Baxter surface tension between liquid and vapor,

492:

Figure 3 shows the line of contact where three phases meet. In

138:

Figure 1: Contact angle for a liquid droplet on a solid surface

4440:

is the fraction of solid surface area wet by the liquid. When

982: 4085:, which is defined as the difference between the advancing (θ 996: 973:

which relates the surface tensions between the three phases:

4077:

Figure 6: Schematic of advancing and receding contact angles

1872: 1848: 1669: 1642: 1618: 1594: 1403: 1106: 985:. Subsequently, this predicts the contact angle of a liquid 416:) of the liquid decreased. Thus, he was able to establish a 377:

Dynamic surfaces have been reported that undergo changes in

30:"Wetness" redirects here. For the biological secretion, see 27:

Ability of a liquid to maintain contact with a solid surface

6326: – Method of determining the surface energy of a solid 6272:

O molecules remain intact at the terminated surface, or as

6227:

and then polymerized to form polyvinylferrocene (PVFc), an

4680:

is the solid vapor surface tension of every component, and

7301:

Jasper, Warren J.; Rasipuram, Srinivasan (December 2017).

3612:

Where the constant parameters A, B, and C are defined as:

358:

The other type of solid is weak molecular crystals (e.g.,

6944:

Philosophical Transactions of the Royal Society of London

6769:

Modern Approaches to Wettability. Theory and Applications

6704:

Mantanis, G. I.; Young, R. A. (1997). "Wetting of wood".

6422:"Fundamental issues of reactive wetting by liquid metals" 855:

Because these three surface energies form the sides of a

6611:"Switching stiction and adhesion of a liquid on a solid" 1094:

is a free parameter. The free energy to be minimized is

7433:

Applied Surface Science, Elsevier, 2019, 478, pp.68-74.

6352:

Pages displaying short descriptions of redirect targets

6319:

Pages displaying short descriptions of redirect targets

6196:

surface. Oxidation of the ferrocenyl groups produces a

2875:

which only has physical solutions for θ when S < 0.

7891:"Wetting transitions on textured hydrophilic surfaces" 7664:

Whyman, G.; Bormashenko, Edward; Stein, Tamir (2008).

7057:

Schrader, Malcolm E. (1995). "Young-Dupre Revisited".

6742:

Eustathopoulos, N.; Nicholas, M.G.; Drevet B. (1999).

4139:{\displaystyle {\text{H}}=\,\theta _{a}-\,\theta _{r}} 1564:

are Lagrange multipliers. By definition, the momentum

859:, they are constrained by the triangle inequalities, γ 6893:

Ed. Berg, John. C. New York, NY: Marcel Dekker, Inc.

5984: 5837: 5428: 5185: 5081: 4955: 4726: 4686: 4650: 4630: 4518: 4488: 4458: 4341: 4277: 4214: 4167: 4102: 3817: 3794: 3743: 3700: 3629: 3295: 3278:

term has been neglected for large droplets, however,

3057: 2896: 2809: 2714: 2337: 2171: 2139: 2110: 2081: 2052: 2023: 2009:

Non-ideal smooth surfaces and the Young contact angle

1937: 1902: 1839: 1816: 1796: 1666: 1615: 1570: 1543: 1400: 1352: 1305: 1255: 1103: 1080: 1036: 1007: 897: 817: 509: 408:

Zisman observed that cos θ increases linearly as the

8117:"Chemical Redox Agents for Organometallic Chemistry" 4908:

The lotus leaf has a randomly rough surface and low

4436:is the roughness ratio of the wet surface area and 876:

Simplification to planar geometry, Young's relation

7150:Wciślik, Sylwia; Mukherjee, Sayantan (June 2022). 6136: 5911: 5717: 5408: 5156: 5009: 4913:low, allowing the water to roll off easily (i.e. " 4832: 4708: 4672: 4636: 4613: 4501: 4471: 4418: 4290: 4260: 4176: 4138: 4027: 3800: 3778:{\displaystyle C={\frac {\gamma }{3\gamma _{LG}}}} 3777: 3729: 3686: 3601: 3263: 3037: 2864: 2778: 2658:The Young–Dupré equation and spreading coefficient 2646: 2317: 2154: 2125: 2096: 2067: 2038: 1997: 1923: 1885: 1822: 1802: 1779: 1649: 1601: 1556: 1526: 1380: 1338: 1291: 1238: 1086: 1066: 1022: 962: 844: 795: 153:cause a liquid drop to spread across the surface. 6525:Amziane, Sofiane; Collet, Florence (2017-03-05). 3730:{\displaystyle B={\frac {\kappa }{\gamma _{LG}}}} 3594: 3416: 303:For water, a wettable surface may also be termed 6977:T. S. Chow (1998). "Wetting of rough surfaces". 5054:Figure 11: Penetration front spreads beyond drop 1790:Now, we recall that the boundary is free in the 7647: 7645: 5409:{\displaystyle r(t)=r_{e}\left^{\frac {1}{6}}.} 7131:Gibbs, Josiah Willard Auteur du texte (1928). 6332: – Thin film of soapy water enclosing air 6235:. Another polymer which can be formed is poly( 4056:. In the theoretical prediction of wetting by 2701:A useful parameter for gauging wetting is the 1998:{\displaystyle (1+y'^{2})^{-1/2}=\cos \theta } 1830:is a free parameter. Therefore, we must have: 993:with the droplet of the first "liquid" phase. 8220:"Rare-Earth Oxides Are Naturally Hydrophobic" 8069: 8067: 8065: 8063: 7954:Quere, D.; Thiele, Uwe; Quéré, David (2008). 7524:. Cambridge, UK: Cambridge University Press. 7337:Jasper, Warren J.; Anand, Nadish (May 2019). 389:conformations of differing surface energies. 8: 8302:Nanorods on Chemically Etched Si Pyramids". 7787:"Why does the Cassie–Baxter equation apply?" 7084:Athanase M. Dupré, Paul Dupré (1869-01-01). 5066:and π/2. If the contact angle is less than Θ 5044:is solid roughness (for flat surface, r = 1) 845:{\displaystyle \alpha +\beta +\theta =2\pi } 806:where α, β, and θ are the angles shown and γ 4873:Figure 9: "Petal effect" vs. "lotus effect" 2046:, to the so-called receding contact angle, 2005:, therefore we recover the Young equation. 66:to displace gas to maintain contact with a 7744:Journal of Adhesion Science and Technology 7543: 7541: 7447:Journal of Adhesion Science and Technology 6885: 6883: 6881: 5718:{\displaystyle r(t)=\left^{\frac {1}{6}},} 4859:environmental scanning electron microscopy 1602:{\displaystyle p=\partial _{y'}{\cal {L}}} 159: 8258: 8091: 8034:Advances in Colloid and Interface Science 7884: 7882: 7659: 7657: 7488: 7431:Hydrophobicity of low index CeO2 planes, 7175: 6672: 6670: 6420:Dezellus, O.; Eustathopoulos, N. (2010). 6223:(ferroceneylethene) can be prepared by a 6117: 6113: 6108: 6081: 6072: 6056: 6047: 6026: 6017: 5988: 5983: 5898: 5885: 5870: 5865: 5836: 5701: 5682: 5674: 5659: 5644: 5621: 5605: 5594: 5575: 5556: 5537: 5521: 5494: 5482: 5469: 5460: 5427: 5392: 5370: 5353: 5332: 5319: 5305: 5300: 5282: 5271: 5266: 5252: 5242: 5205: 5184: 5122: 5113: 5094: 5085: 5080: 4981: 4968: 4959: 4954: 4816: 4787: 4774: 4759: 4742: 4733: 4725: 4691: 4685: 4655: 4649: 4629: 4600: 4587: 4572: 4562: 4551: 4534: 4525: 4517: 4493: 4487: 4463: 4457: 4394: 4385: 4381: 4377: 4371: 4354: 4345: 4340: 4282: 4276: 4246: 4227: 4218: 4213: 4166: 4130: 4125: 4116: 4111: 4103: 4101: 4004: 3979: 3933: 3920: 3907: 3896: 3887: 3873: 3859: 3843: 3836: 3816: 3793: 3763: 3750: 3742: 3716: 3707: 3699: 3673: 3659: 3643: 3636: 3628: 3593: 3592: 3583: 3508: 3496: 3421: 3415: 3414: 3408: 3329: 3294: 3249: 3231: 3220: 3211: 3196: 3178: 3167: 3158: 3144: 3130: 3114: 3107: 3092: 3074: 3064: 3056: 2990: 2974: 2958: 2942: 2926: 2910: 2895: 2820: 2808: 2762: 2746: 2725: 2713: 2633: 2615: 2614: 2597: 2579: 2578: 2542: 2541: 2524: 2517: 2502: 2501: 2474: 2456: 2455: 2438: 2420: 2419: 2383: 2382: 2365: 2358: 2343: 2342: 2336: 2301: 2300: 2286: 2285: 2268: 2267: 2246: 2245: 2227: 2226: 2205: 2204: 2197: 2177: 2176: 2170: 2145: 2144: 2138: 2116: 2115: 2109: 2087: 2086: 2080: 2058: 2057: 2051: 2029: 2028: 2022: 1973: 1966: 1955: 1936: 1901: 1871: 1870: 1847: 1846: 1840: 1838: 1815: 1795: 1768: 1749: 1733: 1713: 1693: 1684: 1668: 1667: 1665: 1650:{\displaystyle {\cal {H}}=py'-{\cal {L}}} 1641: 1640: 1617: 1616: 1614: 1593: 1592: 1581: 1569: 1548: 1542: 1515: 1494: 1475: 1459: 1440: 1424: 1415: 1402: 1401: 1399: 1357: 1351: 1310: 1304: 1254: 1213: 1197: 1178: 1162: 1153: 1138: 1133: 1105: 1104: 1102: 1079: 1035: 1006: 934: 918: 902: 896: 816: 770: 737: 704: 660: 644: 611: 567: 534: 518: 510: 508: 7213:Journal of Colloid and Interface Science 7134:The collected works / of J. W. Gibbs,... 6844:Journal of the American Chemical Society 6737: 6735: 3788:This equation relates the contact angle 420:between cos θ and the surface tension (γ 8115:Connelly, N. G.; Geiger, W. E. (1996). 6373: 5935:is the solid–liquid interfacial tension 5928:is the liquid–vapor interfacial tension 4844:the equation is then expressed as (1 – 1952: 1710: 1437: 1175: 339:are known as 'hard solids' because the 268:Figure 2: Wetting of different fluids: 8027: 8025: 7470: 7468: 6289: – Phenomenon of surface adhesion 6219:which can be tethered onto a surface. 5942:is the solid–vapor interfacial tension 2155:{\displaystyle \theta _{\mathrm {R} }} 2126:{\displaystyle \theta _{\mathrm {A} }} 2097:{\displaystyle \theta _{\mathrm {c} }} 2068:{\displaystyle \theta _{\mathrm {R} }} 2039:{\displaystyle \theta _{\mathrm {A} }} 7332: 7330: 7328: 7145: 7143: 7126: 7124: 7103:"Contact Angle Spreading Coefficient" 6171:is the surfactant transfer time scale 5948:is the area of liquid–vapor interface 7: 8218:Kemsley, Jyllian (28 January 2013). 8004:Macromolecular Chemistry and Physics 6980:Journal of Physics: Condensed Matter 6937:"An Essay on the Cohesion of Fluids" 5954:is the excess pressure inside liquid 472:Minimization of energy, three phases 8371:; Clayton J. Radke (2 April 2007). 8304:The Journal of Physical Chemistry C 8166:Journal of Organometallic Chemistry 6910:Rowlinson, J.S.; Widom, B. (1982). 6476:Physical Chemistry Chemical Physics 5062:The Wenzel model is valid between θ 4043:Computational prediction of wetting 323:High-energy vs. low-energy surfaces 8076:"Polymers with pendant ferrocenes" 7703:Bormashenko, Edward (2009-08-05). 6767:Schrader, M.E; Loeb, G.I. (1992). 6554:"Wetting transparency of graphene" 6109: 6057: 4925:Cassie–Baxter to Wenzel transition 2616: 2580: 2543: 2503: 2457: 2421: 2384: 2344: 2302: 2287: 2269: 2247: 2228: 2206: 2178: 2146: 2117: 2088: 2059: 2030: 1855: 1843: 1578: 1001:Consider the interface as a curve 25: 8334:Capillarity and Wetting Phenomena 7207:Marmur, Abraham (February 1997). 6679:The Journal of Physical Chemistry 4865:"Petal effect" vs. "lotus effect" 2075:. The equilibrium contact angle ( 431:A surface is more wettable when γ 280:shows a fluid with more wetting. 8403: 6744:Wettability at high temperatures 2797:< 0, partial wetting occurs. 276:with very little wetting, while 8224:Chemical & Engineering News 7889:Ishino, C.; Okumura, K (2008). 7392:10.1016/j.fusengdes.2016.06.037 7087:Théorie mécanique de la chaleur 6914:. Oxford, UK: Clarendon Press. 6912:Molecular Theory of Capillarity 6794:"Wetting: statics and dynamics" 6387:Photochemistry and Photobiology 1339:{\displaystyle \int _{I}y'dx=0} 405:produced several key findings: 343:that hold them together (e.g., 284:has a large contact angle, and 8374:Wetting and Spreading Dynamics 7956:"Wetting of Textured Surfaces" 7803:10.1016/j.colsurfa.2008.03.025 7721:10.1016/j.colsurfa.2009.04.054 7604:10.1103/PhysRevLett.109.116101 7499:10.1016/j.colsurfa.2018.07.004 7090:(in French). Gauthier-Villars. 6003: 5997: 5581: 5562: 5438: 5432: 5195: 5189: 4709:{\displaystyle \gamma _{i,sl}} 4673:{\displaystyle \gamma _{i,sv}} 4069:Non-ideal rough solid surfaces 4022: 4019: 4013: 3994: 3988: 3966: 3960: 3945: 3830: 3824: 3580: 3570: 3564: 3555: 3550: 3541: 3535: 3526: 3523: 3517: 3493: 3483: 3477: 3468: 3463: 3454: 3448: 3439: 3436: 3430: 3405: 3395: 3389: 3380: 3377: 3365: 3344: 3338: 3314: 3302: 1963: 1938: 1912: 1906: 1758: 1726: 1484: 1452: 1381:{\displaystyle \int _{I}ydx=A} 1280: 1274: 1265: 1259: 1222: 1190: 1123: 1111: 1061: 1049: 1017: 1011: 393:Wetting of low-energy surfaces 1: 8178:10.1016/S0022-328X(00)00927-X 7975:10.1016/S0927-7757(02)00061-4 7756:10.1080/01694243.2019.1663030 7379:Fusion Engineering and Design 7254:Tadmor, Rafael (2004-08-01). 