1071:
3338:
4276:
passed into the chamber. The hydraulic residence time (HRT) affects the substrate loading rate of the microorganisms that the anodophiles consume, which affects the electrical output. Longer HRTs reduce substrate loading in the anodic chamber which can lead to reduced anodophile population and performance when there is a deficiency of nutrients. Shorter HRTs support the development of non-
140:
1961:
to the exit, or strong internal circulation. Short-circuiting fluid within the reactor would appear in an RTD curve as a small pulse of concentrated tracer that reaches the outlet shortly after injection. Reactants continuously enter and leave a tank where they are mixed. Consequently, the reaction proceeds at a rate dependent on the outlet concentration:
659:
1455:
2354:
In some reactions the reactants and the products have significantly different densities. Consequently, as the reaction proceeds the volume of the reaction changes. This variable volume adds terms to the design equations. Taking this volume change into consideration the volume of the reaction becomes:
1960:
reaches its maximum value and the length of the delay will reflect the rate of mass transfer within the reactor. Just as was noted for a plug-flow reactor, an early mean will indicate some stagnant fluid within the vessel, while the presence of multiple peaks could indicate channeling, parallel paths
1656:
The RTD of a real reactor deviates from that of an ideal reactor, depending on the hydrodynamics within the vessel. A non-zero variance indicates that there is some dispersion along the path of the fluid, which may be attributed to turbulence, a non-uniform velocity profile, or diffusion. If the mean
4159:
a ground water drinking water source and at what concentration it will arrive. This can also work to the opposite effect to determine how long until a ground water source becomes uncontaminated via inflow, outflow, and volume. The residence time of lakes and streams is important as well to determine
4275:
gas, and as the electrons travel through the circuit they feed the external load. The HRT for this application is the rate at which the feed molecules are passed through the anodic chamber. This can be quantified by dividing the volume of the anodic chamber by the rate at which the feed solution is
4184:
in the body and inhibit their activity. In this case it is the drug-target residence time (the length of time the drug stays bound to the target) that is of interest. The residence time is defined as the reciprocal value of the koff rate constant (residence time = 1/koff). Drugs with long residence
3810:
are clay zones that can have such a degree of impermeability that they partially or completely retard water flow. These clay lenses can slow or stop seepage into the water table, although if an aquitard is fractured and contaminated then it can become a long-term source of groundwater contamination
1955:
In reality, it is impossible to obtain such rapid mixing, as there is necessarily a delay between any molecule passing through the inlet and making its way to the outlet, and hence the RTD of a real reactor will deviate from the ideal exponential decay, especially in the case of large reactors. For
3323:
A step experiment is often easier to perform than a pulse experiment, but it tends to smooth over some of the details that a pulse response could show. It is easy to numerically integrate an experimental pulse response to obtain a very high-quality estimate of the step response, but the reverse is
2816:
Generally, when reactions take place in the liquid and solid phases the change in volume due to reaction is not significant enough that it needs to be taken into account. Reactions in the gas phase often have significant changes in volume and in these cases one should use these modified equations.
3836:
chamber to remove as much of the solid matter as possible before applying additional treatments. The amount removed is controlled by the hydraulic residence time (HRT). When water flows through a volume at a slower rate, less energy is available to keep solid particles entrained in the stream and
3750:
simulations. The very same procedure that is performed in experiments can be followed. A pulse of inert tracer particles (during a very short time) is injected into the reactor. The linear motion of tracer particles is governed by Newton's second law of motion and a one-way coupling is stablished
4163:
Hydrology, the study of water, discusses the water budget in terms of residence time. The amount of time that water spends in each different stage of life (glacier, atmosphere, ocean, lake, stream, river), is used to show the relation of all of the water on the earth and how it relates in its
1555:
Design equations are equations relating the space time to the fractional conversion and other properties of the reactor. Different design equations have been derived for different types of the reactor and depending on the reactor the equation more or less resemble that describing the average
3787:. The retention time through a specified vertical distance in clay will be longer than through the same distance in gravel, even though they are both characterized as high porosity materials. This is because the pore sizes are much larger in gravel media than in clay, and so there is less
1668:
In PFRs, reactants enter the reactor at one end and react as they move down the reactor. Consequently, the reaction rate is dependent on the concentrations which vary along the reactor requiring the inverse of the reaction rate to be integrated over the fractional conversion.
3606:
503:
1491:
The residence time of a specific compound in a mixture equals the turnover time (that of the compound, as well as that of the mixture) only if the compound does not take part in any chemical reaction (otherwise its flow is not conservative) and its concentration is
2184:
1311:
4797:
Ejhed, H.; Fång, J.; Hansen, K.; Graae, L.; Rahmberg, M.; Magnér, J.; Dorgeloh, E.; Plaza, G. (March 2018). "The effect of hydraulic retention time in onsite wastewater treatment and removal of pharmaceuticals, hormones and phenolic utility substances".
4209:
Residence time can also refer to the amount of time that a drug spends in the part of the body where it needs to be absorbed. The longer the residence time, the more of it can be absorbed. If the drug is delivered in an oral form and destined for the
2189:
The variance is infinite. In a real reactor, diffusion will eventually mix the layers so that the tail of the RTD becomes exponential and the variance finite; but laminar flow reactors can have variance greater than 1, the maximum for CTSD reactors.
2829:
into the system at the inlet. Its input concentration is changed according to a known function and the output concentration measured. The tracer should not modify the physical characteristics of the fluid (equal density, equal viscosity) or the
2811:
1284:: most of the particles entering the control volume pass through quickly, but most of the particles contained in the control volume pass through slowly. Examples include water in a lake with the inlet and outlet that are close together and
422:
2567:
1868:(CSTR), the flow at the inlet is completely and instantly mixed into the bulk of the reactor. The reactor and the outlet fluid have identical, homogeneous compositions at all times. The residence time distribution is exponential:
4152:. Residence times of water in rivers are a few days, while in large lakes residence time ranges up to several decades. Residence times of continental ice sheets is hundreds of thousands of years, of small glaciers a few decades.
3730:
3318:
2688:
3988:
2042:
1943:
1761:
Batch reactors are reactors in which the reactants are put in the reactor at time 0 and react until the reaction is stopped. Consequently, the space time is the same as the average residence time in a batch reactor.
1065:
962:
4205:
experiment where a target enzyme is incubated with the inhibitor, allowed to approach equilibrium, then rapidly diluted. The amount of product is measured and compared to a control in which no inhibitor is added.
2295:
1854:
3034:
2433:
1751:
654:{\displaystyle \left.{\begin{aligned}{\frac {\partial I}{\partial t}}={\frac {dm}{dt}}=0&\\f_{\text{in}}=f_{\text{out}}=f&\end{aligned}}\ \right\}\implies fE=-m{\frac {\partial I}{\partial \tau }}}
3469:
2056:, the fluid flows through a long tube or parallel plate reactor and the flow is in layers parallel to the walls of the tube. The velocity of the flow is a parabolic function of radius. In the absence of
512:
488:
852:
3779:). The intersection between pore density and size determines the degree or magnitude of the flow rate through the media. This idea can be illustrated by a comparison of the ways water moves through
3415:
1320:
4612:
Colli, A. N.; Bisang, J. M. (September 2015). "Study of the influence of boundary conditions, non ideal stimulus and dynamics of sensors on the evaluation of residence time distributions".
2066:
1450:{\displaystyle \left.{\begin{aligned}{\frac {\partial I}{\partial t}}={\frac {dm}{dt}}=0&\\f_{\text{in}}=f_{\text{out}}=f&\end{aligned}}\ \right\}\implies \tau _{t}={\frac {m}{f}}}
4674:
Colli, A. N.; Bisang, J. M. (August 2011). "Evaluation of the hydrodynamic behaviour of turbulence promoters in parallel plate electrochemical reactors by means of the dispersion model".
3751:
between fluid and tracers. In one-way coupling, fluid affects tracer motion by drag force while tracer does not affect fluid. The size and density of tracers are chosen so small that the
3191:
1644:
1282:
1158:
1112:
1216:
3806:
which must be controlled such that they do not compromise the quality of the water table and also so the runoff does not create environmental problems in the surrounding areas.
1288:
rising from the ocean surface, which for the most part returns quickly to the ocean, while for the rest is retained in the atmosphere and returns much later in the form of rain.
4271:(PEM) and connected in an external circuit with an external load. Anodophiles grow on the anode and consume biodegradable organic molecules to produce electrons, protons, and
4044:
4140:, lakes, streams, and oceans. More specifically it is the time during which water remains within an aquifer, lake, river, or other water body before continuing around the
2701:
4075:
4214:, it usually moves with food and its residence time is roughly that of the food. This generally allows 3 to 8 hours for absorption. If the drug is delivered through a
4105:
3837:
there is more time for them to settle to the bottom. Typical HRTs for sedimentation basins are around two hours, although some groups recommend longer times to remove
4118:. If the chamber can be heated, the above equation shows that the gases can be "baked out"; but if not, then surfaces with a low residence time are needed to achieve
2328:
5265:
MacMullin, R.B.; Weber, M. (1935). "The theory of short-circuiting in continuous-flow mixing vessels in series and kinetics of chemical reactions in such systems".
