147:. It is similar to liquid chromatography, as it works on dilute solutions or suspensions of the solute, carried by a flowing eluent. Separation is achieved by applying a field (hydraulic, centrifugal, thermal, electric, magnetic, gravitational, ...) or cross-flow, perpendicular to the direction of transport of the sample, which is pumped through a long and narrow laminar channel. The field exerts a force on the sample components, concentrating them towards one of the channel walls, which is called accumulation wall. The force interacts with a property of the sample, thereby the separation occurs, in other words, the components show differing "mobilities" under the force exerted by the crossing field. As an example, for the hydraulic, or cross-flow FFF method, the property driving separation is the translational
124:
211:. Because there is no stationary phase, there is less interaction with surfaces or column packing materials. The separation is tunable by modulating the strength of the separation field. FFF is a gentle method and does not exert physical stress on fragile samples, and the carrier solution can be tailored in view of best sample stability. FFF has a well worked-out theory, which can be used to find separation conditions to reach the optimal result, without a series of trial-and-error experiments. It is also possible to extract information of physical parameters of sample fractions from the FFF theory, although almost all users depend mostly on light scattering detectors to measure the size of eluting sample fractions.
1131:), on the other hand, has only one semi-permeable membrane on the bottom wall of the channel. The cross flow is, therefore, created by the carrier liquid exiting the bottom of the channel. This offers an extremely gentle separation and an “ultra-broad” separation range. The majority of FFF instruments in use are AF4 systems. Main applications are in pharmaceutical research and development for proteins, virus and virus-like particles, and liposomes. AF4 can be applied in aqueous and organic solvents, therefore also organic polymers can be separated by this technique.
309:: The field induces a downward drift velocity and concentration towards the accumulation wall, the diffusion works against this concentration gradient. After a certain time (called relaxation time) the two forces equilibrate in a stationary equilibrium. This is best visualized as a particle cloud, with all components in constant motion, but with an exponential decrease of the average concentration going away from the accumulation wall up into the channel. The decrease of air pressure going up from sea level has the same exponential decrease which is described in the
265:
diffuse up against this force. On average the smaller red particles are higher up above the accumulation wall compared to the blue particles. The elution flow in longitudinal direction is shown with the flow arrows indicating the velocity profile. Particles jumping up higher are transported faster compared to others. In the statistical process of many particles and many diffusion steps, the cloud formed by the red, smaller particles, migrates faster and separates from the slower blue particles.
333:
the channel can be milled into the top block as a cavity. The channel is engineered in a way to allow the application of the force field, which means that for each FFF method a dedicated channel is needed. The sample is injected in a dilute solution or suspension into the channel and is separated during migration from inlet to outlet as the carrier solution is pumped through the channel. Downstream of the channel outlet one or several detectors are placed which analyze the eluting fractions.
1119:. (1974). HF5 has been applied towards the analysis of proteins and other macromolecules. HF5 was the first form of flow FFF to be developed in 1974. The advantage is that HF5 offers a disposable channel unit which can be readily replaced in routine applications. One of the drawbacks of HF5 is the limited choice of membrane materials; only polyether sulfone (PES) membranes are available. Currently, HF5 is not widely used, because of the lack of flexibility and limitations in sample load.
320:-velocity profile exists, which is characterized by a strong increase of the flow velocity with increasing distance from the accumulation wall. This determines the velocity of a particular particle, based on its equilibrium position from the wall of the channel. Particles closer to the accumulation wall will migrate slower compared to others being higher up. The ratio of the velocity of a species of particle to the average velocity of the fluid is called the
1201:
FFF where a special alternating current is applied. It allows to separate according to electrophoretic mobility. Another variation is electrical asymmetrical flow FFF (EAF4), where an electrical field is applied in addition to a cross flow field. EAF4 overcomes the limitation of pure electrical FFF which has poor resolution and suffers from electrolysis products and bubbles contaminating the channel outflow and compromising the detector signals.
1164:
channel at low flow-rate, whilst simultaneously pumping a carrier liquid into the second inlet at much higher flow-rate. By controlling the flow rate ratios of the two inlet streams and two outlet streams, the separation can be controlled, and the sample components are separated into two distinct sized fractions. The use of gravity alone as the separating force makes SPLITT the least sensitive FFF technique, limited to particles above 1 μm.