5960:is the radius of droplet base 5807:is drop radius in equilibrium 5032:is the critical contact angle 4323:Figure 8: Cassie–Baxter model 44:For other uses of "Wet", see 8277:10.1016/j.apsusc.2019.01.208 7873:10.1016/j.apsusc.2017.11.261 7690:10.1016/j.cplett.2007.11.033 7355:10.1016/j.molliq.2019.02.039 7343:Journal of Molecular Liquids 7319:10.1016/j.molliq.2017.10.134 7307:Journal of Molecular Liquids 6889:Johnson, Rulon E. (1993) in 6429:Journal of Materials Science 5814:Modifying wetting properties 1557:{\displaystyle \lambda _{i}} 95:Wetting is important in the 7001:10.1088/0953-8984/10/27/001 6706:Wood Science and Technology 4291:{\displaystyle \theta ^{*}} 2162:as was shown by Tadmor as, 1292:{\displaystyle y(0)=y(L)=0} 8454: 7918:10.1140/epje/i2007-10308-y 7419:10.1016/j.jcat.2006.12.007 6771:. New York: Plenum Press. 5798:is experimental delay time 2662:The Young–Dupré equation ( 307:and a nonwettable surface 288:has a small contact angle. 43: 36: 29: 8342:10.1007/978-0-387-21656-0 8046:10.1016/j.cis.2008.08.005 7898:European Physical Journal 7520:De Gennes, P. G. (1994). 6821:10.1103/RevModPhys.57.827 6801:Reviews of Modern Physics 6449:10.1007/s10853-009-4128-x 4933:Figure 10: Mushroom state 4054:density functional theory 2104:) can be calculated from 1657:which is computed to be: 209: 206: 203: 173: 168: 165: 162: 8316:10.1021/acs.jpcc.6b08991 8080:Chemical Society Reviews 7785:Bormashenko, E. (2008). 7670:Chemical Physics Letters 7435:in HAL archives ouvertes 6792:de Gennes, P.G. (1985). 6746:. Oxford, UK: Pergamon. 6237:2-(methacryloyloxy)ethyl 6156:is initial contact angle 4151:contact angle hysteresis 4083:contact angle hysteresis 875: 461:contact angle hysteresis 437:critical surface tension 39:Wetting (disambiguation) 8247:Applied Surface Science 8074:Pietschnig, R. (2016). 7963:Colloids and Surfaces A 7853:Applied Surface Science 7791:Colloids and Surfaces A 7584:Physical Review Letters 7477:Colloids and Surfaces A 7459:10.1163/156856192X00629 6470:Hu, Han; Ji, Hai-Feng; 6274:dissociative adsorption 4637:{\displaystyle \gamma } 3801:{\displaystyle \theta } 2686:and zero wetting when γ 1067:{\displaystyle x\in I=} 8016:10.1002/macp.201100631 7233:10.1006/jcis.1996.4666 6956:10.1098/rstl.1805.0005 6362:USBM wettability index 6324:Sessile drop technique 6201: 6165:is final contact angle 6138: 5913: 5778:gravitational constant 5719: 5410: 5158: 5055: 5011: 4934: 4874: 4834: 4710: 4674: 4638: 4615: 4567: 4503: 4473: 4420: 4324: 4299:to the apparent area. 4292: 4262: 4202: 4201:Figure 7: Wenzel model 4178: 4140: 4078: 4029: 3802: 3779: 3731: 3688: 3620: 3603: 3265: 3039: 2866: 2780: 2648: 2319: 2156: 2127: 2098: 2069: 2040: 1999: 1925: 1924:{\displaystyle y(L)=0} 1887: 1824: 1804: 1781: 1651: 1603: 1558: 1528: 1382: 1340: 1299:which we can write as 1293: 1240: 1088: 1068: 1024: 964: 885: 846: 797: 489: 481: 289: 139: 56: 8336:. Springer New York. 6357:Lak wettability index 6338: – Lab technique 6188: 6139: 5914: 5785:is shape factor, 37.1 5720: 5411: 5159: 5053: 5012: 4932: 4872: 4835: 4711: 4675: 4639: 4616: 4547: 4504: 4502:{\displaystyle f_{i}} 4474: 4472:{\displaystyle f_{i}} 4421: 4322: 4293: 4263: 4200: 4192: 4179: 4141: 4076: 4030: 3803: 3780: 3732: 3689: 3618: 3604: 3266: 3040: 2867: 2781: 2703:spreading parameter S 2649: 2320: 2157: 2128: 2099: 2070: 2041: 2000: 1926: 1888: 1825: 1805: 1782: 1652: 1604: 1559: 1529: 1383: 1341: 1294: 1249:with the constraints 1241: 1089: 1069: 1025: 965: 883: 847: 798: 487: 479: 267: 174:Interaction strength 137: 54: 8412:at Wikimedia Commons 8399:What is wettability? 7407:Journal of Catalysis 7101:Clegg, Carl (2016). 5982: 5835: 5426: 5183: 5176:can be expressed as 5079: 4953: 4897:When comparing the " 4724: 4684: 4648: 4628: 4516: 4486: 4456: 4339: 4275: 4212: 4165: 4100: 3815: 3792: 3741: 3698: 3627: 3293: 3055: 2894: 2807: 2712: 2335: 2169: 2137: 2108: 2079: 2050: 2021: 1935: 1900: 1837: 1814: 1794: 1664: 1613: 1609:and the Hamiltonian 1568: 1541: 1398: 1350: 1303: 1253: 1101: 1078: 1034: 1023:{\displaystyle y(x)} 1005: 895: 815: 507: 451:Ideal solid surfaces 368:van der Waals forces 319:and apolar liquids. 62:is the ability of a 46:Wet (disambiguation) 37:For other uses, see 32:subpreputial wetness 8269:2019ApSS..478...68F 7910:2008EPJE...25..415I 7865:2018ApSS..436..411M 7682:2008CPL...450..355W 7596:2012PhRvL.109k6101C 7590:(11): 116101(1–6). 7225:1997JCIS..186..462M 7168:2022PhFl...34f2006W 7071:10.1021/la00009a049 6993:1998JPCM...10L.445C 6813:1985RvMP...57..827D 6691:10.1021/j100834a002 6638:10.1038/nature18275 6630:2016Natur.534..676M 6573:2012NatMa..11..217R 6488:2013PCCP...1516557H 6441:2010JMatS..45.4256D 5692: 5310: 5276: 4939:Cassie–Baxter model 4482:A summation of all 4315:Cassie–Baxter model 1143: 8367:Victor M. Starov; 8093:10.1039/C6CS00196C 6935:Young, T. (1805). 6718:10.1007/BF01159153 6496:10.1039/C3CP51848E 6202: 6134: 5909: 5715: 5670: 5406: 5296: 5262: 5171:Spreading dynamics 5154: 5056: 5007: 4943:wetting transition 4935: 4875: 4830: 4706: 4670: 4634: 4611: 4499: 4469: 4416: 4325: 4288: 4258: 4203: 4177:{\displaystyle Ca} 4174: 4136: 4079: 4050:molecular dynamics 4025: 3798: 3775: 3727: 3684: 3621: 3599: 3261: 3035: 2862: 2776: 2644: 2315: 2152: 2123: 2094: 2065: 2036: 1995: 1921: 1883: 1820: 1800: 1777: 1647: 1599: 1554: 1524: 1378: 1336: 1289: 1236: 1129: 1084: 1064: 1020: 960: 886: 842: 793: 791: 490: 482: 290: 232:90° ≤ θ < 180° 207:0 < θ < 90° 140: 57: 8408:Media related to 8384:978-1-4200-1617-8 8369:Manuel G. Velarde 8351:978-1-4419-1833-8 8205:10.1021/om400468p 8199:(20): 5873–5878. 8136:10.1021/cr940053x 8086:(19): 5216–5231. 7830:10.1021/la703821h 7562:10.1021/la0344682 7556:(20): 8343–8348. 7531:978-0-521-56417-5 7453:(12): 1269–1302. 7272:10.1021/la049410h 7266:(18): 7659–7664. 7177:10.1063/5.0096644 7156:Physics of Fluids 7036:10.1021/la049410h 6987:(27): L445–L451. 6921:978-0-19-855642-8 6856:10.1021/ja412110t 6778:978-0-306-43985-8 6753:978-0-08-042146-9 6624:(7609): 676–679. 6435:(16): 4256–4264. 6399:10.1111/php.12751 6215:and used to make 6125: 5901: 5888: 5709: 5694: 5690: 5667: 5652: 5629: 5602: 5588: 5545: 5504: 5400: 5380: 5312: 5277: 5005: 4971: 4790: 4777: 4603: 4590: 4397: 4106: 4093:) contact angles 4089:) and receding (θ 3943: 3915: 3905: 3882: 3773: 3725: 3682: 3590: 3503: 3351: 3259: 3229: 3206: 3176: 3153: 3102: 2641: 2627: 2496: 2493: 2487: 2482: 2468: 2309: 1862: 1823:{\displaystyle L} 1803:{\displaystyle x} 1721: 1720: 1447: 1346:and fixed volume 1185: 1087:{\displaystyle L} 262: 261: 210:High wettability 145:forces between a 73:, resulting from 16:(Redirected from 8445: 8407: 8388: 8363: 8320: 8319: 8295: 8289: 8288: 8262: 8238: 8232: 8231: 8215: 8209: 8208: 8188: 8182: 8181: 8161: 8155: 8154: 8152: 8146:. Archived from 8124:Chemical Reviews 8121: 8112: 8106: 8105: 8095: 8071: 8058: 8057: 8029: 8020: 8019: 7999: 7993: 7992: 7990: 7989: 7983: 7977:. Archived from 7960: 7951: 7945: 7944: 7942: 7936:. Archived from 7895: 7886: 7877: 7876: 7848: 7842: 7841: 7824:(8): 4114–4119. 7813: 7807: 7806: 7782: 7776: 7775: 7739: 7733: 7732: 7700: 7694: 7693: 7676:(4–6): 355–359. 7661: 7652: 7649: 7640: 7637: 7631: 7630: 7628: 7622:. Archived from 7581: 7572: 7566: 7565: 7545: 7536: 7535: 7517: 7511: 7510: 7492: 7472: 7463: 7462: 7442: 7436: 7429: 7423: 7422: 7402: 7396: 7395: 7373: 7367: 7366: 7334: 7323: 7322: 7298: 7292: 7291: 7251: 7245: 7244: 7204: 7198: 7197: 7179: 7147: 7138: 7137: 7128: 7119: 7118: 7116: 7114: 7107:www.ramehart.com 7098: 7092: 7091: 7081: 7075: 7074: 7065:(9): 3585–3589. 7054: 7048: 7047: 7019: 7013: 7012: 6974: 6968: 6967: 6941: 6932: 6926: 6925: 6907: 6901: 6887: 6876: 6875: 6850:(8): 3219–3224. 6838: 6832: 6831: 6829: 6823:. Archived from 6798: 6789: 6783: 6782: 6764: 6758: 6757: 6739: 6730: 6729: 6701: 6695: 6694: 6674: 6665: 6664: 6662: 6656:. Archived from 6615: 6606: 6600: 6599: 6597: 6591:. Archived from 6581:10.1038/nmat3228 6561:Nature Materials 6558: 6549: 6543: 6542: 6522: 6516: 6515: 6482:(39): 16557–65. 6467: 6461: 6460: 6426: 6417: 6411: 6410: 6393:(5): 1165–1169. 