3096:
3069:
2916:
742:
263:
193:
4245:, the residence time of a molecule is related to its volume, which is roughly proportional to its molecular weight. Residence times also affect the performance of
3125:
2945:
321:
1525:
4011:
3911:
3461:
3441:
2896:
2876:
765:
722:
702:
682:
310:
283:
236:
213:
4284:
electrochemical performance of the fuel cell if the anodophiles must compete for resources or if they do not have ample time to effectively degrade nutrients.
2449:
3627:
241:
At the moment a particle leaves the control volume, its age is the total time that the particle has spent inside the control volume, which is known as its
2858:. Although an infinitely short injection cannot be produced, it can be made much smaller than the mean residence time of the vessel. If a mass of tracer,
1665:
within the vessel. If the RTD curve shows more than one main peak it may indicate channeling, parallel paths to the exit, or strong internal circulation.
4189:
of the interaction, such as how complementary the shape and charges of the target and drug are and whether outside solvent molecules are kept out of the
2580:
3919:
5363:
1568:(PFR) the fluid particles leave in the same order they arrived, not mixing with those in front and behind. Therefore, the particles entering at time
1967:
1952:
and the variance is 1. A notable difference from the plug flow reactor is that material introduced into the system will never completely leave it.
1874:
3202:
4185:
times are desirable because they remain effective for longer and therefore can be used in lower doses. This residence time is determined by the
3739:, and this determines the achievable yield. A continuous stirred-tank reactor can be anywhere in the spectrum between completely segregated and
5394:
985:
2854:
This method required the introduction of a very small volume of concentrated tracer at the inlet of the reactor, such that it approaches the
885:
5144:"The Hydraulic Retention Time as a Key Parameter for the Performance of a Cyclically Fed Glycerol-Based Microbial Fuel Cell from Biodiesel"
2204:
1768:
5429:
5404:
4658:
4597:
2953:
2361:
1556:
residence time. Often design equations are used to minimize the reactor volume or volumetric flow rate required to operate a reactor.
3601:{\displaystyle {\overline {P_{\mathrm {R} }}}=a_{\mathrm {out} }/a_{\mathrm {in} }=\int _{0}^{\infty }\exp \left(-kt\right)E(t)\,dt.}
1305:, the mean residence time equals the ratio between the amount of fluid contained in the control volume and the flow rate through it:
5325:
5306:
5287:
5255:
5215:
5013:
4934:
4906:
4878:
4850:
4781:
4576:
4556:
1675:
1493:
4711:
4401:
Bolin, Bert; Rodhe, Henning (February 1973). "A note on the concepts of age distribution and transit time in natural reservoirs".
3767:. The amount of time that a pollutant spends traveling through a delineated subsurface space is related to the saturation and the
4319:
4155:
Ground water residence time applications are useful for determining the amount of time it will take for a pollutant to reach and
3851:
of wastewater or drinking water. The types of pathogens that occur in untreated water include those that are easily killed like
434:
3833:
3802:
operations. Waste rock is heterogeneous material with particles varying from boulders to clay-sized particles, and it contains
1865:
120:
773:
5414:
5384:
3611:
If the reaction is more complicated, then the output is not uniquely determined by the RTD. It also depends on the degree of
3363:
5389:
5185:"Water Quality and the Effects of Changes in Phosphorus Loading, Red Cedar Lakes, Barron and Washburn Counties, Wisconsin"
4242:
3763:
Hydraulic residence time (HRT) is an important factor in the transport of environmental toxins or other chemicals through
3893:, and heating the surface increases the probability that an atom will escape within a given time. At a given temperature
3747:
5029:
Cheng, Ka Yu; Ho, Goen; Cord-Ruwisch, Ralf (January 2010). "Anodophilic
Biofilm Catalyzes Cathodic Oxygen Reduction".
4304:
2179:{\displaystyle E(\tau )={\begin{cases}0&\tau \leq T/2\\{\dfrac {T^{2}}{2\tau ^{3}}}&\tau >T/2.\end{cases}}}
20:
4445:"Residence times in reservoirs under non-steady-state conditions: application to atmospheric SO2 and aerosol sulfate"
4259:
bacteria) to convert chemical energy from organic matter into electricity. A biofuel cell mechanism consists of an
2338:
is involved in. The rate expression is often related to the fractional conversion both through the consumption of
5419:
3133:
1598:
3617:, the mixing between molecules that entered at different times. If there is no mixing, the system is said to be
5424:
4268:
4198:
3824:
2834:
conditions and it should be easily detectable. In general, the change in tracer concentration will either be a
2198:
Recycle reactors are PFRs with a recycle loop. Consequently, they behave like a hybrid between PFRs and CSTRs.
1227:
3324:
not the case because any noise in the concentration measurement will be amplified by numeric differentiation.
704:
can be usually traced back to them. For example, the fraction of particles leaving the control volume at time
3755:
of tracers becomes very small. In this way, tracer particles exactly follow the same path as the fluid does.
4299:
4246:
1565:
1540:
1247:
1169:
1123:
1077:
116:
92:
4925:
Keserü, György; Swinney, David C.; Mannhold, Raimund; Kubinyi, Hugo; Folkers, Gerd, eds. (17 August 2015).
4136:
In environmental terms, the residence time definition is adapted to fit with ground water, the atmosphere,
4077:
is a prefactor that is correlated with the vibration times of the surface atoms (generally of the order of
2090:
4592:
Chemical
Engineering Kinetics and Reactor Design by Charles G. Hill, Jr. John Wiley & Sons Inc, 1977.
4211:
4149:
3768:
55:
1181:
5409:
4160:
the concentration of pollutants in a lake and how this may affect the local population and marine life.
3775:
is another significant contributing factor to the mobility of water through the ground (e.g. toward the
74:
1117:
The mean age and the mean transit time generally have different values, even in stationary conditions:
4020:
5038:
4807:
4571:
Elements of
Chemical Reaction Engineering (4th Edition) by H. Scott Fogler, Prentice Hall PTR, 2005.
4500:
4456:
4410:
3354:
2947:
can be transformed into a dimensionless residence time distribution curve by the following relation:
2855:
2053:
1585:
876:
107:
The concept of residence time originated in models of chemical reactors. The first such model was an
4114:, the residence time of gases on the surfaces of a vacuum chamber can determine the pressure due to
497:, then the exit age distribution and the internal age distribution can be related one to the other:
5225:
Leckner, Bo; Ghirelli, Frederico (2004). "Transport equation for local residence time of a fluid".
4309:
4294:
4252:
4156:
4131:
3860:
3852:
2806:{\displaystyle \tau ={\frac {C_{A{\text{ in}}}-C_{A{\text{ out}}}}{-r_{AF}(1-\delta _{A}f_{A})}}\ }
2057:
1302:
494:
43:
5165:
4983:
4518:
4281:
4141:
3886:
3844:
3803:
3798:
Groundwater flow is important parameter for consideration in the design of waste rock basins for
3788:
3044:
The concentration of tracer in a step experiment at the reactor inlet changes abruptly from 0 to
4773:
4766:
4053:
5335:
Wolf, David; Resnick, William (November 1963). "Residence Time
Distribution in Real Systems".
5321:
5302:
5283:
5251:
5211:
5113:
5054:
5009:
4975:
4967:
4930:
4902:
4874:
4846:
4823:
4777:
4654:
4593:
4572:
4552:
4256:
4119:
4111:
4080:
4047:
3838:
3829:
3792:
3350:
1231:
115:
in 1908. This received little attention for 45 years; other models were developed such as the
51:
4950:
Copeland, Robert A. (2015). "The drug–target residence time model: a 10-year retrospective".
4740:
417:{\displaystyle \int _{0}^{\infty }E(\tau ,t)\,d\tau =\int _{0}^{\infty }I(\tau ,t)\,d\tau =1}
5399:
5344:
5234:
5155:
5103:
5093:
5046:
4959:
4815:
4691:
4683:
4629:
4621:
4508:
4487:
Monsen, Nancy E.; Cloern, James E.; Lucas, Lisa V.; Monismith, Stephen G. (September 2002).
4464:
4418:
4366:
4186:
4177:
3848:
3820:
3346:
3071:. The concentration of tracer at the outlet is measured and normalized to the concentration
2303:
1662:
1070:
131:
resurrected the axial dispersion model and formulated the modern concept of residence time.
128:
39:
5079:"Water Quality Monitoring in Developing Countries; Can Microbial Fuel Cells be the Answer?"
3881:
Atoms and molecules of gas or liquid can be trapped on a solid surface in a process called
3074:
3047:
2901:
727:
248:
178:
127:(representing the response to a sudden change in the input) was introduced. Then, in 1953,
4215:
3876:
3867:. The disinfection chamber must have a long enough HRT to kill or deactivate all of them.
3735:
For given RTD, there is an upper limit on the amount of mixing that can occur, called the
3357:, the probability that an atom or molecule will react depends only on its residence time:
3101:
2921:
1536:
1161:
315:
Both distributions are assumed to be positive and to have unitary integral along the age:
112:
96:
5078:
4489:"A comment on the use of flushing time, residence time, and age as transport time scales"
1544:
1502:
5142:
Santos, João B. Costa; de Barros, Vanine V. Silva; Linares, José J. (30 November 2016).