1077:
22:
1090:
flow-velocity. The presence of different species in a sample can thus be identified through detection of a common property at some distance down the long channel, and by the resulting fractogram indicating the presence of the various species by peaks, due to the different times of arrival characteristic of each species and its physical and chemical properties.
1143:
separating synthetic polymers in organic solvents. Thermal FFF is unique amongst FFF techniques in that it can separate macromolecules by both molar mass and chemical composition, allowing for the separation of polymer fractions with the same molecular weight. Today this technique is ideally suited for the characterization of polymers, gels and nanoparticles.
1185:
resolution. This can be particularly useful for novel products, such as composite materials and coated polymers containing nanoparticles, i.e. particles which may not vary in size but which do vary in density. In this way two identically sized particles can still be separated into two peaks, providing that the density is different.
1106:
Of these techniques flow FFF was the first to be offered commercially. Flow FFF separates particles based on size, independent of density and can measure macromolecules in the range of 1 nm to 1 μm. In this respect it is the most versatile FFF sub-technique available. The cross flow in Flow
1085:
In FFF the display of detector signals as a function of time is called fractogram, in contrast to the chromatogram of column chromatography techniques. The fractogram can be converted to a distribution plot of one or several physical properties of the analyte using FFF theory and/or detector signals.
1200:
drift velocity is induced, counteracted by the diffusion from
Brownian motion, so the separation depends on the ratio of electrophoretic mobility and size. Application of electrical FFF has been limited and is currently rarely used. Other modifications have been developed, namely cyclical electrical
1089:
Often these substances are particles initially suspended in a small volume of a liquid buffer and pushed along the FFF channel by the buffer. The varying velocities of a particular species of particles may be due to its size, its mass, and/or its distance from the walls of a channel with non-uniform
1067:
The magnitude of F and ∆F depend on particle properties, field strength and the type of field. This allows for variations and adaptations of the technique. From this basic principle many forms of FFF have evolved varying by the nature of the separative force applied and the range in molecule size to
1180:
Centrifugal FFF has the advantage that particles and macromolecules can be separated by particle density, rather than just particle size. In this instance, two identically sized gold and silver nanoparticles can be separated into two peaks, according to differences in density in the gold and silver
1172:
In centrifugal FFF, the separation field is generated via a centrifugal force. The channel takes the form of a ring, which spins at rotation speeds which can be programmed during the run. The flow and sample are pumped into the channel and centrifuged, allowing the operator to resolve the particles
1146:
One of the major advantage of
Thermal FFF is the simple and very well defined dimensions of the separation channel, which makes the inter-lab or inter-instrument Universal Calibration possible because the Thermal FFF calibration constants closely describe the ratio of ordinary (molecular) diffusion
564:
k is the
Boltzmann constant, T is absolute temperature and F is the force exerted on a single particle by the force field. This shows how the characteristic elevation value is inversely dependent to the force applied. Therefore, F governs the separation process. Hence, by varying the field strength
127:
Flow field-flow fractionation (AF4) channel cross section, where the velocity of laminar flow within the channel is not uniform. The fluid travels in a parabolic pattern with the velocity of the flow, increasing with the distance from the walls up towards the centre of the channel. Separation takes
332:
Separation in field flow fractionation takes place in a laminar channel. It is composed of a top and bottom block which are separated by a spacer. The spacer has a cut-out (rectangular or trapezoidal) void, which creates the channel volume as the spacer is sealed between the blocks. Alternatively,
190:
known from HPLC or SEC. Due to FFF's similarity to Liquid
Chromatography, in ways of a liquid mobile phase passing through the channel, the most common detectors are those that are also used for LC. The most frequently used is a UV-VIS detector, because of its non-destructive nature. Coupling with
1142:
Thermal FFF, as the name suggests, establishes a separation force by applying a temperature gradient to the channel. The top channel wall is heated and the bottom wall is cooled driving polymers and particles towards the cold wall by thermal diffusion. Thermal FFF was developed as a technique for
264:
The animation illustrates how the separation in FFF is driven by particle diffusion in a parabolical flow profile. Shown are two types of particles; the red ones are smaller than the blue ones. A force is applied from the top (here it is a cross flow used in asymmetrical flow fff). The particles
1163:
is a special preparative FFF technique, using gravity or electric, or diffusion differences for separation of over μm-sized particles on a continuous basis. SPLITT system has two inlets and two outlets. It is performed by pumping the sample immerse in a liquid into one inlet at the start of the
348:
The relationship between the separative force field and retention time can be derived from first principles. Consider two particle populations within the FFF channel. The cross field drives both particle clouds towards the bottom "accumulation" wall. Opposing this force field is the particles'
219:
FFF does not work for small molecules, because of their fast diffusion. For an effective separation, the sample has to be concentrated very close to the accumulation wall (a distance less than 10 μm), which requires the drift velocity caused by the force field to be two orders of magnitude
1184:
In AF4 separations, the ratio of mass to time is 1:1. With the addition of the third parameter of density to centrifugal FFF, this produces a ratio more akin to mass:time to the power of three. This results in a significantly larger distinction between peaks and result in a greatly improved
252:
243:
in 1966 and in 1976. Giddings had published many articles on Flow-FFF which is the most important FFF technique today. Giddings, credited for the invention of FFF, was professor of chemistry and specialist of chromatography and separation techniques at the
159:
FFF is applicable in the sub-micron range (from 1 nm to several microns) in the "normal" mode or up to 50 microns in the so-called steric mode. The transition from normal to steric mode takes place when diffusion becomes negligible at sizes above a
1107:
FFF enters through a porous frit at the top of the channel, exiting through a semi-permeable membrane outlet frit on the accumulation wall (i.e. the bottom wall). Symmetrical flow has been replaced by asymmetrical flow in the last two decades.
1151:
which are only polymer dependent. The ThFFF Universal
Calibration is, therefore, instrument and lab transferable, while the well-known size exclusion chromatography Universal Calibration is polymer-transferable on the same instrument only.
1080:
Centrifugal FFF separates by mass (i.e. a combination of particle density and particle size). For example, gold and silver nanoparticles of identical size can be separated into two peaks, according to differences in density of gold and
353:, which produces a counter acting motion. When these two transport processes reach equilibrium the particle concentration c approaches the exponential function of elevation x above the accumulation wall as illustrated in equation (
1766:
W.J. Cao, P.S. Williams, M. N. Myers, and J.C. Giddings, “Thermal Field-Flow
Fractionation Universal Calibration: Extension for Consideration of Variation of Cold Wall Temperature”, Analytical Chemistry, 1999, 71, pp1597 –
220:
higher compared to the diffusion coefficient. The maximum field strength which can be generated in an FFF channel determines the lower size range of separation. For current instrumentation this is approximately 1 nm.
1176:
The unique advantage presented by centrifugal FFF comes from the techniques capability for high resolution given sufficient buoyant density. This allows for the separation of particles with only a 5% difference in size.
1173:
by mass (size and density). The advantage of centrifugal FFF lies in the high size resolution that can be achieved by varying the force applied, since particle size is proportional to particle mass to the third power.
256:
259:
258:
254:
253:
260:
230:
FFF behaves differently from column chromatography and can be counter-intuitive for HPLC or SEC users. Understanding of the working principle of FFF is vital for a successful application of the method.
1188:
The limitation of the method lies in the lower limit of size which depends on the density of the sample. Specifically for biological samples, the limit is in the order of 20 to 50 nm in diameter.
223:
Although FFF is an extremely versatile technique, there is no "one size fits all" method for all applications. Different FFF methods need specialized instrumentation. Currently only the so called
546:
748:
1038:
415:
257:
618:
942:
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represents the characteristic elevation of the particle cloud. This relates to the average height that the particle cloud reaches within the channel and only when the value for
143:. The technique is based on separation of colloidal or high molecular weight substances in liquid solutions, flowing through the separation platform, which does not have a
1064:
in their retention times, is achieved only if the force increment ∆F between them is sufficient. A differential in force of only 10 N is required for this to be the case.
