1082:
3349:
151:
4287:
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-
1972:
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:
670:
1466:
2365:
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:
1971:
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
1667:
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
4170:
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
4286:
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
4195:
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
3821:
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
1966:
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
3334:
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
2827:
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.
3847:
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
3761:
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
4174:
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
1566:
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
3798:. 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
1679:
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.
3617:
514:
1502:
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
2195:
1322:
4808:
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".
4220:
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
2200:
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.
2840:
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
2822:
1295:: 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
433:
2578:
1879:(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:
4163:. 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.
3741:
3329:
2699:
3999:
2053:
1954:
1772:
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.
1076:
973:
4216:
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.
2306:
1865:
3045:
2444:
1762:
665:{\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 }}}
3480:
2067:, 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
523:
499:
863:
3790:). 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
3426:
1331:
4623:
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".
2077:
1461:{\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}}}
4685:
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".
3762:
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
3202:
1655:
1293:
1169:
1123:
1227:
3817:
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.
1299:
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.
4282:(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
4055:
4151:, 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
2712:
4086:
4225:, 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
4116:
3848:
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
4129:. 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
2339:
5276:
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".
3107:
3080:
2927:
753:
274:
204:
4256:, 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
3136:
2956:
332:
1536:
4022:
3922:
3472:
3452:
2907:
2887:
776:
733:
713:
693:
321:
294:
247:
224:
4295:
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.
2460:
3638:
252:
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
2869:. 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,
1676:
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.
4200:
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
2591:
3930:
5374:
1579:(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
1978:
1963:
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.
1885:
3213:
4196:
times are desirable because they remain effective for longer and therefore can be used in lower doses. This residence time is determined by the
3750:, and this determines the achievable yield. A continuous stirred-tank reactor can be anywhere in the spectrum between completely segregated and
996:
2865:
This method required the introduction of a very small volume of concentrated tracer at the inlet of the reactor, such that it approaches the
896:
5155:"The Hydraulic Retention Time as a Key Parameter for the Performance of a Cyclically Fed Glycerol-Based Microbial Fuel Cell from Biodiesel"
2215:
1779:
2964:
2372:
1567:
residence time. Often design equations are used to minimize the reactor volume or volumetric flow rate required to operate a reactor.
3612:{\displaystyle {\overline {P_{\mathrm {R} }}}=a_{\mathrm {out} }/a_{\mathrm {in} }=\int _{0}^{\infty }\exp \left(-kt\right)E(t)\,dt.}
1316:, the mean residence time equals the ratio between the amount of fluid contained in the control volume and the flow rate through it:
1686:
4722:
4412:
Bolin, Bert; Rodhe, Henning (February 1973). "A note on the concepts of age distribution and transit time in natural reservoirs".
3778:. The amount of time that a pollutant spends traveling through a delineated subsurface space is related to the saturation and the
4166:
Ground water residence time applications are useful for determining the amount of time it will take for a pollutant to reach and
3862:
of wastewater or drinking water. The types of pathogens that occur in untreated water include those that are easily killed like
445:
5405:
3813:
operations. Waste rock is heterogeneous material with particles varying from boulders to clay-sized particles, and it contains
784:
3622:
If the reaction is more complicated, then the output is not uniquely determined by the RTD. It also depends on the degree of
3374:
5196:"Water Quality and the Effects of Changes in Phosphorus Loading, Red Cedar Lakes, Barron and Washburn Counties, Wisconsin"
3774:
Hydraulic residence time (HRT) is an important factor in the transport of environmental toxins or other chemicals through
5440:
3904:, and heating the surface increases the probability that an atom will escape within a given time. At a given temperature
4315:
5415:
4669:
4608:
5040:
Cheng, Ka Yu; Ho, Goen; Cord-Ruwisch, Ralf (January 2010). "Anodophilic
Biofilm Catalyzes Cathodic Oxygen Reduction".
2190:{\displaystyle E(\tau )={\begin{cases}0&\tau \leq T/2\\{\dfrac {T^{2}}{2\tau ^{3}}}&\tau >T/2.\end{cases}}}
5336:
5317:
5298:
5266:
5226:
5024:
4945:
4917:
4889:
4861:
4792:
4587:
4567:
4456:"Residence times in reservoirs under non-steady-state conditions: application to atmospheric SO2 and aerosol sulfate"
1504:
4330:
4270:
bacteria) to convert chemical energy from organic matter into electricity. A biofuel cell mechanism consists of an
2349:
is involved in. The rate expression is often related to the fractional conversion both through the consumption of
3844:
3144:
1876:
1609:
131:
3628:, the mixing between molecules that entered at different times. If there is no mixing, the system is said to be
5425:
5395:
2845:
conditions and it should be easily detectable. In general, the change in tracer concentration will either be a
2209:
Recycle reactors are PFRs with a recycle loop. Consequently, they behave like a hybrid between PFRs and CSTRs.
3335:
not the case because any noise in the concentration measurement will be amplified by numeric differentiation.
715:
can be usually traced back to them. For example, the fraction of particles leaving the control volume at time
5400:
4253:
3766:
of tracers becomes very small. In this way, tracer particles exactly follow the same path as the fluid does.
17:
1258:
1134:
1088:
4936:
Keserü, György; Swinney, David C.; Mannhold, Raimund; Kubinyi, Hugo; Folkers, Gerd, eds. (17 August 2015).
4147:
In environmental terms, the residence time definition is adapted to fit with ground water, the atmosphere,
4088:
is a prefactor that is correlated with the vibration times of the surface atoms (generally of the order of
3758:
2101:
4603:
Chemical
Engineering Kinetics and Reactor Design by Charles G. Hill, Jr. John Wiley & Sons Inc, 1977.
1192:
31:
4305:
4171:
the concentration of pollutants in a lake and how this may affect the local population and marine life.
3786:
is another significant contributing factor to the mobility of water through the ground (e.g. toward the
1313:
505:
1309:
1128:
The mean age and the mean transit time generally have different values, even in stationary conditions:
439:
4031:
3859:
5430:
4582:
Elements of
Chemical Reaction Engineering (4th Edition) by H. Scott Fogler, Prentice Hall PTR, 2005.
2958:
can be transformed into a dimensionless residence time distribution curve by the following relation:
118:
The concept of residence time originated in models of chemical reactors. The first such model was an
4125:, the residence time of gases on the surfaces of a vacuum chamber can determine the pressure due to
508:, then the exit age distribution and the internal age distribution can be related one to the other:
5435:
5236:
Leckner, Bo; Ghirelli, Frederico (2004). "Transport equation for local residence time of a fluid".
4279:
4209:
3835:
2817:{\displaystyle \tau ={\frac {C_{A{\text{ in}}}-C_{A{\text{ out}}}}{-r_{AF}(1-\delta _{A}f_{A})}}\ }
1238:
1246:
4310:
4257:
3809:
Groundwater flow is important parameter for consideration in the design of waste rock basins for
3055:
The concentration of tracer in a step experiment at the reactor inlet changes abruptly from 0 to
1576:
1551:
1180:
127:
103:
4784:
4777:
4222:
4160:
4064:
3779:
66:
5346:
Wolf, David; Resnick, William (November 1963). "Residence Time
Distribution in Real Systems".
4091:
3849:
126:
in 1908. This received little attention for 45 years; other models were developed such as the
5420:
4961:
Copeland, Robert A. (2015). "The drug–target residence time model: a 10-year retrospective".