5042:
4811:
4504:
4460:
4414:
175:. In general, each particle has a different age. The frequency of occurrence of the age
5108:
4422:
4272:
4230:
3996:
3896:
3864:
3740:
3446:
3426:
3337:
2881:
2861:
2562:{\displaystyle \tau =N_{AO}\int {\frac {1}{(-r_{A})V_{R}(1-\delta _{A}f_{A})}}\,df_{A}}
1298:
750:
707:
687:
667:
428:
295:
268:
221:
198:
168:
143:
35:
3725:{\displaystyle a_{\mathrm {out} }=\int _{0}^{\infty }a_{\mathrm {batch} }(t)E(t)\,dt.}
5378:
4277:
4193:(thereby preventing them from breaking any bonds formed), and is proportional to the
3752:
3421:
2843:
1235:
490:, which may allow to redefine the distributions as simple functions of the age only.
5169:
4987:
4819:
4687:
4625:
4522:
1527:
does not hold if the flow is not stationary or it is not conservative, it does hold
4190:
4014:
2831:
1165:
1160:: examples include water in a lake with the inlet and outlet on opposite sides and
493:
If the flow is steady (but a generalization to non-steady flow is possible) and is
195:
in the set of all the particles that are located inside the control volume at time
78:
31:
3443:. Given a RTD, the average probability is equal to the ratio of the concentration
2683:{\displaystyle \tau =C_{AO}\int {\frac {1}{(-r_{A})(1-\delta _{A}f_{A})}}\,df_{A}}
5368:
5364:
Mean residence time (MRT): Understanding how long drug molecules stay in the body
1535:, and not necessarily at any instant. Under such conditions, which are common in
4469:
4444:
4324:
4314:
4223:
3983:{\displaystyle \tau =\tau _{0}\exp \left({\frac {E_{\mathrm {a} }}{RT}}\right),}
3776:
3764:
3613:
1285:
1173:
975:, that is the mean age of all the particles leaving the control volume at time
5238:
4513:
4488:
4115:
3882:
2826:
2037:{\displaystyle \tau ={\frac {C_{A{\text{ in}}}-C_{A{\text{ out}}}}{-r_{A}}}\ }
47:
4971:
1938:{\displaystyle E(\tau )={\frac {1}{T}}\exp \left({\frac {-\tau }{T}}\right).}
4551:. Boston, Mass.: McGraw-Hill Higher Education. pp. 150, 267, 480, 500.
4194:
2438:
Plugging this into the design equations results in the following equations:
767:, that is the complementary to one of the cumulative exit age distribution:
265:
in the set of all the particles that are leaving the control volume at time
139:
83:
70:
5117:
5058:
4979:
4827:
3313:{\displaystyle F(t)=\int _{0}^{t}E(t')\,dt'\qquad E(t)={\frac {dF(t)}{dt}}}
99:, where the material that flows is usually discrete instead of continuous.
5184:
5318:
5160:
5143:
4226:
3856:
3772:
3196:
The step- and pulse-responses of a reactor are related by the following:
1239:
5348:
5246:
Lee, Peter I.D.; Amidon, Gordon L. (1996). "2. Time constant approach".
5098:
4963:
2825:
Residence time distributions are measured by introducing a non-reactive
1060:{\displaystyle \tau _{t}(t)=\int _{0}^{\infty }\tau E(\tau ,t)\,d\tau .}
4696:
4634:
4264:
4145:
4137:
3807:
957:{\displaystyle \tau _{a}(t)=\int _{0}^{\infty }\tau I(\tau ,t)\,d\tau }
5050:
4370:
2842:. Other functions are possible, but they require more calculations to
2346:
changes through temperature changes that are dependent on conversion.
4219:
4181:
3799:
3784:
5004:
Mitra, Ashim K.; Kwatra, Deep; Vadlapudi, Aswani Dutt, eds. (2014).
4222:
washes it away. Strategies to increase this residence time include
2290:{\displaystyle \tau =C_{AO}(R+1)\int {\frac {1}{(-r_{A})}}\,df_{A}}
1849:{\displaystyle \tau =N_{AO}\int {\frac {1}{(-r_{A})V_{R}}}\,df_{A}}
1584:
inside the reactor. The residence time distribution will be then a
431:, the distributions are assumed to be independent of time, that is
4260:
3336:
1499:
Although the equivalence between the residence time and the ratio
1069:
138:
4173:
4148:
to millions of years for deep aquifers with very low values for
3890:
3780:
3029:{\displaystyle E(t)={\frac {C(t)}{\int _{0}^{\infty }C(t)\,dt}}}
2428:{\displaystyle V_{R}=V_{R{\text{ initial}}}(1-\delta _{A}f_{A})}
5320:(4th ed.). New York, NY: Lippincott Williams and Wilkins.
4741:"Some physical properties of water transport in waste material"
1746:{\displaystyle \tau =C_{AO}\int {\frac {1}{(-r_{A})}}\,df_{A}}
4764:
Faybishenko, Boris; Witherspoon, Paul A.; Gale, John (2005).
1484:. In the field of chemical engineering this is also known as
4712:"Residence Time Distribution (RTD) in Stirred Tank Reactor"
2172:
1316:
508:
4144:. The time involved may vary from days for shallow gravel
1238:(where the reaction rate is proportional to the amount of
979:, is the first moment of the residence time distribution:
483:{\displaystyle \partial _{t}E=\partial _{t}I=0\;\forall t}
5297:
5267:
Transactions of
American Institute of Chemical Engineers
4607:
4605:
3832:
for wastewater or drinking water includes settling in a
847:{\displaystyle W(\tau ,t)=1-\int _{0}^{\tau }E(s,t)\,ds}
4653:(4th ed.). Upper Saddle River, NJ: Prentice Hall.
3913:, the residence time of an adsorbed atom is given by
871:
of all the particles inside the control volume at time
4357:
Nauman, E. Bruce (May 2008). "Residence Time Theory".
3410:{\displaystyle P_{\mathrm {R} }=\exp \left(-kt\right)}
1657:
of the distribution is earlier than the expected time
4899:
Drug discovery practices, processes, and perspectives
4083:
4056:
4023:
3999:
3922:
3899:
3630:
3472:
3449:
3429:
3366:
3205:
3136:
3104:
3077:
3050:
2956:
2924:
2904:
2884:
2864:
2704:
2583:
2452:
2364:
2306:
2207:
2120:
2069:
1970:
1877:
1771:
1678:
1601:
1505:
1314:
1250:
1184:
1126:
1080:
988:
888:
776:
753:
730:
710:
690:
670:
506:
437:
324:
298:
271:
251:
224:
201:
181:
34:
is the total time that the parcel has spent inside a
5248:
Pharmacokinetic analysis : a practical approach
58:
of the residence time in the set, which is known as
5337:
Industrial & Engineering
Chemistry Fundamentals
5299:
Handbook of
Industrial Mixing: Science and Practice
5250:. Lancaster, Penn.: Technomic Pub. pp. 15–60.
5208:
Principles of environmental engineering and science
4772:. Washington: American Geophysical Union. pp.
4549:
Principles of environmental engineering and science
3349:, the goal is to make components react with a high
2334:, a reactant. This is equal to the rate expression
1468:. When applied to liquids, it is also known as the
5077:Chouler, Jon; Di Lorenzo, Mirella (16 July 2015).
4768:Dynamics of fluids and transport in fractured rock
4765:
4218:in the mouth, the residence time is short because
4099:
4069:
4038:
4005:
3982:
3905:
3724:
3600:
3455:
3435:
3409:
3312:
3185:
3119:
3090:
3063:
3028:
2939:
2910:
2890:
2870:
2805:
2682:
2561:
2427:
2322:
2289:
2178:
2036:
1937:
1848:
1745:
1638:
1519:
1449:
1276:
1210:
1152:
1106:
1059:
956:
846:
759:
736:
716:
696:
676:
653:
482:
416:
304:
277:
257:
230:
207:
187:
4305:Estuarine water circulation § Residence time
4255:utilize the metabolic processes of anodophiles (
4201:. One way to measure the residence time is in a
3746:The RTD of chemical reactors can be obtained by
3341:An RTD curve for a reasonably well-mixed reactor
1956:example, there will be some finite delay before
167:The time that a particle of fluid has been in a
19:For the residence time of a random process, see
4843:Introduction to surface chemistry and catalysis
4359:Industrial & Engineering Chemistry Research
4759:
4757:
4547:Davis, Mackenzie L.; Masten, Susan J. (2004).
8:
5316:Rowland, Malcolm; Tozer, Thomas N. (2011).
4927:Thermodynamics and Kinetics of Drug Binding
4871:Vacuum technology calculations in chemistry
4864:
4862:
3186:{\displaystyle F(t)={\frac {C(t)}{C_{0}}}.}
1639:{\displaystyle E(\tau )=\delta (\tau -T)\,}
5072:
5070:
5068:
4438:
4436:
4434:
4432:
3811:due to its low permeability and high HRT.
3621:, and the output can be given in the form
1423:
1419:
615:
611:
473:
69:Residence time plays an important role in
5159:
5137:
5135:
5133:
5131:
5129:
5127:
5107:
5097:
4920:
4918:
4897:Li, Jie Jack; Corey, E. J., eds. (2013).