1134:
High
Temperature Asymmetric Flow Field-Flow Fractionation is available for the separation of high and ultra-high molar mass polymers soluble at temperatures above 150 C.
1757:
Lee H.L., Reis J.F.G., and
Lightfoot E.N. (1974). Single-phase chromatography: Solute retardation by ultrafiltration and electrophoresis. AIChE Journal, vol. 20, p. 776.
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or the hydrodynamic size. For a thermal field (heating one wall and cooling the other), it is the ratio of the thermal and the translational diffusion coefficient.
196:
123:
492:
of each component can be related to the force applied on each individual particle or to the ratio of the diffusion coefficient D and the drift velocity U.
164:. FFF is unique in its wide dynamic range of sizes covering both soluble macromolecules and particles or colloids which can be separated in one analysis.
1902:"Instrument and Method to Determine the Electrophoretic Mobility of Nanoparticles and Proteins by Combining Electrical and Flow Field-Flow Fractionation"
207:
FFF offers a physical separation of complex and inhomogeneous samples, which potentially cannot be characterized by other separation methods, such as
39:
1196:
In electrical FFF a transverse electrical current (DC) is applied which creates an electric field. Depending on the charge of sample components, an
1128:
224:
1524:"Particle size distribution by sedimentation/steric field-flow fractionation: development of a calibration procedure based on density compensation"
313:. After relaxation has been achieved, elution starts as the channel flow is activated. In the thin channel (typical height 250 to 350 μm) a
255:
1798:
568:
The velocity V of a cloud of molecules is simply the average velocity of an exponential distribution embedded in a parabolic flow profile.
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allows to calculate the size of eluting fractions and compare to values obtained via FFF theory. Another popular specific detection is
86:
58:
105:
1446:"Influence of accumulation wall and carrier solution composition on lift force in sedimentation/steric field-flow fractionation"
65:
336:
Giddings and co-workers have developed a theory describing the general retention equation which is common to all FFF methods.
2003:
43:
1630:"Asymmetrical flow field-flow fractionation technique for separation and characterization of biopolymers and bioparticles"
500:
227:(AF4) has gained wide-spread use. Other methods like centrifugal, thermal or electrical FFF still have a niche existence.
208:
72:
1309:"Evaluation and comparison of gel permeation chromatography and thermal field-flow fractionation for polymer separations"
655:
301:. In all cases, the separation mechanism is produced by differences in particle mobility under the forces of the field,
144:
1822:"Split-Flow Thin (SPLITT) Cell Separations Operating under Sink-Float Mode Using Centrifugal and Gravitational Fields"
1744:
Giddings, J.C., Yang F.J., and Myers M.N. (1976). "Flow Field-Flow
Fractionation: a versatile new separation method."
192:
54:
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Giordani, Stefano; Marassi, Valentina; Placci, Anna; Zattoni, Andrea; Roda, Barbara; Reschiglian, Pierluigi (2023).
988:
367:
32:
1098:
Most techniques available today are advances on those originally created by Prof. Giddings nearly 4 decades ago.
980:. When this is the case the term in the brackets approaches unity. Therefore, equation 5 can be approximated as:
1197:
1346:
Tasci, Tonguc O.; Johnson, William P.; Fernandez, Diego P.; Manangon, Eliana; Gale, Bruce K. (December 2015).
1160:
1060:
is roughly proportional to F. The separation of particle bands X and Y, represented by the finite increment ∆t
324:. In FFF for efficient separation, R needs to be below 0.2, typical values are in the range of 0.02 to 0.1.
2008:
583:
1778:
834:
1953:"Toward Multianalyte Immunoassays: A Flow-Assisted, Solid-Phase Format with Chemiluminescence Detection"
180:
1820:
Barman, Bhajendra N.; Williams, P. Stephen; Myers, Marcus N.; Giddings, J. Calvin (14 February 2018).
1629:
79:
1389:"Magnetic Nanoparticle Drug Carriers and Their Study by Quadrupole Magnetic Field-Flow Fractionation"
1281:
639:
In FFF the retention is usually expressed in terms of the retention ratio, which is the void time t
282:
1522:
Giddings, J. Calvin.; Moon, Myeong Hee.; Williams, P. Stephen.; Myers, Marcus N. (15 July 1991).