4751:
428:{\displaystyle \int _{0}^{\infty }E(\tau ,t)\,d\tau =\int _{0}^{\infty }I(\tau ,t)\,d\tau =1}
85:
4498:
Monsen, Nancy E.; Cloern, James E.; Lucas, Lisa V.; Monismith, Stephen G. (September 2002).
3082:. The concentration of tracer at the outlet is measured and normalized to the concentration
2314:
142:
resurrected the axial dispersion model and formulated the modern concept of residence time.
5090:"Water Quality Monitoring in Developing Countries; Can Microbial Fuel Cells be the Answer?"
5049:
4818:
4511:
4467:
4421:
3892:
Atoms and molecules of gas or liquid can be trapped on a solid surface in a process called
3818:
3365:
3085:
3058:
2912:
2866:
2064:
1596:
887:
738:
259:
189:
138:(representing the response to a sudden change in the input) was introduced. Then, in 1953,
3878:. The disinfection chamber must have a long enough HRT to kill or deactivate all of them.
3746:
For given RTD, there is an upper limit on the amount of mixing that can occur, called the
3368:, the probability that an atom or molecule will react depends only on its residence time:
3112:
2932:
326:
Both distributions are assumed to be positive and to have unitary integral along the age:
8:
5089:
4500:"A comment on the use of flushing time, residence time, and age as transport time scales"
4335:
4320:
4263:
4167:
4142:
3871:
3863:
2068:
1513:
54:
5153:
Santos, João B. Costa; de Barros, Vanine V. Silva; Linares, José J. (30 November 2016).
5053:
4822:
4515:
4471:
4425:
186:. In general, each particle has a different age. The frequency of occurrence of the age
5176:
5119:
4994:
4529:
4433:
4292:
4152:
4007:
3907:
3897:
3855:
3814:
3799:
3457:
3437:
2892:
2872:
2573:{\displaystyle \tau =N_{AO}\int {\frac {1}{(-r_{A})V_{R}(1-\delta _{A}f_{A})}}\,df_{A}}
761:
718:
698:
678:
306:
279:
232:
209:
3736:{\displaystyle a_{\mathrm {out} }=\int _{0}^{\infty }a_{\mathrm {batch} }(t)E(t)\,dt.}
5332:
5313:
5294:
5262:
5222:
5124:
5065:
5020:
4986:
4978:
4941:
4913:
4885:
4857:
4834:
4788:
4665:
4604:
4583:
4563:
4267:
4204:(thereby preventing them from breaking any bonds formed), and is proportional to the
4130:
4122:
4058:
3840:
3803:
3361:
1242:
501:, which may allow to redefine the distributions as simple functions of the age only.
62:
5180:
4998:
4830:
4698:
4636:
4533:
1538:
does not hold if the flow is not stationary or it is not conservative, it does hold
5410:
5355:
5245:
5166:
5114:
5104:
5057:
4970:
4826:
4702:
4694:
4640:
4632:
4519:
4475:
4429:
4377:
4197:
4188:
3831:
3357:
1673:
1171:: examples include water in a lake with the inlet and outlet on opposite sides and
504:
If the flow is steady (but a generalization to non-steady flow is possible) and is
206:
in the set of all the particles that are located inside the control volume at time
139:
50:
3454:. Given a RTD, the average probability is equal to the ratio of the concentration
2694:{\displaystyle \tau =C_{AO}\int {\frac {1}{(-r_{A})(1-\delta _{A}f_{A})}}\,df_{A}}
5379:
5375:
Mean residence time (MRT): Understanding how long drug molecules stay in the body
4226:
3887:
1555:
1547:
1546:, and not necessarily at any instant. Under such conditions, which are common in
1172:
123:
107:
4480:
4455:
3994:{\displaystyle \tau =\tau _{0}\exp \left({\frac {E_{\mathrm {a} }}{RT}}\right),}
4283:
4241:
3875:
3751:
986:, that is the mean age of all the particles leaving the control volume at time
179:
154:
46:
5249:
4524:
4499:
2048:{\displaystyle \tau ={\frac {C_{A{\text{ in}}}-C_{A{\text{ out}}}}{-r_{A}}}\ }
5389:
4982:
4288:
3763:
3432:
2854:
1949:{\displaystyle E(\tau )={\frac {1}{T}}\exp \left({\frac {-\tau }{T}}\right).}
1081:
4562:. Boston, Mass.: McGraw-Hill Higher Education. pp. 150, 267, 480, 500.
2449:
Plugging this into the design equations results in the following equations:
778:, that is the complementary to one of the cumulative exit age distribution:
276:
in the set of all the particles that are leaving the control volume at time
5128:
5069:
4990:
4838:
4201:
4025:
3324:{\displaystyle F(t)=\int _{0}^{t}E(t')\,dt'\qquad E(t)={\frac {dF(t)}{dt}}}
2842:
1176:
110:, where the material that flows is usually discrete instead of continuous.
89:
42:
5195:
5329:
5171:
5154:
4325:
4234:
3867:
3787:
3775:
3624:
3348:
3207:
The step- and pulse-responses of a reactor are related by the following:
1296:
1184:
5359:
5257:
Lee, Peter I.D.; Amidon, Gordon L. (1996). "2. Time constant approach".
5109:
4974:
2836:
Residence time distributions are measured by introducing a non-reactive
1071:{\displaystyle \tau _{t}(t)=\int _{0}^{\infty }\tau E(\tau ,t)\,d\tau .}
4707:
4645:
4126:
3893:
2837:
968:{\displaystyle \tau _{a}(t)=\int _{0}^{\infty }\tau I(\tau ,t)\,d\tau }
58:
5061:
4381:
2853:. Other functions are possible, but they require more calculations to
2357:
changes through temperature changes that are dependent on conversion.
4205:
94:
81:
5015:
Mitra, Ashim K.; Kwatra, Deep; Vadlapudi, Aswani Dutt, eds. (2014).
4237:
4233:
washes it away. Strategies to increase this residence time include
3783:
2301:{\displaystyle \tau =C_{AO}(R+1)\int {\frac {1}{(-r_{A})}}\,df_{A}}
1860:{\displaystyle \tau =N_{AO}\int {\frac {1}{(-r_{A})V_{R}}}\,df_{A}}
1595:
inside the reactor. The residence time distribution will be then a
1250:
442:, the distributions are assumed to be independent of time, that is
1510:
Although the equivalence between the residence time and the ratio
4275:
4156:
4148:
150:
4159:
to millions of years for deep aquifers with very low values for
3040:{\displaystyle E(t)={\frac {C(t)}{\int _{0}^{\infty }C(t)\,dt}}}
2439:{\displaystyle V_{R}=V_{R{\text{ initial}}}(1-\delta _{A}f_{A})}
5331:(4th ed.). New York, NY: Lippincott Williams and Wilkins.
4752:"Some physical properties of water transport in waste material"
4230:
4192:
3810:
3795:
1757:{\displaystyle \tau =C_{AO}\int {\frac {1}{(-r_{A})}}\,df_{A}}
4775:
Faybishenko, Boris; Witherspoon, Paul A.; Gale, John (2005).