4695:
4651:Elements of chemical reaction engineering
4633:
4512:
4468:
4295:Anaerobic digestion § Residence time
4088:
4082:
4061:
4055:
4029:
4028:
4022:
3998:
3956:
3955:
3949:
3933:
3921:
3898:
3859:, and those that are more robust such as
3712:
3672:
3671:
3661:
3656:
3636:
3635:
3629:
3588:
3545:
3540:
3523:
3522:
3513:
3500:
3499:
3480:
3479:
3473:
3471:
3448:
3428:
3372:
3371:
3365:
3281:
3253:
3230:
3225:
3204:
3172:
3152:
3135:
3103:
3082:
3076:
3055:
3049:
3016:
2998:
2993:
2972:
2955:
2923:
2903:
2883:
2863:
2788:
2778:
2756:
2740:
2736:
2722:
2718:
2711:
2703:
2674:
2666:
2654:
2644:
2622:
2606:
2594:
2582:
2553:
2545:
2533:
2523:
2504:
2491:
2475:
2463:
2451:
2416:
2406:
2386:
2382:
2369:
2363:
2314:
2305:
2281:
2273:
2261:
2245:
2218:
2206:
2161:
2140:
2126:
2119:
2107:
2085:
2068:
2022:
2006:
2002:
1988:
1984:
1977:
1969:
1913:
1893:
1876:
1840:
1832:
1823:
1810:
1794:
1782:
1770:
1737:
1729:
1717:
1701:
1689:
1677:
1635:
1600:
1509:
1504:
1437:
1428:
1394:
1381:
1346:
1323:
1319:
1313:
1268:
1255:
1249:
1202:
1189:
1183:
1144:
1131:
1125:
1098:
1085:
1079:
1047:
1020:
1015:
993:
987:
947:
920:
915:
893:
887:
837:
813:
808:
775:
752:
729:
709:
689:
669:
631:
586:
573:
538:
515:
511:
505:
458:
442:
436:
401:
377:
372:
358:
334:
329:
323:
297:
270:
250:
245:. The frequency of occurrence of the age
223:
215:is quantified by means of the (internal)
200:
180:
54:of parcels is quantified in terms of the
5282:(10th ed.). McGraw-Hill Education.
4999:
4997:
4901:. Hoboken, N.J.: John Wiley & Sons.
4482:
4480:
4352:
4350:
4348:
4346:
4344:
4342:
4340:
2878:, is introduced into a vessel of volume
91:it plays a central role respectively in
4734:
4732:
4588:
4586:
4584:
4542:
4540:
4538:
4536:
4534:
4532:
4396:
4394:
4392:
4390:
4388:
4386:
4384:
4382:
4380:
4336:
1531:if the flow is steady and conservative
62:, or in terms of its average, known as
5369:Calculate the Hydraulic Retention Time
5148:Journal of the Electrochemical Society
5031:Environmental Science & Technology
4845:(2nd ed.). Hoboken, N.J.: Wiley.
4841:Somorjai, Gabor A.; Li, Yimin (2010).
3841:such as pharmaceuticals and hormones.
1277:{\displaystyle \tau _{a}>\tau _{t}}
1153:{\displaystyle \tau _{a}<\tau _{t}}
1107:{\displaystyle \tau _{a}>\tau _{t}}
5301:. Wiley Interscience. pp. 1–17.
4892:
4890:
7:
3098:to obtain the non-dimensional curve
1460:This ratio is commonly known as the
5008:. Jones & Bartlett Publishers.
4869:Hucknall, D.J.; Morris, A. (2003).
3463:of the component before and after:
2898:and an expected residence time of
1211:{\displaystyle \tau _{a}=\tau _{t}}
171:(e.g. a reservoir) is known as its
4423:10.1111/j.2153-3490.1973.tb01594.x
4325:Water cycle § Residence times
4267:that are separated by an internal
4030:
3957:
3685:
3682:
3679:
3676:
3673:
3662:
3643:
3640:
3637:
3546:
3527:
3524:
3507:
3504:
3501:
3481:
3373:
2999:
2821:Determining the RTD experimentally
1334:
1326:
1021:
921:
724:with an age greater or equal than
642:
634:
526:
518:
474:
455:
439:
378:
335:
14:
60:residence time distribution (RTD)
5206:Davis, M; Masten, Susan (2013).
4800:Science of the Total Environment
4320:RTD studies of plug flow reactor
4039:{\displaystyle E_{\mathrm {a} }}
2694:Continuous stirred-tank reactors
2300:In all of these equations :
863:Mean age and mean residence time
5189:United States Geological Survey
4820:10.1016/j.scitotenv.2017.11.011
4688:10.1016/j.electacta.2011.06.047
4626:10.1016/j.electacta.2015.07.019
3791:working against the subsurface
3265:
1866:continuous stirred-tank reactor
1860:Continuous stirred-tank reactor
121:continuous stirred-tank reactor
4280:bacteria which can reduce the
3709:
3703:
3697:
3691:
3585:
3579:
3296:
3290:
3275:
3269:
3250:
3239:
3215:
3209:
3164:
3158:
3146:
3140:
3114:
3108:
3013:
3007:
2984:
2978:
2966:
2960:
2934:
2928:
2794:
2765:
2660:
2631:
2628:
2612:
2539:
2510:
2497:
2481:
2422:
2393:
2267:
2251:
2239:
2227:
2079:
2073:
1887:
1881:
1816:
1800:
1723:
1707:
1632:
1620:
1611:
1605:
1420:
1236:first order chemical reactions
1044:
1032:
1005:
999:
944:
932:
905:
899:
834:
822:
792:
780:
744:is quantified by means of the
612:
398:
386:
355:
343:
285:is quantified by means of the
1:
5395:Chemical reaction engineering
5278:Montgomery, Carla W. (2013).
4952:Nature Reviews Drug Discovery
4748:Mine, Water & Environment
4443:Schwartz, Stephen E. (1979).
4243:size-exclusion chromatography
5227:Chemical Engineering Science
3487:
4470:10.3402/tellusa.v31i6.10471
2330:is the consumption rate of
1661:it indicates that there is
1543:, the relation is known as
287:residence time distribution
50:). The residence time of a
21:Residence time (statistics)
5446:
5430:Waste treatment technology
4493:Limnology and Oceanography
4129:
3874:
3818:
1653:and the variance is zero.
1172:and filtering down to the
18:
5405:Environmental engineering
5239:10.1016/j.ces.2003.10.013
5210:. New York: McGraw Hill.
4649:Fogler, H. Scott (2006).
4514:10.4319/lo.2002.47.5.1545
4070:{\displaystyle \tau _{0}}
2918:, the resulting curve of
2350:Variable volume reactions
1228:exponential distributions
1074:This drinking trough has
879:of the age distribution:
664:Distributions other than
4269:proton exchange membrane
4100:{\displaystyle 10^{-12}}
3847:is the last step in the
3825:Waste stabilization pond
3127:which goes from 0 to 1:
1482:hydraulic detention time
1478:hydraulic residence time
1470:hydraulic retention time
146:with incoming flow rate
5183:Robertson, D.M (2016).
4300:Baseflow residence time
3889:involving a release of
1541:supply chain management
1164:introduced high in the
123:, and the concept of a
117:plug flow reactor model
93:supply chain management
4203:preincubation-dilution
4150:hydraulic conductivity
4101:
4071:
4040:
4007:
3984:
3907:
3769:hydraulic conductivity
3726:
3602:
3457:
3437:
3411:
3342:
3314:
3187:
3121:
3092:
3065:
3030:
2941:
2912:
2892:
2872:
2807:
2684:
2563:
2429:
2324:
2323:{\displaystyle -r_{A}}
2291:
2180:
2038:
1939:
1850:
1747:
1640:
1580:, all spending a time
1521:
1451:
1278:
1212:
1154:
1114:
1108:
1061:
958:
848:
761:
738:
718:
698:
678:
655:
484:
418:
306:
279:
259:
232:
209:
189:
164:
109:axial dispersion model
56:frequency distribution
16:Term in fluid dynamics
5415:Hydraulic engineering
5385:Aerospace engineering
5280:Environmental Geology
4750:. 1999 IMWA Congress.
4247:continuous fermentors
4199:chemical dissociation
4102:
4072:
4041:
4008:
3985:
3908:
3771:of the soil or rock.
3727:
3619:completely segregated
3603:
3458:
3438:
3412:
3340:
3315:
3188:
3122:
3093:
3091:{\displaystyle C_{0}}
3066:
3064:{\displaystyle C_{0}}
3031:
2942:
2913:
2911:{\displaystyle \tau }
2893:
2873:
2808:
2685:
2564:
2430:
2325:
2292:
2181:
2039:
1940:
1851:
1748:
1641:
1522:
1452:
1279:
1213:
1155:
1109:
1073:
1062:
959:
849:
762:
739:
737:{\displaystyle \tau }
719:
699:
679:
656:
485:
419:
307:
291:exit age distribution
280:
260:
258:{\displaystyle \tau }
233:
210:
190:
188:{\displaystyle \tau }
153:, outgoing flow rate
142:
75:environmental science
5390:Biogeochemical cycle
5161:10.1149/2.0011703jes
4282:Coulombic efficiency
4081:
4054:
4021:
3997:
3920:
3897:
3628:
3470:
3447:
3427:
3364:
3355:first-order reaction
3353:. In a homogeneous,
3203:
3134:
3120:{\displaystyle F(t)}
3102:
3075:
3048:
2954:
2940:{\displaystyle C(t)}
2922:
2902:
2882:
2862:
2856:Dirac delta function
2702:
2581:
2450:
2362:
2304:
2205:
2067:
2054:laminar flow reactor
2048:Laminar flow reactor
1968:
1875:
1769:
1676:
1599:
1586:Dirac delta function
1503:
1312:
1248:
1182:
1162:radioactive material
1124:
1078:
986:
886:
774:
751:
728:
708:
688:
668:
504:
435:
322:
296:
269:
249:
222:
199:
179:
5349:10.1021/i160008a008
5099:10.3390/bios5030450
5043:2010EnST...44..518C
4964:10.1038/nrd.2015.18
4812:2018ScTEn.618..250E
4676:Electrochimica Acta
4614:Electrochimica Acta
4505:2002LimOc..47.1545M
4461:1979Tell...31..530S
4415:1973Tell...25...58B
4310:Lake retention time
4132:Lake retention time
3804:sulfidic pollutants
3789:hydrostatic tension
3666:
3550:
3235:
3003:
2058:molecular diffusion
1948:Where; the mean is
1520:{\displaystyle m/f}
1230:. Examples include
1025:
969:mean residence time
925:
818:
382:
339:
64:mean residence time
5154:(3): H3001–H3006.