310:
274:
245:
240:
140:
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1483:
Giddings, J. Calvin.; Chen, Xiurong.; Wahlund, Karl Gustav.; Myers, Marcus N. (1 August 1987).
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1779:"Chapter 18 - Theoretical principles of field-flow fractionation and SPLITT fractionation"
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1677:"A New Separation Concept Based on a Coupling of Concentration and Flow Nonuniformities"
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Yang, Feng-Shyang; Caldwell, Karin D; Myers, Marcus N; Giddings, J.Calvin (May 1983).
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Johann, Christoph; Elsenberg, Stephan; Schuch, Horst; Rösch, Ulrich (21 April 2015).
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1270:"Colloid characterization by sedimentation field-flow fractionation. III. Emulsions"
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1708:"Theoretical and experimental characterization of flow field-flow fractionation"
21:
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Capuano, Andrea; Adami, Andrea; Mulloni, Viviana; Lorenzelli, Leandro (2017).
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Williams, P. Stephen; Moon, Myeong Hee; Giddings, J. Calvin (10 August 1996).
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Williams, P. Stephen; Carpino, Francesca; Zborowski, Maciej (5 October 2009).
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Giddings, J. Calvin; Yang, Frank J. F.; Myers, Marcus N. (24 September 1976).
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coefficient D to thermal diffusion coefficient (or, thermophoretic mobility) D
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to characterize metallic nanoparticles with high specificity and sensitivity.
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divided by w, the channel thickness or height. Substituting kT/F in place of
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306:
187:
1986:
1933:
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1614:
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1307:
Giddings, J. Calvin.; Yoon, Young Hee.; Myers, Marcus N. (1 January 1975).
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Yohannes, G.; Jussila, M.; Hartonen, K.; Riekkola, M. -L. (8 July 2011).
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826:
illustrates the retention ratio with respect to the cross force applied.
314:
1723:
1539:
1500:
1348:"Particle Based Modeling of Electrical Field Flow Fractionation Systems"
1324:
168:
1917:
1706:
Giddings, J. Calvin.; Yang, Frank J.; Myers, Marcus N. (1 July 1976).
1404:
472:
is different for the particle populations separation will occur. The
960:
For an efficient operation the channel thickness value w far exceeds
643:(emergence of a non retained tracer) divided by the retention time t
118:
Separation technique to characterize the size of colloidal particles
1485:"Fast particle separation by flow/steric field-flow fractionation"
1223:"Flow-Field-Flow Fractionation: A Versatile New Separation Method"
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250:
176:
122:
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Williams, Philip
Stephen (1 January 2022), Contado, Catia (ed.),
1571:"Field-Flow Fractionation in Molecular Biology and Biotechnology"
1450:
Colloids and Surfaces A: Physicochemical and Engineering Aspects
1785:, Handbooks in Separation Science, Elsevier, pp. 579–620,
15:
1861:"A Miniaturized SPLITT System for On-Line Protein Separation"
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through a semi-permeable membrane as the accumulation wall),
565:
the separation can be controlled to achieve optimal levels.
128:
place close to the accumulation (bottom) wall of the channel
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541:{\displaystyle \ell ={\frac {kT}{F}}={\frac {D}{U}}}
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As mentioned above, in field-flow fractionation the
46:. Unsourced material may be challenged and removed.
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743:{\displaystyle R={\frac {t_{0}}{t_{r}}}=6\lambda }
742:
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1115:Hollow fiber flow FFF (HF5) was developed by Lee
1826:Industrial & Engineering Chemistry Research
179:and virus like particles, lipid nanoparticles,
1033:{\displaystyle R=6\lambda =6{\frac {kT}{Fw}}}
8:
410:{\displaystyle c=c_{0}e^{\frac {-x}{\ell }}}
197:Inductively coupled plasma mass spectrometry
1161:Split flow thin-cell fractionation (SPLITT)
1086:This can be size, molar mass, charge, etc.
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167:Typical applications are high molar mass
106:Learn how and when to remove this message
1274:Journal of Colloid and Interface Science
225:asymmetric flow field-flow fractionation
139:, is a separation technique invented by
1210:
647:. The retention equation then becomes:
340:Relating force (F) to retention time (t
239:FFF was devised and first published by
183:and other types of biological samples.