4271:
1495:. In the field of chemical engineering this is also known as
4935:
4723:"Residence Time Distribution (RTD) in Stirred Tank Reactor"
4184:
3901:
3791:
2183:
1327:
519:
4774:
4497:
4155:. The time involved may vary from days for shallow gravel
1249:(where the reaction rate is proportional to the amount of
990:, is the first moment of the residence time distribution:
494:{\displaystyle \partial _{t}E=\partial _{t}I=0\;\forall t}
5308:
5278:
Transactions of
American Institute of Chemical Engineers
4618:
4616:
3843:
for wastewater or drinking water includes settling in a
858:{\displaystyle W(\tau ,t)=1-\int _{0}^{\tau }E(s,t)\,ds}
4664:(4th ed.). Upper Saddle River, NJ: Prentice Hall.
3924:, the residence time of an adsorbed atom is given by
882:
of all the particles inside the control volume at time
5152:
4678:
4368:
Nauman, E. Bruce (May 2008). "Residence Time Theory".
3421:{\displaystyle P_{\mathrm {R} }=\exp \left(-kt\right)}
1668:
of the distribution is earlier than the expected time
4910:
Drug discovery practices, processes, and perspectives
4613:
4094:
4067:
4034:
4010:
3933:
3910:
3641:
3483:
3460:
3440:
3377:
3216:
3147:
3115:
3088:
3061:
2967:
2935:
2915:
2895:
2875:
2831:
2715:
2594:
2463:
2375:
2317:
2218:
2131:
2080:
1981:
1888:
1782:
1689:
1612:
1516:
1325:
1261:
1195:
1137:
1091:
999:
899:
787:
764:
741:
721:
701:
681:
517:
448:
335:
309:
282:
262:
235:
212:
192:
45:
is the total time that the parcel has spent inside a
5259:
Pharmacokinetic analysis : a practical approach
5014:
4807:
69:
of the residence time in the set, which is known as
5348:
Industrial & Engineering
Chemistry Fundamentals
5310:
Handbook of
Industrial Mixing: Science and Practice
5261:. Lancaster, Penn.: Technomic Pub. pp. 15–60.
5219:
Principles of environmental engineering and science
5039:
4783:. Washington: American Geophysical Union. pp.
4560:
Principles of environmental engineering and science
3360:, the goal is to make components react with a high
2704:
2345:, a reactant. This is equal to the rate expression
1479:. When applied to liquids, it is also known as the
873:
5088:Chouler, Jon; Di Lorenzo, Mirella (16 July 2015).
4779:Dynamics of fluids and transport in fractured rock
4776:
4229:in the mouth, the residence time is short because
4110:
4080:
4049:
4016:
3993:
3916:
3735:
3611:
3466:
3446:
3420:
3323:
3196:
3130:
3101:
3074:
3039:
2950:
2921:
2901:
2881:
2816:
2693:
2572:
2438:
2333:
2300:
2189:
2047:
1948:
1870:
1859:
1756:
1649:
1530:
1460:
1287:
1221:
1163:
1117:
1070:
967:
857:
770:
747:
727:
707:
687:
664:
493:
427:
315:
288:
268:
241:
218:
198:
5087:
4316:Estuarine water circulation § Residence time
5387:
4266:utilize the metabolic processes of anodophiles (
4212:. One way to measure the residence time is in a
3757:The RTD of chemical reactors can be obtained by
3352:An RTD curve for a reasonably well-mixed reactor
1967:example, there will be some finite delay before
178:The time that a particle of fluid has been in a
30:For the residence time of a random process, see
5235:
4854:Introduction to surface chemistry and catalysis
4370:Industrial & Engineering Chemistry Research
5275:
4879:
4770:
4768:
4558:Davis, Mackenzie L.; Masten, Susan J. (2004).
5326:
4954:
2360:
5345:
5327:Rowland, Malcolm; Tozer, Thomas N. (2011).
5216:
4938:Thermodynamics and Kinetics of Drug Binding
4882:Vacuum technology calculations in chemistry
4875:
4873:
4765:
4684:
4622:
4557:
3197:{\displaystyle F(t)={\frac {C(t)}{C_{0}}}.}
1650:{\displaystyle E(\tau )=\delta (\tau -T)\,}
5288:
5083:
5081:
5079:
4851:
4449:
4447:
4445:
4443:
4411:
3822:due to its low permeability and high HRT.
3632:, and the output can be given in the form
1434:
1430:
626:
622:
484:
80:Residence time plays an important role in
5256:
5193:
5170:
5148:
5146:
5144:
5142:
5140:
5138:
5118:
5108:
4931:
4929:
4908:Li, Jie Jack; Corey, E. J., eds. (2013).
4706:
4662:Elements of chemical reaction engineering
4644:
4523:
4479:
4306:Anaerobic digestion § Residence time
3870:, and those that are more robust such as
3723:
3599:
3264:
3027:
2677:
2556:
2284:
1843:
1740:
1646:
1058:
958:
848:
412:
369:
256:. The frequency of occurrence of the age
226:is quantified by means of the (internal)
65:of parcels is quantified in terms of the
5293:(10th ed.). McGraw-Hill Education.
5010:
5008:
4960:
4912:. Hoboken, N.J.: John Wiley & Sons.
4870:
4845:
4493:
4491:
4453:
4363:
4361:
4359:
4357:
4355:
4353:
4351:
3347:
2889:, is introduced into a vessel of volume
1080:
149:
102:it plays a central role respectively in
5076:
4907:
4745:
4743:
4599:
4597:
4595:
4553:
4551:
4549:
4547:
4545:
4543:
4440:
4407:
4405:
4403:
4401:
4399:
4397:
4395:
4393:
4391:
2058:
1542:if the flow is steady and conservative
73:, or in terms of its average, known as
14:
5388:
5380:Calculate the Hydraulic Retention Time
5307:
5159:Journal of the Electrochemical Society
5135:
5042:Environmental Science & Technology
4926:
4856:(2nd ed.). Hoboken, N.J.: Wiley.
4852:Somorjai, Gabor A.; Li, Yimin (2010).
4659:
4367:
3852:such as pharmaceuticals and hormones.
1288:{\displaystyle \tau _{a}>\tau _{t}}
1164:{\displaystyle \tau _{a}<\tau _{t}}
1118:{\displaystyle \tau _{a}>\tau _{t}}
5312:. Wiley Interscience. pp. 1–17.
5005:
4903:
4901:
4488:
4348:
2583:
1561:
4749:
4740:
4592:
4540:
4388:
3343:
3109:to obtain the non-dimensional curve
2860:
1570:
1471:This ratio is commonly known as the
5019:. Jones & Bartlett Publishers.
4880:Hucknall, D.J.; Morris, A. (2003).
3769:
3474:of the component before and after:
3050:
2909:and an expected residence time of
2204:
1222:{\displaystyle \tau _{a}=\tau _{t}}
182:(e.g. a reservoir) is known as its
24:
5209:
4898:
4434:10.1111/j.2153-3490.1973.tb01594.x
4336:Water cycle § Residence times
4278:that are separated by an internal
4041:
3968:
3881:
3825:
3696:
3693:
3690:
3687:
3684:
3673:
3654:
3651:
3648:
3557:
3538:
3535:
3518:
3515:
3512:
3492:
3384:
3010:
2832:Determining the RTD experimentally
1345:
1337:
1032:
932:
735:with an age greater or equal than
653:
645:
537:
529:
485:
466:
450:
389:
346:
25:
5452:
5368:
71:residence time distribution (RTD)
5217:Davis, M; Masten, Susan (2013).