4873:. Cambridge: RSC.
4142:hydrological cycle
4120:ultra-high vacuums
4097:
4067:
4036:
4003:
3980:
3903:
3887:exothermic process
3849:tertiary treatment
3722:
3652:
3598:
3536:
3453:
3433:
3407:
3343:
3310:
3221:
3183:
3117:
3088:
3061:
3026:
2989:
2937:
2908:
2888:
2868:
2803:
2680:
2573:Plug flow reactors
2559:
2425:
2320:
2287:
2176:
2171:
2148:
2034:
1935:
1846:
1743:
1636:
1572:will exit at time
1551:Simple flow models
1517:
1447:
1409:
1274:
1208:
1150:
1115:
1104:
1057:
1011:
954:
911:
844:
804:
757:
734:
714:
694:
674:
651:
601:
480:
414:
368:
325:
302:
275:
255:
228:
205:
185:
165:
160:and amount stored
73:and especially in
5051:10.1021/es9023833
4739:Noel, M. (1999).
4682:(21): 7312–7318.
4371:10.1021/ie071635a
4365:(10): 3752–3766.
4233:and dry powders.
4178:enzyme inhibitors
4172:A large class of
4164:different forms.
4112:vacuum technology
4048:activation energy
4006:{\displaystyle R}
3971:
3906:{\displaystyle T}
3830:Primary treatment
3793:pressure gradient
3737:maximum mixedness
3490:
3456:{\displaystyle a}
3436:{\displaystyle k}
3347:chemical reactors
3333:Chemical reactors
3308:
3178:
3024:
2891:{\displaystyle V}
2871:{\displaystyle M}
2850:Pulse experiments
2802:
2798:
2743:
2725:
2664:
2543:
2389:
2271:
2147:
2033:
2029:
2009:
1991:
1926:
1901:
1830:
1727:
1566:plug flow reactor
1560:Plug flow reactor
1445:
1413:
1397:
1384:
1364:
1341:
1232:radioactive decay
1170:nuclear bomb test
973:mean transit time
760:{\displaystyle W}
717:{\displaystyle t}
697:{\displaystyle I}
677:{\displaystyle E}
649:
605:
589:
576:
556:
533:
305:{\displaystyle E}
278:{\displaystyle t}
231:{\displaystyle I}
208:{\displaystyle t}
81:. Under the name
5437:
5420:Pharmacokinetics
5352:
5331:
5312:
5293:
5274:
5261:
5242:
5221:
5193:
5192:
5180:
5174:
5173:
5163:
5139:
5122:
5121:
5111:
5101:
5083:
5074:
5063:
5062:
5026:
5020:
5019:
5001:
4992:
4991:
4947:
4941:
4940:
4922:
4913:
4912:
4894:
4885:
4884:
4866:
4857:
4856:
4838:
4832:
4831:
4794:
4788:
4787:
4771:
4761:
4752:
4751:
4745:
4736:
4727:
4726:
4724:
4723:
4708:
4702:
4701:
4699:
4671:
4665:
4664:
4646:
4640:
4639:
4637:
4609:
4600:
4590:
4579:
4569:
4563:
4562:
4544:
4527:
4526:
4516:
4499:(5): 1545–1553.
4484:
4475:
4474:
4472:
4440:
4427:
4426:
4398:
4375:
4374:
4354:
4278:exoelectrogenous
4212:upper intestines
4106:
4104:
4103:
4098:
4096:
4095:
4076:
4074:
4073:
4068:
4066:
4065:
4045:
4043:
4042:
4037:
4035:
4034:
4033:
4012:
4010:
4009:
4004:
3989:
3987:
3986:
3981:
3976:
3972:
3970:
3962:
3961:
3960:
3950:
3938:
3937:
3912:
3910:
3909:
3904:
3821:Activated sludge
3759:Groundwater flow
3731:
3729:
3728:
3723:
3690:
3689:
3688:
3665:
3660:
3648:
3647:
3646:
3607:
3605:
3604:
3599:
3575:
3571:
3549:
3544:
3532:
3531:
3530:
3517:
3512:
3511:
3510:
3491:
3486:
3485:
3484:
3474:
3462:
3460:
3459:
3454:
3442:
3440:
3439:
3434:
3416:
3414:
3413:
3408:
3406:
3402:
3378:
3377:
3376:
3319:
3317:
3316:
3311:
3309:
3307:
3299:
3282:
3264:
3249:
3234:
3229:
3192:
3190:
3189:
3184:
3179:
3177:
3176:
3167:
3153:
3126:
3124:
3123:
3118:
3097:
3095:
3094:
3089:
3087:
3086:
3070:
3068:
3067:
3062:
3060:
3059:
3040:Step experiments
3035:
3033:
3032:
3027:
3025:
3023:
3002:
2997:
2987:
2973:
2946:
2944:
2943:
2938:
2917:
2915:
2914:
2909:
2897:
2895:
2894:
2889:
2877:
2875:
2874:
2869:
2812:
2810:
2809:
2804:
2800:
2799:
2797:
2793:
2792:
2783:
2782:
2764:
2763:
2747:
2746:
2745:
2744:
2741:
2728:
2727:
2726:
2723:
2712:
2689:
2687:
2686:
2681:
2679:
2678:
2665:
2663:
2659:
2658:
2649:
2648:
2627:
2626:
2607:
2602:
2601:
2568:
2566:
2565:
2560:
2558:
2557:
2544:
2542:
2538:
2537:
2528:
2527:
2509:
2508:
2496:
2495:
2476:
2471:
2470:
2434:
2432:
2431:
2426:
2421:
2420:
2411:
2410:
2392:
2391:
2390:
2387:
2374:
2373:
2342:and through any
2329:
2327:
2326:
2321:
2319:
2318:
2296:
2294:
2293:
2288:
2286:
2285:
2272:
2270:
2266:
2265:
2246:
2226:
2225:
2194:Recycle reactors
2185:
2183:
2182:
2177:
2175:
2174:
2165:
2149:
2146:
2145:
2144:
2131:
2130:
2121:
2111:
2043:
2041:
2040:
2035:
2031:
2030:
2028:
2027:
2026:
2013:
2012:
2011:
2010:
2007:
1994:
1993:
1992:
1989:
1978:
1944:
1942:
1941:
1936:
1931:
1927:
1922:
1914:
1902:
1894:
1855:
1853:
1852:
1847:
1845:
1844:
1831:
1829:
1828:
1827:
1815:
1814:
1795:
1790:
1789:
1752:
1750:
1749:
1744:
1742:
1741:
1728:
1726:
1722:
1721:
1702:
1697:
1696:
1645:
1643:
1642:
1637:
1526:
1524:
1523:
1518:
1513:
1456:
1454:
1453:
1448:
1446:
1438:
1433:
1432:
1418:
1414:
1411:
1410:
1407:
1399:
1398:
1395:
1386:
1385:
1382:
1373:
1365:
1363:
1355:
1347:
1342:
1340:
1332:
1324:
1283:
1281:
1280:
1275:
1273:
1272:
1260:
1259:
1217:
1215:
1214:
1209:
1207:
1206:
1194:
1193:
1159:
1157:
1156:
1151:
1149:
1148:
1136:
1135:
1113:
1111:
1110:
1105:
1103:
1102:
1090:
1089:
1066:
1064:
1063:
1058:
1024:
1019:
998:
997:
963:
961:
960:
955:
924:
919:
898:
897:
853:
851:
850:
845:
817:
812:
766:
764:
763:
758:
746:washout function
743:
741:
740:
735:
723:
721:
720:
715:
703:
701:
700:
695:
683:
681:
680:
675:
660:
658:
657:
652:
650:
648:
640:
632:
610:
606:
603:
602:
599:
591:
590:
587:
578:
577:
574:
565:
557:
555:
547:
539:
534:
532:
524:
516:
489:
487:
486:
481:
463:
462:
447:
446:
423:
421:
420:
415:
381:
376:
338:
333:
311:
309:
308:
303:
289:, also known as
284:
282:
281:
276:
264:
262:
261:
256:
237:
235:
234:
229:
217:age distribution
214:
212:
211:
206:
194:
192:
191:
186:
129:Peter Danckwerts
125:washout function
40:chemical reactor
5445:
5444:
5440:
5439:
5438:
5436:
5435:
5434:
5425:Queueing theory
5375:
5374:
5360:
5355:
5334:
5328:
5315:
5309:
5296:
5290:
5277:
5264:
5258:
5245:
5224:
5218:
5205:
5201:
5199:Further reading
5196:
5182:
5181:
5177:
5141:
5140:
5125:
5081:
5076:
5075:
5066:
5028:
5027:
5023:
5016:
5003:
5002:
4995:
4949:
4948:
4944:
4937:
4924:
4923:
4916:
4909:
4896:
4895:
4888:
4881:
4868:
4867:
4860:
4853:
4840:
4839:
4835:
4796:
4795:
4791:
4784:
4763:
4762:
4755:
4743:
4738:
4737:
4730:
4721:
4719:
4710:
4709:
4705:
4673:
4672:
4668:
4661:
4648:
4647:
4643:
4611:
4610:
4603:
4591:
4582:
4570:
4566:
4559:
4546:
4545:
4530:
4486:
4485:
4478:
4442:
4441:
4430:
4400:
4399:
4378:
4356:
4355:
4338:
4334:
4329:
4290:
4257:electronegative
4239:
4216:mucous membrane
4170:
4134:
4128:
4084:
4079:
4078:
4057:
4052:
4051:
4024:
4019:
4018:
3995:
3994:
3963:
3951:
3945:
3929:
3918:
3917:
3895:
3894:
3879:
3877:Surface science
3873:
3871:Surface science
3839:micropollutants
3827:
3817:
3815:Water treatment
3761:
3667:
3631:
3626:
3625:
3561:
3557:
3518:
3495:
3475:
3468:
3467:
3445:
3444:
3425:
3424:
3392:
3388:
3367:
3362:
3361:
3335:
3330:
3300:
3283:
3257:
3242:
3201:
3200:
3168:
3154:
3132:
3131:
3100:
3099:
3078:
3073:
3072:
3051:
3046:
3045:
3042:
2988:
2974:
2952:
2951:
2920:
2919:
2900:
2899:
2880:
2879:
2860:
2859:
2852:
2846:the RTD curve.