6378: 6353: 6320: 6256:Oxygen vacancies 6238: 6143: 6141: 6140: 6135: 6133: 6129: 6128: 6127: 6126: 6118: 6112: 6095: 6091: 6090: 6086: 6085: 6065: 6061: 6060: 6035: 6031: 6030: 6010: 6006: 5918: 5916: 5915: 5910: 5908: 5904: 5903: 5902: 5899: 5890: 5889: 5886: 5875: 5874: 5788: 5724: 5722: 5721: 5716: 5711: 5710: 5702: 5700: 5696: 5695: 5693: 5691: 5683: 5681: 5669: 5668: 5660: 5654: 5653: 5645: 5632: 5631: 5630: 5622: 5606: 5604: 5603: 5595: 5593: 5589: 5584: 5580: 5579: 5557: 5547: 5546: 5538: 5536: 5532: 5531: 5527: 5526: 5525: 5505: 5503: 5499: 5498: 5488: 5487: 5486: 5470: 5468: 5467: 5415: 5413: 5412: 5407: 5402: 5401: 5393: 5391: 5387: 5386: 5382: 5381: 5379: 5375: 5374: 5364: 5363: 5359: 5358: 5357: 5337: 5336: 5320: 5318: 5314: 5313: 5311: 5309: 5304: 5291: 5283: 5278: 5275: 5270: 5261: 5260: 5259: 5243: 5210: 5209: 5163: 5161: 5160: 5155: 5153: 5149: 5131: 5127: 5126: 5103: 5099: 5098: 5016: 5014: 5013: 5008: 5006: 5004: 4993: 4982: 4977: 4973: 4972: 4969: 4839: 4837: 4836: 4831: 4826: 4822: 4821: 4820: 4797: 4793: 4792: 4791: 4788: 4779: 4778: 4775: 4764: 4763: 4751: 4747: 4746: 4715: 4713: 4712: 4707: 4705: 4704: 4679: 4677: 4676: 4671: 4669: 4668: 4643: 4641: 4640: 4635: 4620: 4618: 4617: 4612: 4610: 4606: 4605: 4604: 4601: 4592: 4591: 4588: 4577: 4576: 4566: 4561: 4543: 4539: 4538: 4508: 4506: 4505: 4500: 4498: 4497: 4478: 4476: 4475: 4470: 4468: 4467: 4425: 4423: 4422: 4417: 4403: 4399: 4398: 4395: 4376: 4375: 4363: 4359: 4358: 4297: 4295: 4294: 4289: 4287: 4286: 4267: 4265: 4264: 4259: 4257: 4236: 4232: 4231: 4183: 4181: 4180: 4175: 4158:capillary number 4145: 4143: 4142: 4137: 4135: 4134: 4121: 4120: 4107: 4104: 4034: 4032: 4031: 4026: 4009: 4008: 3984: 3983: 3944: 3942: 3941: 3940: 3921: 3916: 3908: 3906: 3904: 3903: 3888: 3883: 3881: 3880: 3868: 3867: 3866: 3851: 3850: 3837: 3807: 3805: 3804: 3799: 3784: 3782: 3781: 3776: 3774: 3772: 3771: 3770: 3751: 3736: 3734: 3733: 3728: 3726: 3724: 3723: 3708: 3693: 3691: 3690: 3685: 3683: 3681: 3680: 3668: 3667: 3666: 3651: 3650: 3637: 3608: 3606: 3605: 3600: 3598: 3597: 3591: 3589: 3588: 3587: 3553: 3509: 3504: 3502: 3501: 3500: 3466: 3422: 3420: 3419: 3413: 3412: 3352: 3347: 3330: 3284:Laplace pressure 3270: 3268: 3267: 3262: 3260: 3258: 3257: 3256: 3240: 3232: 3230: 3228: 3227: 3212: 3207: 3205: 3204: 3203: 3187: 3179: 3177: 3175: 3174: 3159: 3154: 3152: 3151: 3139: 3138: 3137: 3122: 3121: 3108: 3103: 3101: 3100: 3099: 3083: 3082: 3081: 3065: 3044: 3042: 3041: 3036: 2998: 2997: 2982: 2981: 2966: 2965: 2950: 2949: 2934: 2933: 2918: 2917: 2871: 2869: 2868: 2863: 2861: 2857: 2850: 2828: 2827: 2785: 2783: 2782: 2777: 2775: 2771: 2770: 2769: 2754: 2753: 2733: 2732: 2653: 2651: 2650: 2645: 2643: 2642: 2634: 2632: 2628: 2626: 2625: 2621: 2620: 2619: 2602: 2601: 2589: 2585: 2584: 2583: 2553: 2552: 2548: 2547: 2546: 2529: 2528: 2518: 2508: 2507: 2506: 2494: 2491: 2485: 2484: 2483: 2475: 2473: 2469: 2467: 2466: 2462: 2461: 2460: 2443: 2442: 2430: 2426: 2425: 2424: 2394: 2393: 2389: 2388: 2387: 2370: 2369: 2359: 2349: 2348: 2347: 2324: 2322: 2321: 2316: 2314: 2310: 2308: 2307: 2306: 2305: 2292: 2291: 2290: 2279: 2278: 2274: 2273: 2272: 2252: 2251: 2250: 2237: 2233: 2232: 2231: 2211: 2210: 2209: 2198: 2183: 2182: 2181: 2161: 2159: 2158: 2153: 2151: 2150: 2149: 2132: 2130: 2129: 2124: 2122: 2121: 2120: 2103: 2101: 2100: 2095: 2093: 2092: 2091: 2074: 2072: 2071: 2066: 2064: 2063: 2062: 2045: 2043: 2042: 2037: 2035: 2034: 2033: 2004: 2002: 2001: 1996: 1982: 1981: 1977: 1961: 1960: 1959: 1930: 1928: 1927: 1922: 1896:At the boundary 1892: 1890: 1889: 1884: 1876: 1875: 1863: 1861: 1853: 1852: 1851: 1841: 1829: 1827: 1826: 1821: 1809: 1807: 1806: 1801: 1786: 1784: 1783: 1778: 1773: 1772: 1757: 1756: 1741: 1740: 1722: 1719: 1718: 1717: 1698: 1694: 1692: 1691: 1673: 1672: 1656: 1654: 1653: 1648: 1646: 1645: 1636: 1622: 1621: 1608: 1606: 1605: 1600: 1598: 1597: 1591: 1590: 1589: 1563: 1561: 1560: 1555: 1553: 1552: 1533: 1531: 1530: 1525: 1520: 1519: 1507: 1499: 1498: 1483: 1482: 1467: 1466: 1448: 1446: 1445: 1444: 1425: 1423: 1422: 1407: 1406: 1387: 1385: 1384: 1379: 1362: 1361: 1345: 1343: 1342: 1337: 1323: 1315: 1314: 1298: 1296: 1295: 1290: 1245: 1243: 1242: 1237: 1229: 1225: 1221: 1220: 1205: 1204: 1186: 1184: 1183: 1182: 1163: 1161: 1160: 1142: 1137: 1110: 1109: 1093: 1091: 1090: 1085: 1073: 1071: 1070: 1065: 1029: 1027: 1026: 1021: 969: 967: 966: 961: 959: 942: 941: 926: 925: 910: 909: 851: 849: 848: 843: 802: 800: 799: 794: 792: 778: 777: 762: 745: 744: 729: 712: 711: 685: 668: 667: 652: 651: 636: 619: 618: 592: 575: 574: 559: 542: 541: 526: 525: 383:molecular motors 235:Low wettability 160: 122:, boron nitride 21: 8453: 8452: 8448: 8447: 8446: 8444: 8443: 8442: 8433:Surface science 8428:Fluid mechanics 8418: 8417: 8395: 8385: 8366: 8352: 8331: 8328: 8326:Further reading 8323: 8301: 8297: 8296: 8292: 8244: 8240: 8239: 8235: 8217: 8216: 8212: 8193:Organometallics 8190: 8189: 8185: 8163: 8162: 8158: 8150: 8119: 8114: 8113: 8109: 8073: 8072: 8061: 8031: 8030: 8023: 8001: 8000: 7996: 7987: 7985: 7981: 7958: 7953: 7952: 7948: 7940: 7893: 7888: 7887: 7880: 7850: 7849: 7845: 7815: 7814: 7810: 7784: 7783: 7779: 7741: 7740: 7736: 7702: 7701: 7697: 7663: 7662: 7655: 7650: 7643: 7638: 7634: 7626: 7579: 7574: 7573: 7569: 7547: 7546: 7539: 7532: 7522:Soft Interfaces 7519: 7518: 7514: 7474: 7473: 7466: 7444: 7443: 7439: 7430: 7426: 7404: 7403: 7399: 7375: 7374: 7370: 7336: 7335: 7326: 7300: 7299: 7295: 7253: 7252: 7248: 7206: 7205: 7201: 7149: 7148: 7141: 7130: 7129: 7122: 7112: 7110: 7100: 7099: 7095: 7083: 7082: 7078: 7056: 7055: 7051: 7030:(18): 7659–64. 7021: 7020: 7016: 6976: 6975: 6971: 6939: 6934: 6933: 6929: 6922: 6909: 6908: 6904: 6888: 6879: 6840: 6839: 6835: 6827: 6796: 6791: 6790: 6786: 6779: 6766: 6765: 6761: 6754: 6741: 6740: 6733: 6703: 6702: 6698: 6676: 6675: 6668: 6660: 6613: 6608: 6607: 6603: 6595: 6556: 6551: 6550: 6546: 6539: 6524: 6523: 6519: 6469: 6468: 6464: 6424: 6419: 6418: 6414: 6380: 6379: 6375: 6371: 6366: 6351: 6348:Wetting voltage 6342:Wetting current 6318: 6282: 6271: 6262:heat exchangers 6258: 6236: 6225:Wittig reaction 6183: 6181:Surface changes 6164: 6155: 6107: 6100: 6096: 6077: 6073: 6052: 6048: 6043: 6039: 6022: 6018: 5993: 5989: 5980: 5979: 5973: 5970:decreases, or γ 5969: 5941: 5934: 5894: 5881: 5880: 5876: 5866: 5833: 5832: 5821: 5816: 5806: 5797: 5786: 5742:surface tension 5739: 5655: 5640: 5633: 5617: 5607: 5571: 5558: 5552: 5551: 5517: 5510: 5506: 5490: 5489: 5478: 5471: 5456: 5455: 5451: 5450: 5449: 5445: 5444: 5424: 5423: 5366: 5365: 5349: 5342: 5338: 5328: 5321: 5292: 5284: 5248: 5244: 5241: 5237: 5233: 5229: 5216: 5212: 5211: 5201: 5181: 5180: 5173: 5139: 5135: 5118: 5114: 5090: 5086: 5077: 5076: 5071: 5065: 5030: 4994: 4983: 4964: 4960: 4951: 4950: 4927: 4917:" phenomenon). 4867: 4854: 4812: 4805: 4801: 4783: 4770: 4769: 4765: 4755: 4738: 4734: 4722: 4721: 4687: 4682: 4681: 4651: 4646: 4645: 4626: 4625: 4596: 4583: 4582: 4578: 4568: 4530: 4526: 4514: 4513: 4489: 4484: 4483: 4459: 4454: 4453: 4449: 4434: 4390: 4386: 4367: 4350: 4346: 4337: 4336: 4317: 4278: 4273: 4272: 4247: 4223: 4219: 4210: 4209: 4195: 4163: 4162: 4126: 4112: 4098: 4097: 4092: 4088: 4071: 4045: 4000: 3975: 3929: 3925: 3892: 3869: 3855: 3839: 3838: 3813: 3812: 3790: 3789: 3759: 3755: 3739: 3738: 3712: 3696: 3695: 3669: 3655: 3639: 3638: 3625: 3624: 3579: 3554: 3510: 3492: 3467: 3423: 3404: 3331: 3291: 3290: 3245: 3241: 3233: 3216: 3192: 3188: 3180: 3163: 3140: 3126: 3110: 3109: 3088: 3084: 3070: 3066: 3053: 3052: 2986: 2970: 2954: 2938: 2922: 2906: 2892: 2891: 2881: 2840: 2833: 2829: 2816: 2805: 2804: 2758: 2742: 2741: 2737: 2721: 2710: 2709: 2697: 2693: 2689: 2685: 2681: 2677: 2673: 2669: 2660: 2610: 2606: 2593: 2574: 2570: 2554: 2537: 2533: 2520: 2519: 2513: 2512: 2497: 2451: 2447: 2434: 2415: 2411: 2395: 2378: 2374: 2361: 2360: 2354: 2353: 2338: 2333: 2332: 2296: 2281: 2280: 2263: 2259: 2241: 2222: 2218: 2200: 2199: 2193: 2172: 2167: 2166: 2140: 2135: 2134: 2111: 2106: 2105: 2082: 2077: 2076: 2053: 2048: 2047: 2024: 2019: 2018: 2011: 1962: 1951: 1947: 1933: 1932: 1898: 1897: 1854: 1842: 1835: 1834: 1812: 1811: 1792: 1791: 1764: 1745: 1729: 1709: 1705: 1680: 1662: 1661: 1629: 1611: 1610: 1582: 1577: 1566: 1565: 1544: 1539: 1538: 1511: 1500: 1490: 1471: 1455: 1436: 1432: 1411: 1396: 1395: 1353: 1348: 1347: 1316: 1306: 1301: 1300: 1251: 1250: 1209: 1193: 1174: 1170: 1149: 1148: 1144: 1099: 1098: 1076: 1075: 1032: 1031: 1003: 1002: 999: 949: 930: 914: 898: 893: 892: 878: 870: 866: 862: 813: 812: 809: 790: 789: 779: 766: 752: 733: 719: 700: 697: 696: 686: 675: 656: 640: 626: 607: 604: 603: 593: 582: 563: 549: 530: 514: 505: 504: 474: 453: 442: 434: 423: 418:linear function 415: 410:surface tension 395: 325: 193:Perfect wetting 170: 132: 120:carbon nanotube 49: 42: 35: 28: 23: 22: 15: 12: 11: 5: 8451: 8449: 8441: 8440: 8435: 8430: 8420: 8419: 8414: 8413: 8401: 8394: 8393:External links 8391: 8390: 8389: 8383: 8364: 8350: 8327: 8324: 8322: 8321: 8299: 8290: 8242: 8233: 8210: 8183: 8156: 8153:on 2016-01-22. 