175:, both industrial and environmental,
7:
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613:{\displaystyle t_{r}={\frac {L}{V}}}
577:
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44:adding citations to reliable sources
937:{\displaystyle R=6{\frac {kT}{Fw}}}
186:FFF can be coupled to all types of
1791:10.1016/b978-0-323-85486-3.00001-9
1156:Split flow thin-cell fractionation
155:Applications and detection methods
14:
1636:. Flow-Field-Flow Fractionation.
303:in a stationary equilibrium with
235:Discovery and general principles
20:
636:Where L is the channel length.
31:needs additional citations for
1783:Particle Separation Techniques
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1:
1365:10.3390/chromatography2040594
209:Size-exclusion chromatography
1970:10.1373/clinchem.2005.053108
1675:Giddings, J. Calvin (1966).
1646:10.1016/j.chroma.2010.12.110
1462:10.1016/0927-7757(96)03669-2
1294:10.1016/0021-9797(83)90391-0
193:Multi angle light scattering
1634:Journal of Chromatography A
355:
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1878:10.3390/proceedings1040527
55:"Field flow fractionation"
1693:10.1080/01496396608049439
1588:10.3390/molecules28176201
1068:which they are targeted.
1838:10.1021/acs.iecr.7b04223
779:{\displaystyle \lambda }
171:and polymer composites,
133:Field-flow fractionation
1393:Molecular Pharmaceutics
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2004:Laboratory techniques
1127:Asymmetric flow FFF (
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973:{\displaystyle \ell }
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445:{\displaystyle \ell }
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149:diffusion coefficient
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1906:Analytical Chemistry
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1528:Analytical Chemistry
1489:Analytical Chemistry
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40:improve this article
1724:10.1021/ac50002a016
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1501:10.1021/ac00142a014
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1286:1983JCIS...93..115Y
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1957:Clinical Chemistry
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246:University of Utah
241:J. Calvin Giddings
141:J. Calvin Giddings
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1963:(10): 1993–1995.
1951:Roda, A. (2005).
1918:10.1021/ac504712n
1800:978-0-323-85486-3
1640:(27): 4104–4116.
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1495:(15): 1957–1962.
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1441:
1435:
1434:
1424:
1399:(5): 1290–1306.
1384:
1378:
1377:
1367:
1343:
1337:
1336:
1304:
1298:
1297:
1265:
1259:
1258:
1218:
1102:Symmetrical flow
1048:
1039:
1037:
1036:
1031:
1029:
1027:
1019:
1011:
983:
979:
977:
976:
971:
952:
943:
941:
940:
935:
930:
928:
920:
912:
901:
899:
888:
880:
866:
864:
856:
848:
829:
825:
823:
822:
817:
805:
803:
802:
797:
785:
783:
782:
777:
758:
749:
747:
746:
741:
724:
722:
711:
688:
686:
685:
676:
675:
666:
650:
628:
619:
617:
616:
611:
609:
601:
596:
595:
578:
556:
547:
545:
544:
539:
537:
529:
524:
519:
511:
495:
491:
489:
488:
483:
471:
469:
468:
463:
451:
449:
448:
443:
425:
416:
414:
413:
408:
406:
405:
400:
392:
386:
385:
362:
262:
145:stationary phase
111:
104:
100:
97:
91:
89:
48:
24:
16:
2024:
2023:
2019:
2018:
2017:
2015:
2014:
2013:
1994:
1993:
1950:
1947:
1942:
1941:
1899:
1898:
1894:
1858:
1857:
1853:
1819:
1818:
1814:
1805:
1803:
1801:
1776:
1775:
1771:
1765:
1761:
1756:
1752:
1743:
1739:
1705:
1704:
1700:
1674:
1673:
1669:
1627:
1626:
1622:
1568:
1567:
1563:
1521:
1520:
1516:
1482:
1481:
1477:
1443:
1442:
1438:
1386:
1385:
1381:
1345:
1344:
1340:
1306:
1305:
1301:
1267:
1266:
1262:
1220:
1219:
1212:
1207:
1198:electrophoretic
1194:
1170:
1158:
1150:
1140:
1125:
1123:Asymmetric flow
1113:
1104:
1096:
1074:
1063:
1059:
1046:
1020:
1012:
987:
986:
962:
961:
950:
921:
913:
889:
881:
857:
849:
833:
832:
808:
807:
788:
787:
768:
767:
756:
715:
677:
667:
654:
653:
646:
642:
626:
587:
582:
581:
574:
554:
512:
499:
498:
474:
473:
454:
453:
434:
433:
423:
393:
387:
377:
366:
365:
351:Brownian motion
346:
343:
330:
251:
237:
217:
205:
157:
119:
112:
101:
95:
92:
49:
47:
37:
25:
12:
11:
5:
2022:
2020:
2012:
2011:
2006:
1996:
1995:
1992:
1991:
1946:
1945:External links
1943:
1940:
1939:
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1698:
1667:
1620:
1561:
1514:
1475:
1456:(3): 215–228.