2823:
2784:
2774:
2752:
2748:
2732:
2714:
2713:
2700:
2699:
2696:
2670:
2650:
2640:
2618:
2611:
2590:
2579:
2578:
2575:
2549:
2529:
2519:
2500:
2487:
2480:
2459:
2448:
2447:
2444:
2412:
2402:
2378:
2365:
2360:
2359:
2352:
2310:
2302:
2301:
2277:
2257:
2250:
2214:
2203:
2202:
2196:
2170:
2169:
2150:
2136:
2132:
2122:
2116:
2115:
2096:
2086:
2065:
2064:
2050:
2018:
2014:
1998:
1980:
1979:
1966:
1965:
1915:
1909:
1873:
1872:
1862:
1836:
1819:
1806:
1799:
1778:
1767:
1766:
1759:
1733:
1713:
1706:
1685:
1674:
1673:
1597:
1596:
1562:
1553:
1537:queueing theory
1501:
1500:
1424:
1408:
1406:
1390:
1377:
1374:
1372:
1356:
1348:
1333:
1325:
1318:
1315:
1310:
1309:
1297:If the flow is
1295:
1264:
1251:
1246:
1245:
1198:
1185:
1180:
1179:
1140:
1127:
1122:
1121:
1094:
1081:
1076:
1075:
989:
984:
983:
889:
884:
883:
865:
860:
772:
771:
749:
748:
726:
725:
706:
705:
686:
685:
666:
665:
641:
633:
600:
598:
582:
569:
566:
564:
548:
540:
525:
517:
510:
507:
502:
501:
454:
438:
433:
432:
427:In the case of
320:
319:
294:
293:
267:
266:
247:
246:
220:
219:
197:
196:
177:
176:
159:
152:
137:
113:Irving Langmuir
105:
97:queueing theory
24:
17:
12:
11:
5:
5443:
5441:
5433:
5432:
5427:
5422:
5417:
5412:
5407:
5402:
5397:
5392:
5387:
5377:
5376:
5373:
5372:
5366:
5359:
5358:External links
5356:
5354:
5353:
5343:(4): 287–293.
5332:
5326:
5313:
5307:
5294:
5288:
5275:
5262:
5256:
5243:
5233:(3): 513–523.
5222:
5216:
5202:
5200:
5197:
5195:
5194:
5175:
5123:
5092:(3): 450–470.
5064:
5037:(1): 518–525.
5021:
5014:
4993:
4942:
4935:
4914:
4907:
4886:
4879:
4858:
4851:
4833:
4789:
4782:
4753:
4728:
4703:
4666:
4660:978-0130473943
4659:
4641:
4601:
4598:978-0471396093
4580:
4564:
4557:
4528:
4476:
4455:(6): 530–547.
4428:
4376:
4335:
4333:
4330:
4328:
4327:
4322:
4317:
4312:
4307:
4302:
4297:
4291:
4289:
4286:
4273:carbon dioxide
4238:
4235:
4169:
4166:
4127:
4124:
4094:
4091:
4087:
4064:
4060:
4032:
4027:
4002:
3991:
3990:
3979:
3975:
3969:
3966:
3959:
3954:
3948:
3944:
3941:
3936:
3932:
3928:
3925:
3902:
3872:
3869:
3816:
3813:
3760:
3757:
3741:perfect mixing
3733:
3732:
3721:
3718:
3715:
3711:
3708:
3705:
3702:
3699:
3696:
3693:
3687:
3684:
3681:
3678:
3675:
3670:
3664:
3659:
3655:
3651:
3645:
3642:
3639:
3634:
3609:
3608:
3597:
3594:
3591:
3587:
3584:
3581:
3578:
3574:
3570:
3567:
3564:
3560:
3556:
3553:
3548:
3543:
3539:
3535:
3529:
3526:
3521:
3516:
3509:
3506:
3503:
3498:
3494:
3489:
3483:
3478:
3452:
3432:
3418:
3417:
3405:
3401:
3398:
3395:
3391:
3387:
3384:
3381:
3375:
3370:
3334:
3331:
3329:
3326:
3321:
3320:
3306:
3303:
3298:
3295:
3292:
3289:
3286:
3280:
3277:
3274:
3271:
3268:
3263:
3260:
3256:
3252:
3248:
3245:
3241:
3238:
3233:
3228:
3224:
3220:
3217:
3214:
3211:
3208:
3194:
3193:
3182:
3175:
3171:
3166:
3163:
3160:
3157:
3151:
3148:
3145:
3142:
3139:
3116:
3113:
3110:
3107:
3085:
3081:
3058:
3054:
3041:
3038:
3037:
3036:
3022:
3019:
3015:
3012:
3009:
3006:
3001:
2996:
2992:
2986:
2983:
2980:
2977:
2971:
2968:
2965:
2962:
2959:
2936:
2933:
2930:
2927:
2907:
2887:
2867:
2851:
2848:
2822:
2819:
2814:
2813:
2796:
2791:
2787:
2781:
2777:
2773:
2770:
2767:
2762:
2759:
2755:
2751:
2739:
2735:
2731:
2721:
2717:
2710:
2707:
2695:
2692:
2691:
2690:
2677:
2673:
2669:
2662:
2657:
2653:
2647:
2643:
2639:
2636:
2633:
2630:
2625:
2621:
2617:
2614:
2610:
2605:
2600:
2597:
2593:
2589:
2586:
2574:
2571:
2570:
2569:
2556:
2552:
2548:
2541:
2536:
2532:
2526:
2522:
2518:
2515:
2512:
2507:
2503:
2499:
2494:
2490:
2486:
2483:
2479:
2474:
2469:
2466:
2462:
2458:
2455:
2443:
2440:
2436:
2435:
2424:
2419:
2415:
2409:
2405:
2401:
2398:
2395:
2385:
2381:
2377:
2372:
2368:
2351:
2348:
2317:
2313:
2309:
2298:
2297:
2284:
2280:
2276:
2269:
2264:
2260:
2256:
2253:
2249:
2244:
2241:
2238:
2235:
2232:
2229:
2224:
2221:
2217:
2213:
2210:
2195:
2192:
2187:
2186:
2173:
2168:
2164:
2160:
2157:
2154:
2151:
2143:
2139:
2135:
2129:
2125:
2118:
2117:
2114:
2110:
2106:
2103:
2100:
2097:
2095:
2092:
2091:
2089:
2084:
2081:
2078:
2075:
2072:
2060:, the RTD is
2049:
2046:
2045:
2044:
2025:
2021:
2017:
2005:
2001:
1997:
1987:
1983:
1976:
1973:
1946:
1945:
1934:
1930:
1925:
1921:
1918:
1912:
1908:
1905:
1900:
1897:
1892:
1889:
1886:
1883:
1880:
1861:
1858:
1857:
1856:
1843:
1839:
1835:
1826:
1822:
1818:
1813:
1809:
1805:
1802:
1798:
1793:
1788:
1785:
1781:
1777:
1774:
1758:
1755:
1754:
1753:
1740:
1736:
1732:
1725:
1720:
1716:
1712:
1709:
1705:
1700:
1695:
1692:
1688:
1684:
1681:
1663:stagnant fluid
1647:
1646:
1634:
1631:
1628:
1625:
1622:
1619:
1616:
1613:
1610:
1607:
1604:
1561:
1558:
1552:
1549:
1516:
1512:
1508:
1458:
1457:
1444:
1441:
1436:
1431:
1427:
1422:
1417:
1405:
1402:
1393:
1389:
1380:
1376:
1375:
1371:
1368:
1362:
1359:
1354:
1351:
1345:
1339:
1336:
1331:
1328:
1322:
1321:
1317:
1294:
1291:
1290:
1289:
1271:
1267:
1263:
1258:
1254:
1243:
1205:
1201:
1197:
1192:
1188:
1177:
1147:
1143:
1139:
1134:
1130:
1101:
1097:
1093:
1088:
1084:
1068:
1067:
1056:
1053:
1050:
1046:
1043:
1040:
1037:
1034:
1031:
1028:
1023:
1018:
1014:
1010:
1007:
1004:
1001:
996:
992:
965:
964:
953:
950:
946:
943:
940:
937:
934:
931:
928:
923:
918:
914:
910:
907:
904:
901:
896:
892:
864:
861:
859:
856:
855:
854:
843:
840:
836:
833:
830:
827:
824:
821:
816:
811:
807:
803:
800:
797:
794:
791:
788:
785:
782:
779:
756:
733:
713:
693:
673:
662:
661:
647:
644:
639:
636:
630:
627:
624:
621:
618:
614:
609:
597:
594:
585:
581:
572:
568:
567:
563:
560:
554:
551:
546:
543:
537:
531:
528:
523:
520:
514:
513:
509:
479:
476:
472:
469:
466:
461:
457:
453:
450:
445:
441:
425:
424:
413:
410:
407:
404:
400:
397:
394:
391:
388:
385:
380:
375:
371:
367:
364:
361:
357:
354:
351:
348:
345:
342:
337:
332:
328:
301:
274:
254:
243:residence time
227:
204:
184:
169:control volume
157:
150:
144:Control volume
136:
133:
104:
101:
36:control volume
28:residence time
15:
13:
10:
9:
6:
4:
3:
2:
5442:
5431:
5428:
5426:
5423:
5421:
5418:
5416:
5413:
5411:
5408:
5406:
5403:
5401:
5398:
5396:
5393:
5391:
5388:
5386:
5383:
5382:
5380:
5370:
5367:
5365:
5362:
5361:
5357:
5350:
5346:
5342:
5338:
5333:
5329:
5327:9780781750097
5323:
5319:
5314:
5310:
5308:0-471-26919-0
5304:
5300:
5295:
5291:
5289:9781259254598
5285:
5281:
5276:
5273:(2): 409–458.