8130:(2): 877–910. 8107: 8059: 8040:(1–2): 54–65. 8021: 8010:(6): 654–665. 7994: 7969:(1–3): 41–46. 7946: 7943:on 2019-04-11. 7904:(4): 415–424. 7878: 7843: 7808: 7797:(1–3): 47–50. 7777: 7750:(2): 219–230. 7734: 7715:(1): 163–165. 7695: 7653: 7641: 7632: 7629:on 2019-04-11. 7567: 7537: 7530: 7512: 7464: 7437: 7424: 7413:(2): 325–334. 7397: 7368: 7324: 7293: 7246: 7219:(2): 462–466. 7199: 7139: 7120: 7093: 7076: 7049: 7014: 6969: 6927: 6920: 6902: 6877: 6833: 6830:on 2016-09-10. 6807:(3): 827–863. 6784: 6777: 6759: 6752: 6731: 6712:(5): 339–353. 6696: 6685:(5): 519–524. 6666: 6663:on 2019-04-11. 6601: 6598:on 2017-11-15. 6544: 6537: 6517: 6462: 6412: 6372: 6370: 6367: 6365: 6364: 6359: 6354: 6345: 6339: 6333: 6327: 6321: 6312: 6310:Electrowetting 6307: 6301: 6295: 6290: 6283: 6281: 6278: 6269: 6257: 6254: 6221:Vinylferrocene 6182: 6179: 6175: 6174: 6173: 6172: 6166: 6162: 6157: 6153: 6145: 6144: 6132: 6124: 6121: 6116: 6111: 6106: 6103: 6099: 6094: 6089: 6084: 6080: 6076: 6071: 6068: 6064: 6059: 6055: 6051: 6046: 6042: 6038: 6034: 6029: 6025: 6021: 6016: 6013: 6009: 6005: 6002: 5999: 5996: 5992: 5987: 5971: 5967: 5964: 5963: 5962: 5961: 5955: 5949: 5943: 5939: 5936: 5932: 5929: 5920: 5919: 5907: 5897: 5893: 5884: 5879: 5873: 5869: 5864: 5861: 5858: 5855: 5852: 5849: 5846: 5843: 5840: 5820: 5817: 5815: 5812: 5811: 5810: 5809: 5808: 5804: 5799: 5795: 5790: 5780: 5771: 5761: 5751: 5750:is drop volume 5745: 5737: 5726: 5725: 5714: 5708: 5705: 5699: 5689: 5686: 5680: 5677: 5673: 5666: 5663: 5658: 5651: 5648: 5643: 5639: 5636: 5628: 5625: 5620: 5616: 5613: 5610: 5601: 5598: 5592: 5587: 5583: 5578: 5574: 5570: 5567: 5564: 5561: 5555: 5550: 5544: 5541: 5535: 5530: 5524: 5520: 5516: 5513: 5509: 5502: 5497: 5493: 5485: 5481: 5477: 5474: 5466: 5463: 5459: 5454: 5448: 5443: 5440: 5437: 5434: 5431: 5417: 5416: 5405: 5399: 5396: 5390: 5385: 5378: 5373: 5369: 5362: 5356: 5352: 5348: 5345: 5341: 5335: 5331: 5327: 5324: 5317: 5308: 5303: 5299: 5295: 5290: 5287: 5281: 5274: 5269: 5265: 5258: 5255: 5251: 5247: 5240: 5236: 5232: 5228: 5225: 5222: 5219: 5215: 5208: 5204: 5200: 5197: 5194: 5191: 5188: 5172: 5169: 5165: 5164: 5152: 5148: 5145: 5142: 5138: 5134: 5130: 5125: 5121: 5117: 5112: 5109: 5106: 5102: 5097: 5093: 5089: 5084: 5067: 5063: 5048: 5047: 5046: 5045: 5039: 5033: 5028: 5018: 5017: 5003: 5000: 4997: 4992: 4989: 4986: 4980: 4976: 4967: 4963: 4958: 4926: 4923: 4879:hydrophobicity 4877:The intrinsic 4866: 4863: 4853: 4852:Precursor film 4850: 4841: 4840: 4829: 4825: 4819: 4815: 4811: 4808: 4804: 4800: 4796: 4786: 4782: 4773: 4768: 4762: 4758: 4754: 4750: 4745: 4741: 4737: 4732: 4729: 4703: 4700: 4697: 4694: 4690: 4667: 4664: 4661: 4658: 4654: 4633: 4622: 4621: 4609: 4599: 4595: 4586: 4581: 4575: 4571: 4565: 4560: 4557: 4554: 4550: 4546: 4542: 4537: 4533: 4529: 4524: 4521: 4496: 4492: 4466: 4462: 4447: 4432: 4427: 4426: 4415: 4412: 4409: 4406: 4402: 4393: 4389: 4384: 4380: 4374: 4370: 4366: 4362: 4357: 4353: 4349: 4344: 4316: 4313: 4285: 4281: 4269: 4268: 4256: 4253: 4250: 4245: 4242: 4239: 4235: 4230: 4226: 4222: 4217: 4194: 4193:Wenzel's model 4191: 4173: 4170: 4147: 4146: 4133: 4129: 4124: 4119: 4115: 4110: 4090: 4086: 4070: 4067: 4044: 4041: 4036: 4035: 4024: 4021: 4018: 4015: 4012: 4007: 4003: 3999: 3996: 3993: 3990: 3987: 3982: 3978: 3974: 3971: 3968: 3965: 3962: 3959: 3956: 3953: 3950: 3947: 3939: 3936: 3932: 3928: 3924: 3919: 3914: 3911: 3902: 3899: 3895: 3891: 3886: 3879: 3876: 3872: 3865: 3862: 3858: 3854: 3849: 3846: 3842: 3835: 3832: 3829: 3826: 3823: 3820: 3797: 3786: 3785: 3769: 3766: 3762: 3758: 3754: 3749: 3746: 3722: 3719: 3715: 3711: 3706: 3703: 3679: 3676: 3672: 3665: 3662: 3658: 3654: 3649: 3646: 3642: 3635: 3632: 3610: 3609: 3596: 3586: 3582: 3578: 3575: 3572: 3569: 3566: 3563: 3560: 3557: 3552: 3549: 3546: 3543: 3540: 3537: 3534: 3531: 3528: 3525: 3522: 3519: 3516: 3513: 3507: 3499: 3495: 3491: 3488: 3485: 3482: 3479: 3476: 3473: 3470: 3465: 3462: 3459: 3456: 3453: 3450: 3447: 3444: 3441: 3438: 3435: 3432: 3429: 3426: 3418: 3411: 3407: 3403: 3400: 3397: 3394: 3391: 3388: 3385: 3382: 3379: 3376: 3373: 3370: 3367: 3364: 3361: 3358: 3355: 3350: 3346: 3343: 3340: 3337: 3334: 3328: 3325: 3322: 3319: 3316: 3313: 3310: 3307: 3304: 3301: 3298: 3272: 3271: 3255: 3252: 3248: 3244: 3239: 3236: 3226: 3223: 3219: 3215: 3210: 3202: 3199: 3195: 3191: 3186: 3183: 3173: 3170: 3166: 3162: 3157: 3150: 3147: 3143: 3136: 3133: 3129: 3125: 3120: 3117: 3113: 3106: 3098: 3095: 3091: 3087: 3080: 3077: 3073: 3069: 3063: 3060: 3046: 3045: 3034: 3031: 3028: 3025: 3022: 3019: 3016: 3013: 3010: 3007: 3004: 3001: 2996: 2993: 2989: 2985: 2980: 2977: 2973: 2969: 2964: 2961: 2957: 2953: 2948: 2945: 2941: 2937: 2932: 2929: 2925: 2921: 2916: 2913: 2909: 2905: 2902: 2899: 2880: 2877: 2873: 2872: 2860: 2856: 2853: 2849: 2846: 2843: 2839: 2836: 2832: 2826: 2823: 2819: 2815: 2812: 2787: 2786: 2774: 2768: 2765: 2761: 2757: 2752: 2749: 2745: 2740: 2736: 2731: 2728: 2724: 2720: 2717: 2695: 2691: 2687: 2683: 2679: 2675: 2671: 2667: 2659: 2656: 2655: 2654: 2640: 2637: 2631: 2624: 2618: 2613: 2609: 2605: 2600: 2596: 2592: 2588: 2582: 2577: 2573: 2569: 2566: 2563: 2560: 2557: 2551: 2545: 2540: 2536: 2532: 2527: 2523: 2516: 2511: 2505: 2500: 2490: 2481: 2478: 2472: 2465: 2459: 2454: 2450: 2446: 2441: 2437: 2433: 2429: 2423: 2418: 2414: 2410: 2407: 2404: 2401: 2398: 2392: 2386: 2381: 2377: 2373: 2368: 2364: 2357: 2352: 2346: 2341: 2326: 2325: 2313: 2304: 2299: 2295: 2289: 2284: 2277: 2271: 2266: 2262: 2258: 2255: 2249: 2244: 2240: 2236: 2230: 2225: 2221: 2217: 2214: 2208: 2203: 2196: 2192: 2189: 2186: 2180: 2175: 2148: 2143: 2119: 2114: 2090: 2085: 2061: 2056: 2032: 2027: 2010: 2007: 1994: 1991: 1988: 1985: 1980: 1976: 1972: 1969: 1965: 1958: 1954: 1950: 1946: 1943: 1940: 1920: 1917: 1914: 1911: 1908: 1905: 1894: 1893: 1882: 1879: 1874: 1869: 1866: 1860: 1857: 1850: 1845: 1819: 1810:direction and 1799: 1788: 1787: 1776: 1771: 1767: 1763: 1760: 1755: 1752: 1748: 1744: 1739: 1736: 1732: 1728: 1725: 1716: 1712: 1708: 1704: 1701: 1697: 1690: 1687: 1683: 1679: 1676: 1671: 1644: 1639: 1635: 1632: 1628: 1625: 1620: 1596: 1588: 1585: 1580: 1576: 1573: 1551: 1547: 1535: 1534: 1523: 1518: 1514: 1510: 1506: 1503: 1497: 1493: 1489: 1486: 1481: 1478: 1474: 1470: 1465: 1462: 1458: 1454: 1451: 1443: 1439: 1435: 1431: 1428: 1421: 1418: 1414: 1410: 1405: 1377: 1374: 1371: 1368: 1365: 1360: 1356: 1335: 1332: 1329: 1326: 1322: 1319: 1313: 1309: 1288: 1285: 1282: 1279: 1276: 1273: 1270: 1267: 1264: 1261: 1258: 1247: 1246: 1235: 1232: 1228: 1224: 1219: 1216: 1212: 1208: 1203: 1200: 1196: 1192: 1189: 1181: 1177: 1173: 1169: 1166: 1159: 1156: 1152: 1147: 1141: 1136: 1132: 1128: 1125: 1122: 1119: 1116: 1113: 1108: 1083: 1063: 1060: 1057: 1054: 1051: 1048: 1045: 1042: 1039: 1019: 1016: 1013: 1010: 998: 995: 971: 970: 958: 955: 952: 948: 945: 940: 937: 933: 929: 924: 921: 917: 913: 908: 905: 901: 877: 874: 868: 864: 860: 841: 838: 835: 832: 829: 826: 823: 820: 807: 804: 803: 788: 785: 782: 780: 776: 773: 769: 765: 761: 758: 755: 751: 748: 743: 740: 736: 732: 728: 725: 722: 718: 715: 710: 707: 703: 699: 698: 695: 692: 689: 687: 684: 681: 678: 674: 671: 666: 663: 659: 655: 650: 647: 643: 639: 635: 632: 629: 625: 622: 617: 614: 610: 606: 605: 602: 599: 596: 594: 591: 588: 585: 581: 578: 573: 570: 566: 562: 558: 555: 552: 548: 545: 540: 537: 533: 529: 524: 521: 517: 513: 512: 473: 470: 452: 449: 440: 432: 424:) for various 421: 413: 403:William Zisman 394: 391: 379:surface energy 372:hydrogen bonds 341:chemical bonds 324: 321: 260: 259: 256: 253: 250: 247: 243: 242: 239: 236: 233: 230: 226: 225: 222: 218: 217: 214: 211: 208: 205: 201: 200: 197: 194: 191: 188: 184: 183: 182:Liquid–liquid 180: 176: 175: 172: 167: 166:Contact angle 164: 131: 128: 75:intermolecular 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 8450: 8439: 8436: 8434: 8431: 8429: 8426: 8425: 8423: 8416: 8411: 8406: 8402: 8400: 8397: 8396: 8392: 8386: 8380: 8377:. CRC Press. 