1436:
1379:
1358:(4): 594–610.
1352:Chromatography
1338:
1319:(1): 126–131.
1299:
1280:(1): 115–125.
1260:
1209:
1208:
1206:
1203:
1193:
1190:
1169:
1166:
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345:
341:
338:
329:
326:
305:the forces of
277:(with a cross
236:
233:
216:
213:
204:
201:
156:
153:
135:, abbreviated
117:
114:
113:
28:
26:
19:
13:
10:
9:
6:
4:
3:
2:
2021:
2010:
2009:Fractionation
2007:
2005:
2002:
2001:
1999:
1988:
1984:
1980:
1976:
1971:
1966:
1962:
1958:
1954:
1949:
1948:
1944:
1935:
1931:
1927:
1923:
1919:
1915:
1911:
1907:
1903:
1896:
1893:
1888:
1884:
1879:
1874:
1870:
1866:
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1855:
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1823:
1816:
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1802:
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1607:
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1565:
1562:
1557:
1553:
1549:
1545:
1541:
1537:
1533:
1529:
1525:
1518:
1515:
1510:
1506:
1502:
1498:
1494:
1490:
1486:
1479:
1476:
1471:
1467:
1463:
1459:
1455:
1451:
1447:
1440:
1437:
1432:
1428:
1423:
1418:
1414:
1410:
1406:
1402:
1398:
1394:
1390:
1383:
1380:
1375:
1371:
1366:
1361:
1357:
1353:
1349:
1342:
1339:
1334:
1330:
1326:
1322:
1318:
1314:
1310:
1303:
1300:
1295:
1291:
1287:
1283:
1279:
1275:
1271:
1264:
1261:
1256:
1252:
1248:
1244:
1240:
1236:
1232:
1228:
1224:
1217:
1215:
1211:
1204:
1202:
1199:
1191:
1189:
1186:
1182:
1178:
1174:
1167:
1165:
1162:
1155:
1153:
1144:
1137:
1135:
1132:
1130:
1122:
1120:
1118:
1110:
1108:
1101:
1099:
1093:
1091:
1087:
1078:
1071:
1069:
1065:
1050:
1043:
1041:
1024:
1021:
1016:
1013:
1007:
1004:
1001:
998:
995:
992:
985:
984:
981:
967:
954:
947:
945:
925:
922:
917:
914:
908:
905:
896:
893:
890:
885:
882:
873:
870:
861:
858:
853:
850:
844:
841:
838:
831:
830:
827:
813:
793:
773:
760:
753:
751:
734:
731:
728:
719:
716:
712:
704:
701:
695:
692:
689:
682:
678:
672:
668:
662:
659:
652:
651:
648:
637:
630:
623:
621:
605:
602:
597:
592:
588:
580:
579:
576:
569:
566:
558:
551:
549:
533:
530:
525:
520:
516:
513:
507:
504:
497:
496:
493:
479:
459:
439:
427:
420:
418:
401:
397:
394:
388:
382:
378:
374:
371:
364:
363:
360:
358:
357:
352:
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337:
334:
327:
325:
323:
319:
316:
312:
308:
304:
300:
296:
292:
288:
284:
283:gravitational
280:
276:
272:
249:
247:
242:
234:
232:
228:
226:
221:
214:
212:
210:
202:
200:
198:
194:
189:
184:
182:
178:
174:
173:nanoparticles
170:
165:
163:
154:
152:
150:
146:
142:
138:
134:
125:
121:
110:
107:
99:
88:
85:
81:
78:
74:
71:
67:
64:
60:
57: –
56:
52:
51:Find sources:
45:
41:
35:
34:
29:This article
27:
23:
18:
17:
1960:
1956:
1909:
1905:
1895:
1868:
1864:
1854:
1829:
1825:
1815:
1804:, retrieved
1782:
1772:
1762:
1753:
1745:
1740:
1715:
1711:
1701:
1684:
1680:
1670:
1637:
1633:
1623:
1581:(17): 6201.