4811:Science of the Total Environment
4331:RTD studies of plug flow reactor
4136:
4050:{\displaystyle E_{\mathrm {a} }}
2705:Continuous stirred-tank reactors
2311:In all of these equations :
1767:
1303:
874:Mean age and mean residence time
145:
5200:United States Geological Survey
5187:
5033:
4831:10.1016/j.scitotenv.2017.11.011
4801:
4715:
4699:10.1016/j.electacta.2011.06.047
4637:10.1016/j.electacta.2015.07.019
4178:
3802:working against the subsurface
3338:
3276:
1877:continuous stirred-tank reactor
1871:Continuous stirred-tank reactor
132:continuous stirred-tank reactor
4653:
4576:
4291:bacteria which can reduce the
4247:
3720:
3714:
3708:
3702:
3596:
3590:
3307:
3301:
3286:
3280:
3261:
3250:
3226:
3220:
3175:
3169:
3157:
3151:
3125:
3119:
3024:
3018:
2995:
2989:
2977:
2971:
2945:
2939:
2805:
2776:
2671:
2642:
2639:
2623:
2550:
2521:
2508:
2492:
2433:
2404:
2278:
2262:
2250:
2238:
2090:
2084:
1898:
1892:
1827:
1811:
1734:
1718:
1643:
1631:
1622:
1616:
1431:
1247:first order chemical reactions
1055:
1043:
1016:
1010:
955:
943:
916:
910:
845:
833:
803:
791:
755:is quantified by means of the
623:
409:
397:
366:
354:
296:is quantified by means of the
13:
1:
5406:Chemical reaction engineering
5289:Montgomery, Carla W. (2013).
4963:Nature Reviews Drug Discovery
4759:Mine, Water & Environment
4454:Schwartz, Stephen E. (1979).
4342:
4254:size-exclusion chromatography
5238:Chemical Engineering Science
3498:
7:
4481:10.3402/tellusa.v31i6.10471
4298:
2341:is the consumption rate of
1672:it indicates that there is
1554:, the relation is known as
868:
298:residence time distribution
61:). The residence time of a
32:Residence time (statistics)
10:
5457:
5441:Waste treatment technology
4504:Limnology and Oceanography
4140:
3885:
3829:
1664:and the variance is zero.
1183:and filtering down to the
113:
29:
5416:Environmental engineering
5250:10.1016/j.ces.2003.10.013
5221:. New York: McGraw Hill.
4660:Fogler, H. Scott (2006).
4525:10.4319/lo.2002.47.5.1545
4081:{\displaystyle \tau _{0}}
2929:, the resulting curve of
2361:Variable volume reactions
1239:exponential distributions
1085:This drinking trough has
890:of the age distribution:
675:Distributions other than
4280:proton exchange membrane
4111:{\displaystyle 10^{-12}}
3858:is the last step in the
3836:Waste stabilization pond
3138:which goes from 0 to 1:
2452:
1493:hydraulic detention time
1489:hydraulic residence time
1481:hydraulic retention time
157:with incoming flow rate
5194:Robertson, D.M (2016).
4311:Baseflow residence time
3900:involving a release of
1552:supply chain management
1175:introduced high in the
134:, and the concept of a
128:plug flow reactor model
104:supply chain management
4214:preincubation-dilution
4161:hydraulic conductivity
4112:
4082:
4051:
4018:
3995:
3918:
3780:hydraulic conductivity
3737:
3613:
3468:
3448:
3422:
3353:
3325:
3198:
3132:
3103:
3076:
3041:
2952:
2923:
2903:
2883:
2818:
2695:
2574:
2440:
2335:
2334:{\displaystyle -r_{A}}
2302:
2191:
2049:
1950:
1861:
1758:
1651:
1591:, all spending a time
1532:
1462:
1289:
1223:
1165:
1125:
1119:
1072:
969:
859:
772:
749:
729:
709:
689:
666:
495:
429:
317:
290:
270:
243:
220:
200:
175:
120:axial dispersion model
67:frequency distribution
27:Term in fluid dynamics
5426:Hydraulic engineering
5396:Aerospace engineering
5291:Environmental Geology
4761:. 1999 IMWA Congress.
4258:continuous fermentors
4210:chemical dissociation
4113:
4083:
4052:
4019:
3996:
3919:
3782:of the soil or rock.
3738:
3630:completely segregated
3614:
3469:
3449:
3423:
3351:
3326:
3199:
3133:
3104:
3102:{\displaystyle C_{0}}
3077:
3075:{\displaystyle C_{0}}
3042:
2953:
2924:
2922:{\displaystyle \tau }
2904:
2884:
2819:
2696:
2575:
2441:
2336:
2303:
2192:
2050:
1951:
1862:
1759:
1652:
1533:
1463:
1290:
1224:
1166:
1120:
1084:
1073:
970:
860:
773:
750:
748:{\displaystyle \tau }
730:
710:
690:
667:
496:
430:
318:
302:exit age distribution
291:
271:
269:{\displaystyle \tau }
244:
221:
201:
199:{\displaystyle \tau }
164:, outgoing flow rate
153:
86:environmental science
5401:Biogeochemical cycle
5172:10.1149/2.0011703jes
4293:Coulombic efficiency
4092:
4065:
4032:
4008:
3931:
3908:
3639:
3481:
3458:
3438:
3375:
3366:first-order reaction
3364:. In a homogeneous,
3214:
3145:
3131:{\displaystyle F(t)}
3113:
3086:
3059:
2965:
2951:{\displaystyle C(t)}
2933:
2913:
2893:
2873:
2867:Dirac delta function
2713:
2592:
2461:
2373:
2315:
2216:
2078:
2065:laminar flow reactor
2059:Laminar flow reactor
1979:
1886:
1780:
1687:
1610:
1597:Dirac delta function
1514:
1323:
1259:
1193:
1173:radioactive material
1135:
1089:
997:
897:
785:
762:
739:
719:
699:
679:
515:
446:
333:
307:
280:
260:
233:
210:
190:
5360:10.1021/i160008a008
5110:10.3390/bios5030450
5054:2010EnST...44..518C
4975:10.1038/nrd.2015.18
4823:2018ScTEn.618..250E
4687:Electrochimica Acta
4625:Electrochimica Acta
4516:2002LimOc..47.1545M
4472:1979Tell...31..530S
4426:1973Tell...25...58B
4321:Lake retention time
4143:Lake retention time
3815:sulfidic pollutants
3800:hydrostatic tension
3677:
3561:
3246:
3014:
2069:molecular diffusion
1959:Where; the mean is
1531:{\displaystyle m/f}
1241:. Examples include
1036:
980:mean residence time
936:
829:
393:
350:
75:mean residence time
5165:(3): H3001–H3006.
4884:. Cambridge: RSC.
4153:hydrological cycle
4131:ultra-high vacuums
4108:
4078:
4047:
4014:
3991:
3914:
3898:exothermic process
3860:tertiary treatment
3733:
3663:
3609:
3547:
3464:
3444:
3418:
3354:
3321:
3232:
3194:
3128:
3099:
3072:
3037:
3000:
2948:
2919:
2899:
2879:
2814:
2691:
2584:Plug flow reactors
2570:
2436:
2331:
2298:
2187:
2182:
2159:
2045:
1946:
1857:
1754:
1647:
1583:will exit at time
1562:Simple flow models
1528:
1458:
1420:
1285:
1219:
1161:
1126:
1115:
1068:
1022:
965:
922:
855:
815:
768:
745:
725:
705:
685:
662:
612:
491:
425:
379:
336:
313:
286:
266:
239:
216:
196:
176:
171:and amount stored
84:and especially in
5062:10.1021/es9023833
4750:Noel, M. (1999).