8376: 8375: 8370: 8365: 8361: 8357: 8353: 8347: 8343: 8339: 8335: 8330: 8329: 8325: 8317: 8313: 8309: 8305: 8294: 8291: 8286: 8282: 8278: 8274: 8270: 8266: 8261: 8256: 8252: 8248: 8237: 8234: 8229: 8225: 8221: 8214: 8211: 8206: 8202: 8198: 8194: 8187: 8184: 8179: 8175: 8171: 8167: 8160: 8157: 8149: 8145: 8141: 8137: 8133: 8129: 8125: 8118: 8111: 8108: 8103: 8099: 8094: 8089: 8085: 8081: 8077: 8070: 8068: 8066: 8064: 8060: 8055: 8051: 8047: 8043: 8039: 8035: 8028: 8026: 8022: 8017: 8013: 8009: 8005: 7998: 7995: 7984:on 2012-05-27 7980: 7976: 7972: 7968: 7964: 7957: 7950: 7947: 7939: 7935: 7931: 7927: 7923: 7919: 7915: 7911: 7907: 7903: 7899: 7892: 7885: 7883: 7879: 7874: 7870: 7866: 7862: 7858: 7854: 7847: 7844: 7839: 7835: 7831: 7827: 7823: 7819: 7812: 7809: 7804: 7800: 7796: 7792: 7788: 7781: 7778: 7773: 7769: 7765: 7761: 7757: 7753: 7749: 7745: 7738: 7735: 7730: 7726: 7722: 7718: 7714: 7710: 7706: 7699: 7696: 7691: 7687: 7683: 7679: 7675: 7671: 7667: 7660: 7658: 7654: 7648: 7646: 7642: 7636: 7633: 7625: 7621: 7617: 7613: 7609: 7605: 7601: 7597: 7593: 7589: 7585: 7578: 7571: 7568: 7563: 7559: 7555: 7551: 7544: 7542: 7538: 7533: 7527: 7523: 7516: 7513: 7508: 7504: 7500: 7496: 7491: 7486: 7482: 7478: 7471: 7469: 7465: 7460: 7456: 7452: 7448: 7441: 7438: 7434: 7428: 7425: 7420: 7416: 7412: 7408: 7401: 7398: 7393: 7389: 7385: 7381: 7380: 7372: 7369: 7364: 7360: 7356: 7352: 7348: 7344: 7340: 7333: 7331: 7329: 7325: 7320: 7316: 7312: 7308: 7304: 7297: 7294: 7289: 7285: 7281: 7277: 7273: 7269: 7265: 7261: 7257: 7250: 7247: 7242: 7238: 7234: 7230: 7226: 7222: 7218: 7214: 7210: 7203: 7200: 7195: 7191: 7187: 7183: 7178: 7173: 7169: 7165: 7162:(6): 062006. 7161: 7157: 7153: 7146: 7144: 7140: 7136: 7135: 7127: 7125: 7121: 7108: 7104: 7097: 7094: 7089: 7088: 7080: 7077: 7072: 7068: 7064: 7060: 7053: 7050: 7045: 7041: 7037: 7033: 7029: 7025: 7018: 7015: 7010: 7006: 7002: 6998: 6994: 6990: 6986: 6982: 6981: 6973: 6970: 6965: 6961: 6957: 6953: 6949: 6945: 6938: 6931: 6928: 6923: 6917: 6913: 6906: 6903: 6900: 6899:0-8247-9046-4 6896: 6892: 6886: 6884: 6882: 6878: 6873: 6869: 6865: 6861: 6857: 6853: 6849: 6845: 6837: 6834: 6826: 6822: 6818: 6814: 6810: 6806: 6802: 6795: 6788: 6785: 6780: 6774: 6770: 6763: 6760: 6755: 6749: 6745: 6738: 6736: 6732: 6727: 6723: 6719: 6715: 6711: 6707: 6700: 6697: 6692: 6688: 6684: 6680: 6673: 6671: 6667: 6659: 6655: 6651: 6647: 6643: 6639: 6635: 6631: 6627: 6623: 6619: 6612: 6605: 6602: 6594: 6590: 6586: 6582: 6578: 6574: 6570: 6567:(3): 217–22. 6566: 6562: 6555: 6548: 6545: 6540: 6538:9789402410310 6534: 6530: 6529: 6521: 6518: 6513: 6509: 6505: 6501: 6497: 6493: 6489: 6485: 6481: 6477: 6473: 6466: 6463: 6458: 6454: 6450: 6446: 6442: 6438: 6434: 6430: 6423: 6416: 6413: 6408: 6404: 6400: 6396: 6392: 6388: 6384: 6377: 6374: 6368: 6363: 6360: 6358: 6355: 6349: 6346: 6343: 6340: 6337: 6334: 6331: 6328: 6325: 6322: 6316: 6313: 6311: 6308: 6305: 6302: 6299: 6296: 6294: 6291: 6288: 6285: 6284: 6279: 6277: 6275: 6267: 6263: 6255: 6253: 6251: 6246: 6242: 6234: 6230: 6226: 6222: 6218: 6214: 6210: 6206: 6199: 6195: 6192: 6187: 6180: 6178: 6170: 6167: 6161: 6158: 6152: 6149: 6148: 6147: 6146: 6130: 6122: 6119: 6114: 6104: 6101: 6097: 6092: 6087: 6082: 6078: 6074: 6069: 6066: 6062: 6053: 6049: 6044: 6040: 6036: 6032: 6027: 6023: 6019: 6014: 6011: 6007: 6000: 5994: 5990: 5985: 5978: 5977: 5976: 5959: 5956: 5953: 5950: 5947: 5944: 5937: 5930: 5927: 5924: 5923: 5922: 5921: 5905: 5895: 5891: 5882: 5877: 5871: 5867: 5862: 5859: 5856: 5853: 5850: 5847: 5844: 5841: 5838: 5831: 5830: 5829: 5827: 5818: 5813: 5803: 5800: 5794: 5791: 5784: 5781: 5779: 5775: 5772: 5769: 5765: 5762: 5759: 5755: 5752: 5749: 5746: 5743: 5736: 5733: 5732: 5731: 5730: 5729: 5712: 5706: 5703: 5697: 5687: 5684: 5678: 5675: 5671: 5664: 5661: 5656: 5649: 5646: 5641: 5637: 5634: 5626: 5623: 5618: 5614: 5611: 5608: 5599: 5596: 5590: 5585: 5576: 5572: 5568: 5565: 5559: 5553: 5548: 5542: 5539: 5533: 5528: 5522: 5518: 5514: 5511: 5507: 5500: 5495: 5491: 5483: 5479: 5475: 5472: 5464: 5461: 5457: 5452: 5446: 5441: 5435: 5429: 5422: 5421: 5420: 5403: 5397: 5394: 5388: 5383: 5376: 5371: 5367: 5360: 5354: 5350: 5346: 5343: 5339: 5333: 5329: 5325: 5322: 5315: 5306: 5301: 5297: 5293: 5288: 5285: 5279: 5272: 5267: 5263: 5256: 5253: 5249: 5245: 5238: 5234: 5230: 5226: 5223: 5220: 5217: 5213: 5206: 5202: 5198: 5192: 5186: 5179: 5178: 5177: 5170: 5168: 5150: 5146: 5143: 5140: 5136: 5132: 5128: 5123: 5119: 5115: 5110: 5107: 5104: 5100: 5095: 5091: 5087: 5082: 5075: 5074: 5073: 5070: 5060: 5052: 5043: 5040: 5037: 5034: 5031: 5025: 5024: 5023: 5022: 5021: 5001: 4998: 4995: 4990: 4987: 4984: 4978: 4974: 4965: 4961: 4956: 4949: 4948: 4947: 4944: 4940: 4931: 4924: 4922: 4918: 4916: 4915:self-cleaning 4911: 4910:contact angle 4906: 4904: 4900: 4895: 4893: 4888: 4884: 4880: 4871: 4864: 4862: 4860: 4851: 4849: 4847: 4827: 4823: 4817: 4813: 4809: 4806: 4802: 4798: 4794: 4784: 4780: 4771: 4766: 4760: 4756: 4752: 4748: 4743: 4739: 4735: 4730: 4727: 4720: 4719: 4718: 4701: 4698: 4695: 4692: 4688: 4665: 4662: 4659: 4656: 4652: 4631: 4607: 4597: 4593: 4584: 4579: 4573: 4569: 4563: 4558: 4555: 4552: 4548: 4544: 4540: 4535: 4531: 4527: 4522: 4519: 4512: 4511: 4510: 4494: 4490: 4480: 4464: 4460: 4451: 4443: 4439: 4435: 4413: 4410: 4407: 4404: 4400: 4391: 4387: 4382: 4378: 4372: 4368: 4364: 4360: 4355: 4351: 4347: 4342: 4335: 4334: 4333: 4331: 4321: 4314: 4312: 4310: 4305: 4304:contact angle 4300: 4283: 4279: 4254: 4251: 4248: 4243: 4240: 4237: 4233: 4228: 4224: 4220: 4215: 4208: 4207: 4206: 4199: 4190: 4186: 4184: 4171: 4168: 4159: 4154: 4152: 4131: 4127: 4122: 4117: 4113: 4108: 4096: 4095: 4094: 4084: 4075: 4068: 4066: 4064: 4063:absolute zero 4059: 4055: 4051: 4042: 4040: 4016: 4010: 4005: 4001: 3997: 3991: 3985: 3980: 3976: 3972: 3969: 3963: 3957: 3954: 3951: 3948: 3937: 3934: 3930: 3926: 3922: 3917: 3912: 3909: 3900: 3897: 3893: 3889: 3884: 3877: 3874: 3870: 3863: 3860: 3856: 3852: 3847: 3844: 3840: 3833: 3827: 3821: 3818: 3811: 3810: 3809: 3795: 3767: 3764: 3760: 3756: 3752: 3747: 3744: 3720: 3717: 3713: 3709: 3704: 3701: 3677: 3674: 3670: 3663: 3660: 3656: 3652: 3647: 3644: 3640: 3633: 3630: 3623: 3622: 3617: 3613: 3584: 3576: 3573: 3567: 3561: 3558: 3547: 3544: 3538: 3532: 3529: 3520: 3514: 3511: 3505: 3497: 3489: 3486: 3480: 3474: 3471: 3460: 3457: 3451: 3445: 3442: 3433: 3427: 3424: 3409: 3401: 3398: 3392: 3386: 3383: 3374: 3371: 3368: 3362: 3359: 3356: 3353: 3348: 3341: 3335: 3332: 3326: 3323: 3320: 3317: 3311: 3308: 3305: 3299: 3296: 3289: 3288: 3287: 3285: 3281: 3277: 3274:Usually, the 3253: 3250: 3246: 3242: 3237: 3234: 3224: 3221: 3217: 3213: 3208: 3200: 3197: 3193: 3189: 3184: 3181: 3171: 3168: 3164: 3160: 3155: 3148: 3145: 3141: 3134: 3131: 3127: 3123: 3118: 3115: 3111: 3104: 3096: 3093: 3089: 3085: 3078: 3075: 3071: 3067: 3061: 3058: 3051: 3050: 3049: 3032: 3029: 3026: 3023: 3020: 3017: 3014: 3011: 3008: 3005: 3002: 2999: 2994: 2991: 2987: 2983: 2978: 2975: 2971: 2967: 2962: 2959: 2955: 2951: 2946: 2943: 2939: 2935: 2930: 2927: 2923: 2919: 2914: 2911: 2907: 2903: 2900: 2897: 2890: 2889: 2888: 2885: 2878: 2876: 2858: 2854: 2851: 2847: 2844: 2841: 2837: 2834: 2830: 2824: 2821: 2817: 2813: 2810: 2803: 2802: 2801: 2798: 2796: 2792: 2772: 2766: 2763: 2759: 2755: 2750: 2747: 2743: 2738: 2734: 2729: 2726: 2722: 2718: 2715: 2708: 2707: 2706: 2704: 2699: 2665: 2657: 2638: 2635: 2629: 2622: 2611: 2607: 2603: 2598: 2594: 2590: 2586: 2575: 2571: 2567: 2564: 2561: 2558: 2555: 2549: 2538: 2534: 2530: 2525: 2521: 2514: 2509: 2498: 2488: 2479: 2476: 2470: 2463: 2452: 2448: 2444: 2439: 2435: 2431: 2427: 2416: 2412: 2408: 2405: 2402: 2399: 2396: 2390: 2379: 2375: 2371: 2366: 2362: 2355: 2350: 2339: 2331: 2330: 2329: 2311: 2297: 2293: 2282: 2275: 2264: 2260: 2256: 2253: 2242: 2238: 2234: 2223: 2219: 2215: 2212: 2201: 2194: 2190: 2187: 2184: 2173: 2165: 2164: 2163: 2141: 2112: 2083: 2054: 2025: 2016: 2015:ideal surface 2008: 2006: 1992: 1989: 1986: 1983: 1978: 1974: 1970: 1967: 1956: 1948: 1944: 1941: 1918: 1915: 1909: 1903: 1880: 1877: 1867: 1864: 1858: 1833: 1832: 1831: 1817: 1797: 1774: 1769: 1765: 1761: 1753: 1750: 1746: 1742: 1737: 1734: 1730: 1723: 1714: 1706: 1702: 1699: 1695: 1688: 1685: 1681: 1677: 1674: 1660: 1659: 1658: 1637: 1633: 