1578:
1574:
1564:
1531:
1527:
1517:
1492:
1488:
1478:
1453:
1449:
1439:
1396:
1392:
1382:
1355:
1351:
1341:
1316:
1312:
1302:
1277:
1273:
1263:
1230:
1226:
1195:
1187:
1183:
1179:
1175:
1171:
1159:
1145:
1141:
1133:
1126:
1116:
1114:
1105:
1097:
1088:
1084:
1066:
1055:
1044:
959:
948:
765:
754:
638:
635:
624:
570:
567:
563:
552:
432:
421:
354:
347:
335:
331:
321:
318:laminar-flow
302:
278:
270:
268:
238:
229:
222:
218:
206:
185:
166:
158:
136:
132:
131:
120:
102:
93:
83:
76:
69:
62:
50:
38:Please help
33:verification
30:
1865:Proceedings
1687:: 123–125.
1168:Centrifugal
287:centrifugal
215:Limitations
1998:Categories
1871:(4): 527.
1806:14 October
1205:References
1192:Electrical
1072:Fractogram
295:electrical
203:Advantages
66:newspapers
1979:0009-9147
1926:0003-2700
1887:2504-3900
1846:0888-5885
1732:0003-2700
1654:0021-9673
1597:1420-3049
1575:Molecules
1548:0003-2700
1509:0003-2700
1470:0927-7757
1413:1543-8384
1374:2227-9075
1333:0003-2700
1247:0036-8075
1002:λ
968:ℓ
906:−
874:
814:ℓ
794:ℓ
774:λ
735:λ
729:−
720:λ
705:
696:λ
505:ℓ
480:ℓ
460:ℓ
440:ℓ
402:ℓ
395:−
315:parabolic
307:diffusion
275:hydraulic
188:detectors
1987:16299900
1934:25789885
1662:21292269
1615:37687030
1606:10488451
1431:19591456
299:magnetic
169:polymers
96:May 2022
1746:Science
1556:1928720
1422:2757515
1282:Bibcode
1227:Science
1138:Thermal
1081:silver.
291:thermal
273:can be
177:viruses
80:scholar
1985:
1977:
1932:
1924:
1885:
1844:
1797:
1730:
1660:
1652:
1613:
1603:
1595:
1554:
1546:
1507:
1468:
1429:
1419:
1411:
1372:
1331:
1255:959835
1253:
1245:
1056:Thus t
766:where
162:micron
82:
75:
68:
61:
53:
1117:et al
1094:Forms
297:, or
271:field
87:JSTOR
73:books
1983:PMID
1975:ISSN
1930:PMID
1922:ISSN
1883:ISSN
1842:ISSN
1808:2023
1795:ISBN
1767:1609
1728:ISSN
1658:PMID
1650:ISSN
1638:1218
1611:PMID
1593:ISSN
1552:PMID
1544:ISSN
1505:ISSN
1466:ISSN
1427:PMID
1409:ISSN
1370:ISSN
1329:ISSN
1251:PMID
1243:ISSN
871:coth
702:coth
279:flow
59:news
1965:doi
1914:doi
1873:doi
1834:doi
1787:doi
1720:doi
1689:doi
1642:doi
1601:PMC
1583:doi
1536:doi
1497:doi
1458:doi
1454:113
1417:PMC
1401:doi
1360:doi
1321:doi
1290:doi
1235:doi
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1936:.
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