4693:(21): 7312–7318.
4382:10.1021/ie071635a
4376:(10): 3752–3766.
4244:and dry powders.
4189:enzyme inhibitors
4183:A large class of
4175:different forms.
4123:vacuum technology
4059:activation energy
4017:{\displaystyle R}
3982:
3917:{\displaystyle T}
3841:Primary treatment
3804:pressure gradient
3748:maximum mixedness
3501:
3467:{\displaystyle a}
3447:{\displaystyle k}
3358:chemical reactors
3344:Chemical reactors
3319:
3189:
3035:
2902:{\displaystyle V}
2882:{\displaystyle M}
2861:Pulse experiments
2813:
2809:
2754:
2736:
2675:
2554:
2400:
2282:
2158:
2044:
2040:
2020:
2002:
1937:
1912:
1841:
1738:
1577:plug flow reactor
1571:Plug flow reactor
1456:
1424:
1408:
1395:
1375:
1352:
1243:radioactive decay
1181:nuclear bomb test
984:mean transit time
771:{\displaystyle W}
728:{\displaystyle t}
708:{\displaystyle I}
688:{\displaystyle E}
660:
616:
600:
587:
567:
544:
316:{\displaystyle E}
289:{\displaystyle t}
242:{\displaystyle I}
219:{\displaystyle t}
92:. Under the name
16:(Redirected from
5448:
5431:Pharmacokinetics
5363:
5342:
5323:
5304:
5285:
5272:
5253:
5232:
5204:
5203:
5191:
5185:
5184:
5174:
5150:
5133:
5132:
5122:
5112:
5094:
5085:
5074:
5073:
5037:
5031:
5030:
5012:
5003:
5002:
4958:
4952:
4951:
4933:
4924:
4923:
4905:
4896:
4895:
4877:
4868:
4867:
4849:
4843:
4842:
4805:
4799:
4798:
4782:
4772:
4763:
4762:
4756:
4747:
4738:
4737:
4735:
4734:
4719:
4713:
4712:
4710:
4682:
4676:
4675:
4657:
4651:
4650:
4648:
4620:
4611:
4601:
4590:
4580:
4574:
4573:
4555:
4538:
4537:
4527:
4510:(5): 1545–1553.
4495:
4486:
4485:
4483:
4451:
4438:
4437:
4409:
4386:
4385:
4365:
4289:exoelectrogenous
4223:upper intestines
4117:
4115:
4114:
4109:
4107:
4106:
4087:
4085:
4084:
4079:
4077:
4076:
4056:
4054:
4053:
4048:
4046:
4045:
4044:
4023:
4021:
4020:
4015:
4000:
3998:
3997:
3992:
3987:
3983:
3981:
3973:
3972:
3971:
3961:
3949:
3948:
3923:
3921:
3920:
3915:
3832:Activated sludge
3770:Groundwater flow
3742:
3740:
3739:
3734:
3701:
3700:
3699:
3676:
3671:
3659:
3658:
3657:
3618:
3616:
3615:
3610:
3586:
3582:
3560:
3555:
3543:
3542:
3541:
3528:
3523:
3522:
3521:
3502:
3497:
3496:
3495:
3485:
3473:
3471:
3470:
3465:
3453:
3451:
3450:
3445:
3427:
3425:
3424:
3419:
3417:
3413:
3389:
3388:
3387:
3330:
3328:
3327:
3322:
3320:
3318:
3310:
3293:
3275:
3260:
3245:
3240:
3203:
3201:
3200:
3195:
3190:
3188:
3187:
3178:
3164:
3137:
3135:
3134:
3129:
3108:
3106:
3105:
3100:
3098:
3097:
3081:
3079:
3078:
3073:
3071:
3070:
3051:Step experiments
3046:
3044:
3043:
3038:
3036:
3034:
3013:
3008:
2998:
2984:
2957:
2955:
2954:
2949:
2928:
2926:
2925:
2920:
2908:
2906:
2905:
2900:
2888:
2886:
2885:
2880:
2823:
2821:
2820:
2815:
2811:
2810:
2808:
2804:
2803:
2794:
2793:
2775:
2774:
2758:
2757:
2756:
2755:
2752:
2739:
2738:
2737:
2734:
2723:
2700:
2698:
2697:
2692:
2690:
2689:
2676:
2674:
2670:
2669:
2660:
2659:
2638:
2637:
2618:
2613:
2612:
2579:
2577:
2576:
2571:
2569:
2568:
2555:
2553:
2549:
2548:
2539:
2538:
2520:
2519:
2507:
2506:
2487:
2482:
2481:
2445:
2443:
2442:
2437:
2432:
2431:
2422:
2421:
2403:
2402:
2401:
2398:
2385:
2384:
2353:and through any
2340:
2338:
2337:
2332:
2330:
2329:
2307:
2305:
2304:
2299:
2297:
2296:
2283:
2281:
2277:
2276:
2257:
2237:
2236:
2205:Recycle reactors
2196:
2194:
2193:
2188:
2186:
2185:
2176:
2160:
2157:
2156:
2155:
2142:
2141:
2132:
2122:
2054:
2052:
2051:
2046:
2042:
2041:
2039:
2038:
2037:
2024:
2023:
2022:
2021:
2018:
2005:
2004:
2003:
2000:
1989:
1955:
1953:
1952:
1947:
1942:
1938:
1933:
1925:
1913:
1905:
1866:
1864:
1863:
1858:
1856:
1855:
1842:
1840:
1839:
1838:
1826:
1825:
1806:
1801:
1800:
1763:
1761:
1760:
1755:
1753:
1752:
1739:
1737:
1733:
1732:
1713:
1708:
1707:
1656:
1654:
1653:
1648:
1537:
1535:
1534:
1529:
1524:
1467:
1465:
1464:
1459:
1457:
1449:
1444:
1443:
1429:
1425:
1422:
1421:
1418:
1410:
1409:
1406:
1397:
1396:
1393:
1384:
1376:
1374:
1366:
1358:
1353:
1351:
1343:
1335:
1294:
1292:
1291:
1286:
1284:
1283:
1271:
1270:
1228:
1226:
1225:
1220:
1218:
1217:
1205:
1204:
1170:
1168:
1167:
1162:
1160:
1159:
1147:
1146:
1124:
1122:
1121:
1116:
1114:
1113:
1101:
1100:
1077:
1075:
1074:
1069:
1035:
1030:
1009:
1008:
974:
972:
971:
966:
935:
930:
909:
908:
864:
862:
861:
856:
828:
823:
777:
775:
774:
769:
757:washout function
754:
752:
751:
746:
734:
732:
731:
726:
714:
712:
711:
706:
694:
692:
691:
686:
671:
669:
668:
663:
661:
659:
651:
643:
621:
617:
614:
613:
610:
602:
601:
598:
589:
588:
585:
576:
568:
566:
558:
550:
545:
543:
535:
527:
500:
498:
497:
492:
474:
473:
458:
457:
434:
432:
431:
426:
392:
387:
349:
344:
322:
320:
319:
314:
300:, also known as
295:
293:
292:
287:
275:
273:
272:
267:
248:
246:
245:
240:
228:age distribution
225:
223:
222:
217:
205:
203:
202:
197:
140:Peter Danckwerts
136:washout function
51:chemical reactor
21:
5456:
5455:
5451:
5450:
5449:
5447:
5446:
5445:
5436:Queueing theory
5386:
5385:
5371:
5366:
5339:
5320:
5301:
5269:
5229:
5212:
5210:Further reading
5207:
5192:
5188:
5151:
5136:
5092:
5086:
5077:
5038:
5034:
5027:
5013:
5006:
4959:
4955:
4948:
4934:
4927:
4920:
4906:
4899:
4892:
4878:
4871:
4864:
4850:
4846:
4806:
4802:
4795:
4773:
4766:
4754:
4748:
4741:
4732:
4730:
4721:
4720:
4716:
4683:
4679:
4672:
4658:
4654:
4621:
4614:
4602:
4593:
4581:
4577:
4570:
4556:
4541:
4496:
4489:
4452:
4441:
4410:
4389:
4366:
4349:
4345:
4340:
4301:
4268:electronegative
4250:
4227:mucous membrane
4181:
4145:
4139:
4099:
4095:
4093:
4090:
4089:
4072:
4068:
4066:
4063:
4062:
4040:
4039:
4035:
4033:
4030:
4029:
4009:
4006:
4005:
3974:
3967:
3966:
3962:
3960:
3956:
3944:
3940:
3932:
3929:
3928:
3909:
3906:
3905:
3890:
3888:Surface science
3884:
3882:Surface science
3850:micropollutants
3838:
3828:
3826:Water treatment
3772:
3683:
3682:
3678:
3672:
3667:
3647:
3646:
3642:
3640:
3637:
3636:
3572:
3568:
3556:
3551:
3534:
3533:
3529:
3524:
3511:
3510:
3506:
3491:
3490:
3486:
3484:
3482:
3479:
3478:
3459:
3456:
3455:
3439:
3436:
3435:
3403:
3399:
3383:
3382:
3378:
3376:
3373:
3372:
3346:
3341:
3311:
3294:
3292:
3268:
3253:
3241:
3236:
3215:
3212:
3211:
3183:
3179:
3165:
3163:
3146:
3143:
3142:
3114:
3111:
3110:
3093:
3089:
3087:
3084:
3083:
3066:
3062:
3060:
3057:
3056:
3053:
3009:
3004:
2999:
2985:
2983:
2966:
2963:
2962:
2934:
2931:
2930:
2914:
2911:
2910:
2894:
2891:
2890:
2874:
2871:
2870:
2863:
2857:the RTD curve.
2834:
2799:
2795:
2789:
2785:
2767:
2763:
2759:
2751:
2747:
2743:
2733:
2729:
2725:
2724:
2722:
2714:
2711:
2710:
2707:
2685:
2681:
2665:
2661:
2655:
2651:
2633:
2629:
2622:
2617:
2605:
2601:
2593:
2590:
2589:
2586:
2564:
2560:
2544:
2540:
2534:
2530:
2515:
2511:
2502:
2498:
2491:
2486:
2474:
2470:
2462:
2459:
2458:
2455:
2427:
2423:
2417:
2413:
2397:
2393:
2389:
2380:
2376:
2374:
2371:
2370:
2363:
2325:
2321:
2316:
2313:
2312:
2292:
2288:
2272:
2268:
2261:
2256:
2229:
2225:
2217:
2214:
2213:
2207:
2181:
2180:
2172:
2161:
2151:
2147:
2143:
2137:
2133:
2130:
2127:
2126:
2118:
2107:
2097:
2096:
2079:
2076:
2075:
2061:
2033:
2029:
2025:
2017:
2013:
2009:
1999:
1995:
1991:
1990:
1988:
1980:
1977:
1976:
1926:
1924:
1920:
1904:
1887:
1884:
1883:
1873:
1851:
1847:
1834:
1830:
1821:
1817:
1810:
1805:
1793:
1789:
1781:
1778:
1777:
1770:
1748:
1744:
1728:
1724:
1717:
1712:
1700:
1696:
1688:
1685:
1684:
1611:
1608:
1607:
1573:
1564:
1548:queueing theory
1520:
1515:
1512:
1511:
1448:
1439:
1435:
1419:
1417:
1405:
1401:
1392:
1388:
1385:
1383:
1367:
1359:
1357:
1344:
1336:
1334:
1330:
1329:
1326:
1324:
1321:
1320:
1308:If the flow is
1306:
1279:
1275:
1266:
1262:
1260:
1257:
1256:
1213:
1209:
1200:
1196:
1194:
1191:
1190:
1155:
1151:
1142:
1138:
1136:
1133:
1132:
1109:
1105:
1096:
1092:
1090:
1087:
1086:
1031:
1026:
1004:
1000:
998:
995:
994:
931:
926:
904:
900:
898:
895:
894:
876:
871:
824:
819:
786:
783:
782:
763:
760:
759:
740:
737:
736:
720:
717:
716:
700:
697:
696:
680:
677:
676:
652:
644:
642:
611:
609:
597:
593:
584:
580:
577:
575:
559:
551:
549:
536:
528:
526:
522:
521:
518:
516:
513:
512:
469:
465:
453:
449:
447:
444:
443:
438:In the case of
388:
383:
345:
340:
334:
331:
330:
308:
305:
304:
281:
278:
277:
261:
258:
257:
234:
231:
230:
211:
208:
207:
191:
188:
187:
170:
163:
148:
124:Irving Langmuir
116:
108:queueing theory
35:
28:
23:
22:
15:
12:
11:
5:
5454:
5444:
5443:
5438:
5433:
5428:
5423:
5418:
5413:
5408:
5403:
5398:
5384:
5383:
5377:
5370:
5369:External links
5367:
5365:
5364:
5354:(4): 287–293.
5343:
5337:
5324:
5318:
5305:
5299:
5286:
5273:
5267:
5254:
5244:(3): 513–523.
5233:
5227:
5213:
5211:
5208:
5206:
5205:
5186:
5134:
5103:(3): 450–470.
5075:
5048:(1): 518–525.
5032:
5025:
5004:
4953:
4946:
4925:
4918:
4897:
4890:
4869:
4862:
4844:
4800:
4793:
4764:
4739:
4714:
4677:
4671:978-0130473943
4670:
4652:
4612:
4609:978-0471396093
4591:
4575:
4568:
4539:
4487:
4466:(6): 530–547.