1630: 1626: 1623: 1586: 1583: 1574: 1571: 1549: 1545: 1521: 1516: 1512: 1508: 1504: 1501: 1495: 1491: 1487: 1479: 1476: 1472: 1468: 1463: 1460: 1456: 1449: 1441: 1433: 1429: 1426: 1419: 1416: 1412: 1408: 1394: 1393: 1392: 1389: 1375: 1372: 1369: 1366: 1363: 1358: 1354: 1333: 1330: 1327: 1324: 1320: 1317: 1311: 1307: 1286: 1283: 1277: 1271: 1268: 1262: 1256: 1233: 1230: 1226: 1217: 1214: 1210: 1206: 1201: 1198: 1194: 1187: 1179: 1171: 1167: 1164: 1157: 1154: 1150: 1145: 1139: 1134: 1130: 1126: 1120: 1117: 1114: 1097: 1096: 1095: 1081: 1058: 1055: 1052: 1046: 1043: 1040: 1037: 1014: 1008: 994: 992: 988: 984: 980: 976: 956: 953: 950: 946: 943: 938: 935: 931: 927: 922: 919: 915: 911: 906: 903: 899: 891: 890: 889: 882: 873: 858: 853: 839: 836: 833: 830: 827: 824: 821: 818: 786: 783: 781: 774: 771: 767: 763: 759: 756: 753: 749: 746: 741: 738: 734: 730: 726: 723: 720: 716: 713: 708: 705: 701: 693: 690: 688: 682: 679: 676: 672: 669: 664: 661: 657: 653: 648: 645: 641: 637: 633: 630: 627: 623: 620: 615: 612: 608: 600: 597: 595: 589: 586: 583: 579: 576: 571: 568: 564: 560: 556: 553: 550: 546: 543: 538: 535: 531: 527: 522: 519: 515: 503: 502: 501: 499: 495: 486: 478: 471: 469: 466: 462: 458: 457:ideal surface 450: 448: 444: 438: 429: 427: 419: 411: 406: 404: 400: 399:van der Waals 392: 390: 388: 384: 380: 375: 373: 369: 365: 361: 360:fluorocarbons 356: 354: 350: 346: 342: 338: 334: 330: 322: 320: 318: 314: 310: 306: 301: 297: 295: 294:contact angle 287: 283: 279: 275: 271: 266: 257: 254: 251: 248: 245: 244: 240: 237: 234: 231: 228: 227: 223: 220: 219: 215: 212: 202: 198: 195: 192: 189: 186: 185: 181: 179:Solid–liquid 178: 177: 161: 158: 156: 152: 148: 144: 136: 129: 127: 125: 121: 117: 112: 110: 106: 102: 98: 93: 91: 88: 84: 80: 76: 72: 69: 65: 61: 53: 47: 40: 33: 19: 8415: 8373: 8333: 8307: 8303: 8293: 8250: 8246: 8236: 8227: 8223: 8213: 8196: 8192: 8186: 8169: 8165: 8159: 8148:the original 8127: 8123: 8110: 8083: 8079: 8037: 8033: 8007: 8003: 7997: 7986:. Retrieved 7979:the original 7966: 7962: 7949: 7938:the original 7901: 7897: 7856: 7852: 7846: 7821: 7817: 7811: 7794: 7790: 7780: 7747: 7743: 7737: 7712: 7708: 7698: 7673: 7669: 7635: 7624:the original 7587: 7583: 7570: 7553: 7549: 7521: 7515: 7480: 7476: 7450: 7446: 7440: 7427: 7410: 7406: 7400: 7383: 7377: 7371: 7346: 7342: 7310: 7306: 7296: 7263: 7259: 7249: 7216: 7212: 7202: 7159: 7155: 7133: 7111:. Retrieved 7106: 7096: 7086: 7079: 7062: 7058: 7052: 7027: 7023: 7017: 6984: 6978: 6972: 6947: 6943: 6930: 6911: 6905: 6890: 6847: 6843: 6836: 6825:the original 6804: 6800: 6787: 6768: 6762: 6743: 6709: 6705: 6699: 6682: 6678: 6658:the original 6621: 6617: 6604: 6593:the original 6564: 6560: 6547: 6531:. Springer. 6527: 6520: 6479: 6475: 6465: 6432: 6428: 6415: 6390: 6386: 6376: 6336:Rise in core 6259: 6203: 6176: 6168: 6159: 6150: 5965: 5957: 5951: 5945: 5925: 5822: 5801: 5792: 5782: 5773: 5770:of the fluid 5763: 5760:of the fluid 5753: 5747: 5744:of the fluid 5734: 5727: 5418: 5174: 5166: 5068: 5061: 5057: 5041: 5035: 5026: 5019: 4936: 4919: 4907: 4903:lotus effect 4899:petal effect 4896: 4892:petal effect 4876: 4855: 4845: 4842: 4623: 4481: 4445: 4441: 4437: 4430: 4428: 4330:Cassie's law 4326: 4301: 4270: 4204: 4187: 4161: 4155: 4148: 4080: 4057: 4046: 4037: 3787: 3611: 3279: 3275: 3273: 3047: 2886: 2882: 2874: 2799: 2794: 2790: 2788: 2702: 2700: 2664:Thomas Young 2661: 2327: 2012: 1895: 1789: 1536: 1390: 1248: 1000: 972: 887: 854: 805: 491: 454: 445: 430: 407: 396: 376: 364:hydrocarbons 357: 326: 313:Lotus effect 302: 298: 291: 285: 281: 277: 269: 252:Non-wetting 141: 113: 94: 59: 58: 8310:: 278–283. 8245:surfaces". 8172:: 128–132. 7859:: 411–418. 7483:: 365–371. 7386:: 188–193. 7349:: 196–203. 7313:: 920–926. 7109:. ramé-hart 6891:Wettability 6330:Soap bubble 6233:polystyrene 6198:hydrophilic 6191:hydrophobic 5826:surfactants 5819:Surfactants 494:equilibrium 309:hydrophobic 305:hydrophilic 130:Explanation 109:Surfactants 8438:Hysteresis 8422:Categories 8260:1902.02662 7988:2011-12-17 7490:1712.04703 6369:References 6293:Amott test 6287:Adsorption 6266:Adsorption 6250:molar mass 4901:" to the " 4885:. The red 4309:hysteresis 991:immiscible 496:, the net 465:hysteresis 401:) forces. 169:Degree of 8360:137894832 8285:118895100 8253:: 68–74. 7772:203537637 7764:0169-4243 7729:0927-7757 7363:104412970 7280:0743-7463 7194:249715372 7186:1070-6631 7113:6 January 7009:250874015 6964:116124581 6950:: 65–87. 6872:207106544 6726:0043-7719 6654:205249367 6512:205850095 6472:Sun, Ying 6407:0031-8655 6315:Flotation 6304:Dewetting 6205:Ferrocene 6123:τ 6115:− 6105:− 6079:θ 6067:− 6058:∞ 6054:θ 6024:θ 5995:θ 5896:γ 5892:− 5883:γ 5863:π 5845:γ 5839:σ 5758:viscosity 5672:γ 5657:π 5638:⋅ 5612:ρ 5586:η 5560:λ 5501:η 5492:π 5476:λ 5458:γ 5377:η 5368:π 5326:λ 5286:ρ 5250:γ 5235:− 5227:⁡ 5221:− 5147:ϕ 5144:− 5120:θ 5108:ϕ 5096:∗ 5092:θ 5002:ϕ 4999:− 4988:− 4985:ϕ 4966:θ 4883:roughness 4828:γ 4810:− 4799:− 4785:γ 4781:− 4772:γ 4744:∗ 4740:θ 4728:γ 4689:γ 4653:γ 4632:γ 4598:γ 4594:− 4585:γ 4549:∑ 4536:∗ 4532:θ 4520:γ 4429:Here the 4411:− 4392:θ 4356:∗ 4352:θ 4302:θ is the 4284:∗ 4280:θ 4252:θ 4229:∗ 4225:θ 4128:θ 4123:− 4114:θ 4058:ab initio 4017:θ 4011:⁡ 3998:− 3992:θ 3986:⁡ 3970:− 3964:θ 3958:⁡ 3931:γ 3923:γ 3918:− 3894:γ 3890:κ 3871:γ 3857:γ 3853:− 3841:γ 3828:θ 3822:⁡ 3796:θ 3761:γ 3753:γ 3714:γ 3710:κ 3671:γ 3657:γ 3653:− 3641:γ 3568:θ 3562:⁡ 3539:θ 3533:⁡ 3521:θ 3515:⁡ 3506:∓ 3481:α 3475:⁡ 3452:α 3446:⁡ 3434:α 3428:⁡ 3393:θ 3387:⁡ 3375:α 3372:∓ 3369:θ 3363:⁡ 3354:± 3342:α 3336:⁡ 3312:α 3309:∓ 3306:θ 3300:⁡ 3218:γ 3209:− 3165:γ 3161:κ 3156:− 3142:γ 3128:γ 3124:− 3112:γ 3024:− 3012:− 3003:κ 3000:− 2972:γ 2940:γ 2908:γ 2898:δ 2852:− 2845:θ 2838:⁡ 2818:γ 2760:γ 2744:γ 2735:− 2723:γ 2612:θ 2604:⁡ 2576:θ 2568:⁡ 2559:− 2539:θ 2531:⁡ 2453:θ 2445:⁡ 2417:θ 2409:⁡ 2400:− 2380:θ 2372:⁡ 2265:θ 2257:⁡ 2224:θ 2216:⁡ 2191:⁡ 2174:θ 2142:θ 2113:θ 2084:θ 2055:θ 2026:θ 1993:θ 1990:⁡ 1968:− 1868:− 1856:∂ 1844:∂ 1766:λ 1747:γ 1743:− 1731:γ 1724:− 1682:γ 1678:− 1638:− 1579:∂ 1546:λ 1513:λ 1509:− 1492:λ 1488:− 1473:γ 1469:− 1457:γ 1413:γ 1355:∫ 1308:∫ 1211:γ 1207:− 1195:γ 1151:γ 1131:∫ 1041:∈ 954:θ 947:⁡ 932:γ 916:γ 900:γ 840:π 831:θ 825:β 819:α 775:β 772:α 768:γ 757:β 750:⁡ 742:β 739:θ 735:γ 724:α 717:⁡ 709:θ 706:α 702:γ 680:β 673:⁡ 665:β 662:α 658:γ 649:β 646:θ 642:γ 631:θ 624:⁡ 616:θ 613:α 609:γ 587:α 580:⁡ 572:β 569:α 565:γ 554:θ 547:⁡ 539:β 536:θ 532:γ 523:θ 520:α 516:γ 428:liquids. 249:θ = 180° 107:effects. 105:capillary 101:adherence 8144:11848774 8102:27156979 8054:18834966 7934:35973585 7926:18431542 7838:18312016 7818:Langmuir 7620:29794436 7612:23005650 7550:Langmuir 7507:51916594 7288:15323516 7260:Langmuir 7059:Langmuir 7044:15323516 7024:Langmuir 6864:24490770 6646:27357755 6589:22266468 6504:23949186 6298:Anti-fog 6280:See also 6245:moieties 6217:polymers 6213:monomers 4444:= 1 and 1953:′ 1711:′ 1634:′ 1587:′ 1505:′ 1438:′ 1321:′ 1176:′ 857:triangle 387:bistable 353:metallic 345:covalent 337:ceramics 272:shows a 171:wetting 155:Cohesive 143:Adhesive 124:nanomesh 116:graphene 87:cohesive 83:adhesive 79:miscible 8410:Wetting 8265:Bibcode 7906:Bibcode 7861:Bibcode 7678:Bibcode 7592:Bibcode 7241:9056376 7221:Bibcode 7164:Bibcode 6989:Bibcode 6809:Bibcode 6626:Bibcode 6569:Bibcode 6484:Bibcode 6457:4512480 6437:Bibcode 5768:density 4937:In the 987:droplet 463:. Zero 426:organic 333:glasses 258:Strong 241:Strong 216:Strong 163:Fig. 2 97:bonding 71:surface 60:Wetting 18:Wetness 8381: 8358: 8348: 8283: 8142: 8100: 8052: 7932: 7924: 7836: 7770: 7762: 7727: 7618: 7610: 7528: 7505: 7361: 7286: 7278: 7239: 7192: 7184: 7042: 7007: 6962: 6918: 6897: 6870: 6862: 6775: 6750: 6724: 6652: 6644: 6618:Nature 6587: 6535: 6510: 6502: 6455: 6405: 6241:silica 6229:analog 6194:silica 5787: 5728:where 5020:where 4271:where 2690:> γ 2678:> γ 2495: 2492: 2486: 2328:where 2188:arccos 1537:where 1074:where 979:liquid 863:< γ 335:, and 329:energy 213:Strong 196:Strong 190:θ = 0 147:liquid 90:forces 64:liquid 8356:S2CID 8281:S2CID 8255:arXiv 8151:(PDF) 8120:(PDF) 7982:(PDF) 7959:(PDF) 7941:(PDF) 7930:S2CID 7894:(PDF) 7768:S2CID 7627:(PDF) 7616:S2CID 7580:(PDF) 7503:S2CID 7485:arXiv 7359:S2CID 7190:S2CID 7005:S2CID 6960:S2CID 6940:(PDF) 6868:S2CID 6828:(PDF) 6797:(PDF) 6661:(PDF) 6650:S2CID 6614:(PDF) 6596:(PDF) 6557:(PDF) 6508:S2CID 6453:S2CID 6425:(PDF) 6209:redox 6207:is a 4624:Here 2789:When 2670:nor γ 975:solid 498:force 351:, or 349:ionic 317:polar 274:fluid 224:Weak 199:Weak 151:solid 68:solid 8379:ISBN 8346:ISBN 8230:(4). 