5272:
5268:
5263:
5259:
5257:9781566764254
5253:
5249:
5244:
5240:
5236:
5232:
5228:
5223:
5219:
5217:9780077492199
5213:
5209:
5204:
5203:
5198:
5190:
5186:
5179:
5176:
5171:
5167:
5162:
5157:
5153:
5149:
5145:
5138:
5136:
5134:
5132:
5130:
5128:
5124:
5119:
5115:
5110:
5105:
5100:
5095:
5091:
5087:
5080:
5073:
5071:
5069:
5065:
5060:
5056:
5052:
5048:
5044:
5040:
5036:
5032:
5025:
5022:
5017:
5015:9781449674267
5011:
5007:
5006:Drug Delivery
5000:
4998:
4994:
4989:
4985:
4981:
4977:
4973:
4969:
4965:
4961:
4957:
4953:
4946:
4943:
4938:
4936:9783527335824
4932:
4928:
4921:
4919:
4915:
4910:
4908:9781118354469
4904:
4900:
4893:
4891:
4887:
4882:
4880:9781847552273
4876:
4872:
4865:
4863:
4859:
4854:
4852:9780470508237
4848:
4844:
4837:
4834:
4829:
4825:
4821:
4817:
4813:
4809:
4805:
4801:
4793:
4790:
4785:
4783:9780875904276
4779:
4775:
4770:
4769:
4760:
4758:
4754:
4749:
4742:
4735:
4733:
4729:
4717:
4713:
4707:
4704:
4698:
4693:
4689:
4685:
4681:
4677:
4670:
4667:
4662:
4656:
4652:
4645:
4642:
4636:
4631:
4627:
4623:
4619:
4615:
4608:
4606:
4602:
4599:
4595:
4589:
4587:
4585:
4581:
4578:
4577:0-13-047394-4
4574:
4568:
4565:
4560:
4558:9780072921861
4554:
4550:
4543:
4541:
4539:
4537:
4535:
4533:
4529:
4524:
4520:
4515:
4510:
4506:
4502:
4498:
4494:
4490:
4483:
4481:
4477:
4471:
4466:
4462:
4458:
4454:
4450:
4446:
4439:
4437:
4435:
4433:
4429:
4424:
4420:
4416:
4412:
4408:
4404:
4397:
4395:
4393:
4391:
4389:
4387:
4385:
4383:
4381:
4377:
4372:
4368:
4364:
4360:
4353:
4351:
4349:
4347:
4345:
4343:
4341:
4337:
4331:
4326:
4323:
4321:
4318:
4316:
4313:
4311:
4308:
4306:
4303:
4301:
4298:
4296:
4293:
4292:
4287:
4285:
4283:
4279:
4274:
4270:
4266:
4262:
4258:
4254:
4253:Biofuel cells
4250:
4248:
4244:
4236:
4234:
4232:
4228:
4225:
4221:
4217:
4213:
4207:
4204:
4200:
4196:
4192:
4188:
4183:
4180:that bind to
4179:
4175:
4167:
4165:
4161:
4158:
4153:
4151:
4147:
4143:
4139:
4133:
4126:Environmental
4125:
4123:
4121:
4117:
4113:
4108:
4092:
4089:
4085:
4062:
4058:
4049:
4025:
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4000:
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3973:
3967:
3964:
3952:
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3939:
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3892:
3888:
3885:. This is an
3884:
3878:
3870:
3868:
3866:
3862:
3858:
3854:
3850:
3846:
3842:
3840:
3835:
3834:sedimentation
3831:
3826:
3822:
3814:
3812:
3809:
3805:
3801:
3796:
3795:and gravity.
3794:
3790:
3786:
3782:
3778:
3774:
3770:
3766:
3758:
3756:
3754:
3753:time constant
3749:
3744:
3742:
3738:
3719:
3716:
3713:
3706:
3700:
3694:
3668:
3657:
3653:
3649:
3632:
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3562:
3558:
3554:
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3519:
3514:
3496:
3492:
3476:
3466:
3465:
3464:
3450:
3430:
3423:
3422:rate constant
3403:
3399:
3396:
3393:
3389:
3385:
3382:
3379:
3368:
3360:
3359:
3358:
3356:
3352:
3348:
3339:
3332:
3327:
3325:
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3301:
3293:
3287:
3284:
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3243:
3236:
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3218:
3212:
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3198:
3197:
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3130:
3129:
3128:
3111:
3105:
3083:
3079:
3056:
3052:
3039:
3020:
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3010:
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2994:
2990:
2981:
2975:
2969:
2963:
2957:
2950:
2949:
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2931:
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2828:
2820:
2818:
2789:
2785:
2779:
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2757:
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2608:
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2383:
2379:
2375:
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2356:
2349:
2347:
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2337:
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2307:
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2247:
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2233:
2230:
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2211:
2208:
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2112:
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2104:
2101:
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2093:
2087:
2082:
2076:
2070:
2063:
2062:
2061:
2059:
2055:
2047:
2023:
2019:
2015:
2003:
1999:
1995:
1985:
1981:
1974:
1971:
1964:
1963:
1962:
1959:
1953:
1951:
1932:
1928:
1923:
1919:
1916:
1910:
1906:
1903:
1898:
1895:
1890:
1884:
1878:
1871:
1870:
1869:
1867:
1859:
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1837:
1833:
1824:
1820:
1811:
1807:
1803:
1796:
1791:
1786:
1783:
1779:
1775:
1772:
1765:
1764:
1763:
1757:Batch reactor
1756:
1738:
1734:
1730:
1718:
1714:
1710:
1703:
1698:
1693:
1690:
1686:
1682:
1679:
1672:
1671:
1670:
1666:
1664:
1660:
1654:
1652:
1629:
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1497:
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1489:
1487:
1483:
1479:
1475:
1471:
1467:
1466:flushing time
1463:
1462:turnover time
1442:
1439:
1434:
1429:
1425:
1415:
1403:
1400:
1391:
1387:
1378:
1369:
1366:
1360:
1357:
1352:
1349:
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1337:
1329:
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1307:
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1293:Turnover time
1292:
1287:
1269:
1265:
1261:
1256:
1252:
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1233:
1229:
1225:
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1035:
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1016:
1012:
1008:
1002:
994:
990:
982:
981:
980:
978:
974:
970:
951:
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938:
935:
929:
926:
916:
912:
908:
902:
894:
890:
882:
881:
880:
878:
875:is the first
874:
870:
862:
857:
841:
838:
831:
828:
825:
819:
814:
809:
805:
801:
798:
795:
789:
786:
783:
777:
770:
769:
768:
754:
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731:
711:
691:
671:
645:
637:
628:
625:
622:
619:
616:
607:
595:
592:
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570:
561:
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521:
500:
499:
498:
496:
491:
477:
470:
467:
464:
459:
451:
448:
443:
430:
411:
408:
405:
402:
395:
392:
389:
383:
373:
369:
365:
362:
359:
352:
349:
346:
340:
330:
326:
318:
317:
316:
313:
299:
292:
288:
272:
252:
244:
239:
225:
218:
202:
182:
174:
170:
163:
156:
149:
145:
141:
135:Distributions
134:
132:
130:
126:
122:
118:
114:
110:
102:
100:
98:
94:
90:
86:
85:
80:
76:
72:
67:
65:
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53:
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5410:Geochemistry
5340:
5336:
5317:
5298:
5279:
5270:
5266:
5247:
5230:
5226:
5207:
5188:
5178:
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5089:
5085:
5034:
5030:
5024:
5005:
4958:(2): 87–95.