4439:
4387:
4346:
4344:
4341:
4339:
4338:
4333:
4328:
4323:
4318:
4313:
4308:
4302:
4300:
4297:
4284:carbon dioxide
4249:
4246:
4180:
4177:
4138:
4135:
4105:
4102:
4098:
4075:
4071:
4043:
4038:
4013:
4002:
4001:
3990:
3986:
3980:
3977:
3970:
3965:
3959:
3955:
3952:
3947:
3943:
3939:
3936:
3913:
3883:
3880:
3827:
3824:
3771:
3768:
3752:perfect mixing
3744:
3743:
3732:
3729:
3726:
3722:
3719:
3716:
3713:
3710:
3707:
3704:
3698:
3695:
3692:
3689:
3686:
3681:
3675:
3670:
3666:
3662:
3656:
3653:
3650:
3645:
3620:
3619:
3608:
3605:
3602:
3598:
3595:
3592:
3589:
3585:
3581:
3578:
3575:
3571:
3567:
3564:
3559:
3554:
3550:
3546:
3540:
3537:
3532:
3527:
3520:
3517:
3514:
3509:
3505:
3500:
3494:
3489:
3463:
3443:
3429:
3428:
3416:
3412:
3409:
3406:
3402:
3398:
3395:
3392:
3386:
3381:
3345:
3342:
3340:
3337:
3332:
3331:
3317:
3314:
3309:
3306:
3303:
3300:
3297:
3291:
3288:
3285:
3282:
3279:
3274:
3271:
3267:
3263:
3259:
3256:
3252:
3249:
3244:
3239:
3235:
3231:
3228:
3225:
3222:
3219:
3205:
3204:
3193:
3186:
3182:
3177:
3174:
3171:
3168:
3162:
3159:
3156:
3153:
3150:
3127:
3124:
3121:
3118:
3096:
3092:
3069:
3065:
3052:
3049:
3048:
3047:
3033:
3030:
3026:
3023:
3020:
3017:
3012:
3007:
3003:
2997:
2994:
2991:
2988:
2982:
2979:
2976:
2973:
2970:
2947:
2944:
2941:
2938:
2918:
2898:
2878:
2862:
2859:
2833:
2830:
2825:
2824:
2807:
2802:
2798:
2792:
2788:
2784:
2781:
2778:
2773:
2770:
2766:
2762:
2750:
2746:
2742:
2732:
2728:
2721:
2718:
2706:
2703:
2702:
2701:
2688:
2684:
2680:
2673:
2668:
2664:
2658:
2654:
2650:
2647:
2644:
2641:
2636:
2632:
2628:
2625:
2621:
2616:
2611:
2608:
2604:
2600:
2597:
2585:
2582:
2581:
2580:
2567:
2563:
2559:
2552:
2547:
2543:
2537:
2533:
2529:
2526:
2523:
2518:
2514:
2510:
2505:
2501:
2497:
2494:
2490:
2485:
2480:
2477:
2473:
2469:
2466:
2454:
2451:
2447:
2446:
2435:
2430:
2426:
2420:
2416:
2412:
2409:
2406:
2396:
2392:
2388:
2383:
2379:
2362:
2359:
2328:
2324:
2320:
2309:
2308:
2295:
2291:
2287:
2280:
2275:
2271:
2267:
2264:
2260:
2255:
2252:
2249:
2246:
2243:
2240:
2235:
2232:
2228:
2224:
2221:
2206:
2203:
2198:
2197:
2184:
2179:
2175:
2171:
2168:
2165:
2162:
2154:
2150:
2146:
2140:
2136:
2129:
2128:
2125:
2121:
2117:
2114:
2111:
2108:
2106:
2103:
2102:
2100:
2095:
2092:
2089:
2086:
2083:
2071:, the RTD is
2060:
2057:
2056:
2055:
2036:
2032:
2028:
2016:
2012:
2008:
1998:
1994:
1987:
1984:
1957:
1956:
1945:
1941:
1936:
1932:
1929:
1923:
1919:
1916:
1911:
1908:
1903:
1900:
1897:
1894:
1891:
1872:
1869:
1868:
1867:
1854:
1850:
1846:
1837:
1833:
1829:
1824:
1820:
1816:
1813:
1809:
1804:
1799:
1796:
1792:
1788:
1785:
1769:
1766:
1765:
1764:
1751:
1747:
1743:
1736:
1731:
1727:
1723:
1720:
1716:
1711:
1706:
1703:
1699:
1695:
1692:
1674:stagnant fluid
1658:
1657:
1645:
1642:
1639:
1636:
1633:
1630:
1627:
1624:
1621:
1618:
1615:
1572:
1569:
1563:
1560:
1527:
1523:
1519:
1469:
1468:
1455:
1452:
1447:
1442:
1438:
1433:
1428:
1416:
1413:
1404:
1400:
1391:
1387:
1386:
1382:
1379:
1373:
1370:
1365:
1362:
1356:
1350:
1347:
1342:
1339:
1333:
1332:
1328:
1305:
1302:
1301:
1300:
1282:
1278:
1274:
1269:
1265:
1254:
1216:
1212:
1208:
1203:
1199:
1188:
1158:
1154:
1150:
1145:
1141:
1112:
1108:
1104:
1099:
1095:
1079:
1078:
1067:
1064:
1061:
1057:
1054:
1051:
1048:
1045:
1042:
1039:
1034:
1029:
1025:
1021:
1018:
1015:
1012:
1007:
1003:
976:
975:
964:
961:
957:
954:
951:
948:
945:
942:
939:
934:
929:
925:
921:
918:
915:
912:
907:
903:
875:
872:
870:
867:
866:
865:
854:
851:
847:
844:
841:
838:
835:
832:
827:
822:
818:
814:
811:
808:
805:
802:
799:
796:
793:
790:
767:
744:
724:
704:
684:
673:
672:
658:
655:
650:
647:
641:
638:
635:
632:
629:
625:
620:
608:
605:
596:
592:
583:
579:
578:
574:
571:
565:
562:
557:
554:
548:
542:
539:
534:
531:
525:
524:
520:
490:
487:
483:
480:
477:
472:
468:
464:
461:
456:
452:
436:
435:
424:
421:
418:
415:
411:
408:
405:
402:
399:
396:
391:
386:
382:
378:
375:
372:
368:
365:
362:
359:
356:
353:
348:
343:
339:
312:
285:
265:
254:residence time
238:
215:
195:
180:control volume
168:
161:
155:Control volume
147:
144:
115:
112:
47:control volume
39:residence time
26:
9:
6:
4:
3:
2:
5453:
5442:
5439:
5437:
5434:
5432:
5429:
5427:
5424:
5422:
5419:
5417:
5414:
5412:
5409:
5407:
5404:
5402:
5399:
5397:
5394:
5393:
5391:
5381:
5378:
5376:
5373:
5372:
5361:
5357:
5353:
5349:
5344:
5340:
5338:9780781750097
5334:
5330:
5325:
5321:
5319:0-471-26919-0
5315:
5311:
5306:
5302:
5300:9781259254598
5296:
5292:
5287:
5284:(2): 409–458.