8140:PMID 8098:PMID 8050:PMID 7922:PMID 7834:PMID 7760:ISSN 7725:ISSN 7608:PMID 7526:ISBN 7284:PMID 7276:ISSN 7237:PMID 7182:ISSN 7115:2016 7040:PMID 6916:ISBN 6895:ISBN 6860:PMID 6773:ISBN 6748:ISBN 6722:ISSN 6642:PMID 6585:PMID 6533:ISBN 6500:PMID 6403:ISSN 4887:rose 4789:1,sl 4776:1,sv 4602:i,sl 4589:i,sv 4052:and 3737:and 2133:and 1931:and 1030:for 981:and 370:and 292:The 255:Weak 238:Weak 221:Weak 149:and 85:and 8338:doi 8312:doi 8308:121 8273:doi 8251:478 8201:doi 8174:doi 8170:625 8132:doi 8088:doi 8042:doi 8038:144 8012:doi 8008:213 7971:doi 7967:206 7914:doi 7869:doi 7857:436 7826:doi 7799:doi 7795:324 7752:doi 7717:doi 7713:345 7686:doi 7674:450 7600:doi 7588:109 7558:doi 7495:doi 7481:555 7455:doi 7415:doi 7411:246 7388:doi 7384:117 7351:doi 7347:281 7315:doi 7311:248 7268:doi 7229:doi 7217:186 7172:doi 7067:doi 7032:doi 6997:doi 6952:doi 6852:doi 6848:136 6817:doi 6714:doi 6687:doi 6634:doi 6622:534 6577:doi 6492:doi 6445:doi 6395:doi 6231:of 6070:cos 6045:cos 6015:cos 5986:cos 5776:is 5766:is 5756:is 5740:is 5224:exp 5111:cos 5083:cos 4957:cos 4731:cos 4523:cos 4450:= r 4383:cos 4343:cos 4332:): 4244:cos 4216:cos 4002:cos 3977:cos 3955:cos 3819:cos 3559:cos 3530:cos 3512:sin 3472:cos 3443:cos 3425:sin 3384:cos 3360:sin 3333:cos 3297:cos 3280:VdP 3276:VdP 2835:cos 2694:+ γ 2682:+ γ 2595:cos 2565:cos 2522:sin 2436:cos 2406:cos 2363:sin 2254:cos 2213:cos 1987:cos 983:gas 944:cos 867:+ γ 747:cos 714:cos 670:cos 621:cos 577:cos 544:cos 455:An 126:). 99:or 8424:: 8354:. 8344:. 8306:. 8279:. 8271:. 8263:. 8249:. 8228:91 8226:. 8222:. 8197:32 8195:. 8168:. 8138:. 8128:96 8126:. 8122:. 8096:. 8084:45 8082:. 8078:. 8062:^ 8048:. 8036:. 8024:^ 8006:. 7965:. 7961:. 7928:. 7920:. 7912:. 7902:25 7900:. 7896:. 7881:^ 7867:. 7855:. 7832:. 7822:24 7820:. 7793:. 7789:. 7766:. 7758:. 7748:34 7746:. 7723:. 7711:. 7707:. 7684:. 7672:. 7668:. 7656:^ 7644:^ 7614:. 7606:. 7598:. 7586:. 7582:. 7554:19 7552:. 7540:^ 7501:. 7493:. 7479:. 7467:^ 7449:. 7409:. 7382:. 7357:. 7345:. 7341:. 7327:^ 7309:. 7305:. 7282:. 7274:. 7264:20 7262:. 7258:. 7235:. 7227:. 7215:. 7211:. 7188:. 7180:. 7170:. 7160:34 7158:. 7154:. 7142:^ 7123:^ 7105:. 7063:11 7061:. 7038:. 7028:20 7026:. 7003:. 6995:. 6985:10 6983:. 6958:. 6948:95 6946:. 6942:. 6880:^ 6866:. 6858:. 6846:. 6815:. 6805:57 6803:. 6799:. 6734:^ 6720:. 6710:31 6708:. 6683:64 6681:. 6669:^ 6648:. 6640:. 6632:. 6620:. 6616:. 6583:. 6575:. 6565:11 6563:. 6559:. 6506:. 6498:. 6490:. 6480:15 6478:. 6451:. 6443:. 6433:45 6431:. 6427:. 6401:. 6391:93 6389:. 6385:. 5972:SV 5968:SL 5940:SV 5933:SL 5900:SV 5887:SL 5738:LG 5642:96 5609:24 5473:96 5323:24 5307:10 5273:12 4479:. 4311:. 4160:, 3694:, 2705:, 2696:LG 2692:SG 2688:SL 2684:LG 2680:SL 2676:SG 2672:SL 2668:SG 1388:. 977:, 869:ik 865:jk 861:ij 808:ij 439:(γ 433:LV 422:LV 414:LV 412:(γ 362:, 347:, 246:A 229:B 204:C 118:, 8387:. 8362:. 8340:: 8318:. 8314:: 8300:2 8287:. 8275:: 8267:: 8257:: 8243:2 8207:. 8203:: 8180:. 8176:: 8134:: 8104:. 8090:: 8056:. 8044:: 8018:. 8014:: 7991:. 7973:: 7916:: 7908:: 7875:. 7871:: 7863:: 7840:. 7828:: 7805:. 7801:: 7774:. 7754:: 7731:. 7719:: 7692:. 7688:: 7680:: 7602:: 7594:: 7564:. 7560:: 7534:. 7509:. 7497:: 7487:: 7461:. 7457:: 7451:6 7421:. 7417:: 7394:. 7390:: 7365:. 7353:: 7321:. 7317:: 7290:. 7270:: 7243:. 7231:: 7223:: 7196:. 7174:: 7166:: 7117:. 7073:. 7069:: 7046:. 7034:: 7011:. 6999:: 6991:: 6966:. 6954:: 6924:. 6874:. 6854:: 6819:: 6811:: 6781:. 6756:. 6728:. 6716:: 6693:. 6689:: 6636:: 6628:: 6579:: 6571:: 6541:. 6514:. 6494:: 6486:: 6459:. 6447:: 6439:: 6409:. 6397:: 6270:2 6169:τ 6163:∞ 6160:θ 6154:0 6151:θ 6131:) 6120:t 6110:e 6102:1 6098:( 6093:) 6088:) 6083:0 6075:( 6063:) 6050:( 6041:( 6037:+ 6033:) 6028:0 6020:( 6012:= 6008:) 6004:) 6001:t 5998:( 5991:( 5958:R 5952:P 5946:S 5938:γ 5931:γ 5926:γ 5906:) 5878:( 5872:2 5868:R 5860:+ 5857:V 5854:P 5851:+ 5848:S 5842:= 5805:e 5802:r 5796:0 5793:t 5789:m 5783:λ 5774:g 5764:ρ 5754:η 5748:V 5735:γ 5713:, 5707:6 5704:1 5698:] 5688:3 5685:1 5679:G 5676:L 5665:3 5662:4 5650:3 5647:1 5635:7 5627:8 5624:3 5619:V 5615:g 5600:3 5597:2 5591:) 5582:) 5577:0 5573:t 5569:+ 5566:t 5563:( 5554:( 5549:+ 5543:2 5540:1 5534:) 5529:) 5523:0 5519:t 5515:+ 5512:t 5508:( 5496:2 5484:4 5480:V 5465:G 5462:L 5453:( 5447:[ 5442:= 5439:) 5436:t 5433:( 5430:r 5404:. 5398:6 5395:1 5389:] 5384:) 5372:2 5361:) 5355:0 5351:t 5347:+ 5344:t 5340:( 5334:4 5330:V 5316:) 5302:e 5298:r 5294:9 5289:g 5280:+ 5268:e 5264:r 5257:G 5254:L 5246:2 5239:( 5231:( 5218:1 5214:[ 5207:e 5203:r 5199:= 5196:) 5193:t 5190:( 5187:r 5151:) 5141:1 5137:( 5133:+ 5129:) 5124:C 5116:( 5105:= 5101:) 5088:( 5069:C 5064:C 5042:r 5036:Φ 5029:C 5027:θ 4996:r 4991:1 4979:= 4975:) 4970:C 4962:( 4890:" 4846:f 4824:) 4818:1 4814:f 4807:1 4803:( 4795:) 4767:( 4761:1 4757:f 4753:= 4749:) 4736:( 4702:l 4699:s 4696:, 4693:i 4666:v 4663:s 4660:, 4657:i 4608:) 4580:( 4574:i 4570:f 4564:N 4559:1 4556:= 4553:n 4545:= 4541:) 4528:( 4495:i 4491:f 4465:i 4461:f 4448:f 4446:r 4442:f 4438:f 4433:f 4431:r 4414:1 4408:f 4405:+ 4401:) 4396:Y 4388:( 4379:f 4373:f 4369:r 4365:= 4361:) 4348:( 4328:( 4255:) 4249:( 4241:r 4238:= 4234:) 4221:( 4172:a 4169:C 4132:r 4118:a 4109:= 4105:H 4091:r 4087:a 4023:) 4020:) 4014:( 4006:3 3995:) 3989:( 3981:2 3973:2 3967:) 3961:( 3952:+ 3949:2 3946:( 3938:G 3935:L 3927:3 3913:a 3910:1 3901:G 3898:L 3885:+ 3878:G 3875:L 3864:L 3861:S 3848:G 3845:S 3834:= 3831:) 3825:( 3768:G 3765:L 3757:3 3748:= 3745:C 3721:G 3718:L 3705:= 3702:B 3678:G 3675:L 3664:L 3661:S 3648:G 3645:S 3634:= 3631:A 3595:) 3585:2 3581:) 3577:1 3574:+ 3571:) 3565:( 3556:( 3551:) 3548:2 3545:+ 3542:) 3536:( 3527:( 3524:) 3518:( 3498:2 3494:) 3490:1 3487:+ 3484:) 3478:( 3469:( 3464:) 3461:2 3458:+ 3455:) 3449:( 3440:( 3437:) 3431:( 3417:( 3410:2 3406:) 3402:1 3399:+ 3396:) 3390:( 3381:( 3378:) 3366:( 3357:C 3349:a 3345:) 3339:( 3327:B 3324:+ 3321:A 3318:= 3315:) 3303:( 3254:L 3251:S 3247:A 3243:d 3238:P 3235:d 3225:G 3222:L 3214:V 3201:L 3198:S 3194:A 3190:d 3185:L 3182:d 3172:G 3169:L 3149:G 3146:L 3135:G 3132:S 3119:L 3116:S 3105:+ 3097:L 3094:S 3090:A 3086:d 3079:G 3076:L 3072:A 3068:d 3062:= 3059:0 3033:P 3030:d 3027:V 3021:V 3018:d 3015:P 3009:L 3006:d 2995:V 2992:S 2988:A 2984:d 2979:V 2976:S 2968:+ 2963:L 2960:S 2956:A 2952:d 2947:L 2944:S 2936:+ 2931:V 2928:L 2924:A 2920:d 2915:V 2912:L 2904:= 2901:w 2859:) 2855:1 2848:) 2842:( 2831:( 2825:G 2822:L 2814:= 2811:S 2795:S 2791:S 2773:) 2767:G 2764:L 2756:+ 2751:L 2748:S 2739:( 2730:G 2727:S 2719:= 2716:S 2639:3 2636:1 2630:) 2623:) 2617:R 2608:( 2599:3 2591:+ 2587:) 2581:R 2572:( 2562:3 2556:2 2550:) 2544:R 2535:( 2526:3 2515:( 2510:= 2504:R 2499:r 2489:; 2480:3 2477:1 2471:) 2464:) 2458:A 2449:( 2440:3 2432:+ 2428:) 2422:A 2413:( 2403:3 2397:2 2391:) 2385:A 2376:( 2367:3 2356:( 2351:= 2345:A 2340:r 2312:) 2303:R 2298:r 2294:+ 2288:A 2283:r 2276:) 2270:R 2261:( 2248:R 2243:r 2239:+ 2235:) 2229:A 2220:( 2207:A 2202:r 2195:( 2185:= 2179:c 2147:R 2118:A 2089:c 2060:R 2031:A 1984:= 1979:2 1975:/ 1971:1 1964:) 1957:2 1949:y 1945:+ 1942:1 1939:( 1919:0 1916:= 1913:) 1910:L 1907:( 1904:y 1881:0 1878:= 1873:H 1865:= 1859:L 1849:F 1818:L 1798:x 1775:y 1770:2 1762:+ 1759:) 1754:G 1751:S 1738:L 1735:S 1727:( 1715:2 1707:y 1703:+ 1700:1 1696:1 1689:G 1686:L 1675:= 1670:H 1643:L 1631:y 1627:p 1624:= 1619:H 1595:L 1584:y 1575:= 1572:p 1550:i 1522:y 1517:2 1502:y 1496:1 1485:) 1480:G 1477:S 1464:L 1461:S 1453:( 1450:+ 1442:2 1434:y 1430:+ 1427:1 1420:G 1417:L 1409:= 1404:L 1376:A 1373:= 1370:x 1367:d 1364:y 1359:I 1334:0 1331:= 1328:x 1325:d 1318:y 1312:I 1287:0 1284:= 1281:) 1278:L 1275:( 1272:y 1269:= 1266:) 1263:0 1260:( 1257:y 1234:x 1231:d 1227:) 1223:) 1218:G 1215:S 1202:L 1199:S 1191:( 1188:+ 1180:2 1172:y 1168:+ 1165:1 1158:G 1155:L 1146:( 1140:L 1135:0 1127:= 1124:] 1121:L 1118:, 1115:y 1112:[ 1107:F 1082:L 1062:] 1059:L 1056:, 1053:0 1050:[ 1047:= 1044:I 1038:x 1018:) 1015:x 1012:( 1009:y 957:) 951:( 939:G 936:L 928:+ 923:L 920:S 912:= 907:G 904:S 837:2 834:= 828:+ 822:+ 787:0 784:= 764:+ 760:) 754:( 731:+ 727:) 721:( 694:0 691:= 683:) 677:( 654:+ 638:+ 634:) 628:( 601:0 598:= 590:) 584:( 561:+ 557:) 551:( 528:+ 441:c 286:C 282:A 278:C 270:A 187:S 48:. 41:. 34:. 20:)

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

Index