4955:
4951:
4945:
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4870:
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4803:
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4767:
4747:
4720:. Retrieved
4718:. 2020-06-22
4715:
4706:
4679:
4675:
4669:
4650:
4644:
4617:
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4567:
4548:
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4448:
4409:(1): 58–62.
4406:
4402:
4362:
4358:
4251:
4240:
4208:
4202:
4191:binding site
4171:
4168:Pharmacology
4162:
4154:
4135:
4109:
4015:gas constant
3992:
3880:
3845:Disinfection
3843:
3828:
3797:
3762:
3745:
3736:
3734:
3618:
3612:
3610:
3419:
3344:
3328:Applications
3322:
3195:
3043:
2853:
2839:
2835:
2832:hydrodynamic
2824:
2815:
2437:
2353:
2343:
2339:
2335:
2331:
2299:
2197:
2188:
2051:
1957:
1954:
1949:
1947:
1864:In an ideal
1863:
1760:
1667:
1658:
1655:
1650:
1649:The mean is
1648:
1589:
1581:
1577:
1573:
1569:
1564:In an ideal
1563:
1554:
1545:Little's Law
1532:
1528:
1498:
1490:
1485:
1481:
1477:
1473:
1469:
1465:
1461:
1459:
1303:conservative
1296:
1223:
1219:
1166:stratosphere
1116:
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972:
968:
966:
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868:
866:
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495:conservative
492:
426:
314:
290:
286:
242:
240:
216:
172:
166:
161:
154:
147:
124:
108:
106:
89:waiting time
88:
82:
79:pharmacology
68:
63:
59:
32:fluid parcel
27:
25:
4806:: 250–261.
4697:11336/74207
4635:11336/45663
4620:: 463–471.
4315:Micromixing
4237:Biochemical
4224:bioadhesive
4157:contaminate
3777:water table
3765:groundwater
3614:micromixing
2844:deconvolute
1588:delayed by
1286:water vapor
1174:troposphere
429:steady flow
5379:Categories
5371:(Lenntech)
5086:Biosensors
4722:2020-07-23
4332:References
4130:See also:
4116:outgassing
4107:seconds).
3883:adsorption
3875:See also:
3819:See also:
1533:on average
1529:on average
1486:space time
48:human body
4972:1474-1776
4195:half-life
4090:−
4059:τ
3943:
3931:τ
3924:τ
3808:Aquitards
3663:∞
3654:∫
3563:−
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3538:∫
3488:¯
3394:−
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3000:∞
2991:∫
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2776:δ
2772:−
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2730:−
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2642:δ
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2604:∫
2585:τ
2521:δ
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2404:δ
2400:−
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2243:∫
2209:τ
2153:τ
2138:τ
2102:≤
2099:τ
2077:τ
2016:−
2008: out
1996:−
1972:τ
1920:τ
1917:−
1907:
1885:τ
1804:−
1792:∫
1773:τ
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1680:τ
1627:−
1624:τ
1618:δ
1609:τ
1426:τ
1421:⟹
1335:∂
1327:∂
1266:τ
1253:τ
1200:τ
1187:τ
1142:τ
1129:τ
1096:τ
1083:τ
1052:τ
1036:τ
1027:τ
1022:∞
1013:∫
991:τ
952:τ
936:τ
927:τ
922:∞
913:∫
891:τ
815:τ
806:∫
802:−
784:τ
732:τ
646:τ
643:∂
635:∂
626:−
613:⟹
527:∂
519:∂
475:∀
456:∂
440:∂
406:τ
390:τ
379:∞
370:∫
363:τ
347:τ
336:∞
327:∫
253:τ
183:τ
84:lead time
71:chemistry
38:(e.g.: a
5170:99856827
5118:26193327
5059:19954225
4988:22955177
4980:26678621
4828:29128774
4523:11505988
4288:See also
4231:lozenges
4229:, gums,
4227:polymers
4187:kinetics
4146:aquifers
4138:glaciers
3861:protozoa
3853:bacteria
3773:Porosity
3262:′
3247:′
2724: in
1990: in
1240:reactant
869:mean age
858:Averages
119:and the
5400:Ecology
5109:4600167
5039:Bibcode
4808:Bibcode
4774:165–167
4716:CEMF.ir
4501:Bibcode
4457:Bibcode
4411:Bibcode
4265:cathode
4197:of the
4182:enzymes
4013:is the
3857:viruses
3783:versus
1494:uniform
103:History
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4403:Tellus
4263:and a
4220:saliva
4050:, and
4046:is an
3993:where
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3785:gravel
3420:for a
2827:tracer
2801:
2032:
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1299:steady
877:moment
604:
5166:S2CID
5082:(PDF)
4984:S2CID
4744:(PDF)
4519:S2CID
4261:anode
4174:drugs
3865:cysts
3351:yield
2838:or a
2836:pulse
2442:Batch
2052:In a
1168:by a
30:of a
5322:ISBN
5303:ISBN
5284:ISBN
5252:ISBN
5212:ISBN
5114:PMID
5055:PMID
5010:ISBN
4976:PMID
4968:ISSN
4931:ISBN
4903:ISBN
4875:ISBN
4847:ISBN
4824:PMID
4778:ISBN
4655:ISBN
4594:ISBN
4573:ISBN
4553:ISBN
4176:are
3891:heat
3863:and
3855:and
3823:and
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1539:and
1301:and
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1234:and
1226:are
1222:and
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967:The
867:The
684:and
95:and
77:and
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44:lake
42:, a
26:The
5345:doi
5235:doi
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4960:doi
4816:doi
4804:618
4692:hdl
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4630:hdl
4622:doi
4618:176
4509:doi
4465:doi
4419:doi
4367:doi
4241:In
4110:In
3940:exp
3748:CFD
3552:exp
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1904:exp
1480:or
1476:),
1474:HRT
1464:or
1396:out
971:or
588:out
173:age
158:out
111:by
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2489:r
2482:(
2478:1
2468:O
2465:A
2461:N
2457:=
2423:)
2418:A
2414:f
2408:A
2397:1
2394:(
2384:R
2380:V
2376:=
2371:R
2367:V
2344:k
2340:A
2336:A
2332:A
2316:A
2312:r
2283:A
2279:f
2275:d
2268:)
2263:A
2259:r
2252:(
2248:1
2240:)
2237:1
2234:+
2231:R
2228:(
2223:O
2220:A
2216:C
2212:=
2163:/
2159:T
2142:3
2134:2
2128:2
2124:T
2113:2
2109:/
2105:T
2094:0
2088:{
2083:=
2080:)
2074:(
2071:E
2024:A
2020:r
2004:A
2000:C
1986:A
1982:C
1975:=
1958:E
1950:T
1933:.
1929:)
1924:T
1911:(
1899:T
1896:1
1891:=
1888:)
1882:(
1879:E
1842:A
1838:f
1834:d
1825:R
1821:V
1817:)
1812:A
1808:r
1801:(
1797:1
1787:O
1784:A
1780:N
1776:=
1739:A
1735:f
1731:d
1724:)
1719:A
1715:r
1708:(
1704:1
1694:O
1691:A
1687:C
1683:=
1659:T
1651:T
1633:)
1630:T
1621:(
1615:=
1612:)
1606:(
1603:E
1590:T
1582:T
1578:T
1574:t
1570:t
1515:f
1511:/
1507:m
1472:(
1443:f
1440:m
1435:=
1430:t
1416:}
1404:f
1401:=
1392:f
1388:=
1379:f
1370:0
1367:=
1361:t
1358:d
1353:m
1350:d
1344:=
1338:t
1330:I
1270:t
1257:a
1224:I
1220:E
1204:t
1196:=
1191:a
1176:.
1146:t
1133:a
1100:t
1087:a
1055:.
1049:d
1045:)
1042:t
1039:,
1033:(
1030:E
1017:0
1009:=
1006:)
1003:t
1000:(
995:t
977:t
949:d
945:)
942:t
939:,
933:(
930:I
917:0
909:=
906:)
903:t
900:(
895:a
873:t
842:s
839:d
835:)
832:t
829:,
826:s
823:(
820:E
810:0
799:1
796:=
793:)
790:t
787:,
781:(
778:W
755:W
712:t
692:I
672:E
638:I
629:m
623:=
620:E
617:f
608:}
596:f
593:=
584:f
580:=
571:f
562:0
559:=
553:t
550:d
545:m
542:d
536:=
530:t
522:I
478:t
471:0
468:=
465:I
460:t
452:=
449:E
444:t
412:1
409:=
403:d
399:)
396:t
393:,
387:(
384:I
374:0
366:=
360:d
356:)
353:t
350:,
344:(
341:E
331:0
300:E
273:t
226:I
203:t
162:m
155:f
148:f
23:.
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