5283:
5279:
5274:
5270:
5268:9781566764254
5264:
5260:
5255:
5251:
5247:
5243:
5239:
5234:
5230:
5228:9780077492199
5224:
5220:
5215:
5214:
5201:
5197:
5190:
5182:
5178:
5173:
5168:
5164:
5160:
5156:
5149:
5147:
5145:
5143:
5141:
5139:
5130:
5126:
5121:
5116:
5111:
5106:
5102:
5098:
5091:
5084:
5082:
5080:
5071:
5067:
5063:
5059:
5055:
5051:
5047:
5043:
5036:
5028:
5026:9781449674267
5022:
5018:
5017:Drug Delivery
5011:
5009:
5000:
4996:
4992:
4988:
4984:
4980:
4976:
4972:
4968:
4964:
4957:
4949:
4947:9783527335824
4943:
4939:
4932:
4930:
4921:
4919:9781118354469
4915:
4911:
4904:
4902:
4893:
4891:9781847552273
4887:
4883:
4876:
4874:
4865:
4863:9780470508237
4859:
4855:
4848:
4840:
4836:
4832:
4828:
4824:
4820:
4816:
4812:
4804:
4796:
4794:9780875904276
4790:
4786:
4781:
4780:
4771:
4769:
4760:
4753:
4746:
4744:
4728:
4724:
4718:
4709:
4704:
4700:
4696:
4692:
4688:
4681:
4673:
4667:
4663:
4656:
4647:
4642:
4638:
4634:
4630:
4626:
4619:
4617:
4610:
4606:
4600:
4598:
4596:
4589:
4588:0-13-047394-4
4585:
4579:
4571:
4569:9780072921861
4565:
4561:
4554:
4552:
4550:
4548:
4546:
4544:
4535:
4531:
4526:
4521:
4517:
4513:
4509:
4505:
4501:
4494:
4492:
4482:
4477:
4473:
4469:
4465:
4461:
4457:
4450:
4448:
4446:
4444:
4435:
4431:
4427:
4423:
4419:
4415:
4408:
4406:
4404:
4402:
4400:
4398:
4396:
4394:
4392:
4383:
4379:
4375:
4371:
4364:
4362:
4360:
4358:
4356:
4354:
4352:
4347:
4337:
4334:
4332:
4329:
4327:
4324:
4322:
4319:
4317:
4314:
4312:
4309:
4307:
4304:
4303:
4296:
4294:
4290:
4285:
4281:
4277:
4273:
4269:
4265:
4264:Biofuel cells
4261:
4259:
4255:
4245:
4243:
4239:
4236:
4232:
4228:
4224:
4218:
4215:
4211:
4207:
4203:
4199:
4194:
4191:that bind to
4190:
4186:
4176:
4172:
4169:
4164:
4162:
4158:
4154:
4150:
4144:
4137:Environmental
4134:
4132:
4128:
4124:
4119:
4103:
4100:
4096:
4073:
4069:
4060:
4036:
4027:
4011:
3988:
3984:
3978:
3975:
3963:
3957:
3953:
3950:
3945:
3941:
3937:
3934:
3927:
3926:
3925:
3911:
3903:
3899:
3896:. This is an
3895:
3889:
3879:
3877:
3873:
3869:
3865:
3861:
3857:
3853:
3851:
3846:
3845:sedimentation
3842:
3837:
3833:
3823:
3820:
3816:
3812:
3807:
3806:and gravity.
3805:
3801:
3797:
3793:
3789:
3785:
3781:
3777:
3767:
3765:
3764:time constant
3760:
3755:
3753:
3749:
3730:
3727:
3724:
3717:
3711:
3705:
3679:
3668:
3664:
3660:
3643:
3635:
3634:
3633:
3631:
3627:
3626:
3606:
3603:
3600:
3593:
3587:
3583:
3579:
3576:
3573:
3569:
3565:
3562:
3552:
3548:
3544:
3530:
3525:
3507:
3503:
3487:
3477:
3476:
3475:
3461:
3441:
3434:
3433:rate constant
3414:
3410:
3407:
3404:
3400:
3396:
3393:
3390:
3379:
3371:
3370:
3369:
3367:
3363:
3359:
3350:
3336:
3315:
3312:
3304:
3298:
3295:
3289:
3283:
3277:
3272:
3269:
3265:
3257:
3254:
3247:
3242:
3237:
3233:
3229:
3223:
3217:
3210:
3209:
3208:
3191:
3184:
3180:
3172:
3166:
3160:
3154:
3148:
3141:
3140:
3139:
3122:
3116:
3094:
3090:
3067:
3063:
3031:
3028:
3021:
3015:
3005:
3001:
2992:
2986:
2980:
2974:
2968:
2961:
2960:
2959:
2942:
2936:
2916:
2896:
2876:
2868:
2858:
2856:
2852:
2848:
2844:
2839:
2829:
2800:
2796:
2790:
2786:
2782:
2779:
2771:
2768:
2764:
2760:
2748:
2744:
2740:
2730:
2726:
2719:
2716:
2709:
2708:
2686:
2682:
2678:
2666:
2662:
2656:
2652:
2648:
2645:
2634:
2630:
2626:
2619:
2614:
2609:
2606:
2602:
2598:
2595:
2588:
2587:
2565:
2561:
2557:
2545:
2541:
2535:
2531:
2527:
2524:
2516:
2512:
2503:
2499:
2495:
2488:
2483:
2478:
2475:
2471:
2467:
2464:
2457:
2456:
2450:
2428:
2424:
2418:
2414:
2410:
2407:
2399: initial
2394:
2390:
2386:
2381:
2377:
2369:
2368:
2367:
2358:
2356:
2352:
2348:
2344:
2326:
2322:
2318:
2293:
2289:
2285:
2273:
2269:
2265:
2258:
2253:
2247:
2244:
2241:
2233:
2230:
2226:
2222:
2219:
2212:
2211:
2210:
2202:
2177:
2173:
2169:
2166:
2163:
2152:
2148:
2144:
2138:
2134:
2123:
2119:
2115:
2112:
2109:
2104:
2098:
2093:
2087:
2081:
2074:
2073:
2072:
2070:
2066:
2034:
2030:
2026:
2014:
2010:
2006:
1996:
1992:
1985:
1982:
1975:
1974:
1973:
1970:
1964:
1962:
1943:
1939:
1934:
1930:
1927:
1921:
1917:
1914:
1909:
1906:
1901:
1895:
1889:
1882:
1881:
1880:
1878:
1852:
1848:
1844:
1835:
1831:
1822:
1818:
1814:
1807:
1802:
1797:
1794:
1790:
1786:
1783:
1776:
1775:
1774:
1768:Batch reactor
1749:
1745:
1741:
1729:
1725:
1721:
1714:
1709:
1704:
1701:
1697:
1693:
1690:
1683:
1682:
1681:
1677:
1675:
1671:
1665:
1663:
1640:
1637:
1634:
1628:
1625:
1619:
1613:
1606:
1605:
1604:
1602:
1598:
1594:
1590:
1586:
1582:
1578:
1568:
1559:
1557:
1553:
1549:
1545:
1541:
1525:
1521:
1517:
1508:
1506:
1500:
1498:
1494:
1490:
1486:
1482:
1478:
1477:flushing time
1474:
1473:turnover time
1453:
1450:
1445:
1440:
1436:
1426:
1414:
1411:
1402:
1398:
1389:
1380:
1377:
1371:
1368:
1363:
1360:
1354:
1348:
1340:
1319:
1318:
1317:
1315:
1311:
1304:Turnover time
1298:
1280:
1276:
1272:
1267:
1263:
1255:
1252:
1248:
1244:
1240:
1236:
1232:
1214:
1210:
1206:
1201:
1197:
1189:
1186:
1182:
1178:
1174:
1156:
1152:
1148:
1143:
1139:
1131:
1130:
1129:
1110:
1106:
1102:
1097:
1093:
1083:
1065:
1062:
1059:
1052:
1049:
1046:
1040:
1037:
1027:
1023:
1019:
1013:
1005:
1001:
993:
992:
991:
989:
985:
981:
962:
959:
952:
949:
946:
940:
937:
927:
923:
919:
913:
905:
901:
893:
892:
891:
889:
886:is the first
885:
881:
852:
849:
842:
839:
836:
830:
825:
820:
816:
812:
809:
806:
800:
797:
794:
788:
781:
780:
779:
765:
758:
742:
722:
702:
682:
656:
648:
639:
636:
633:
630:
627:
618:
606:
603:
594:
590:
581:
572:
569:
563:
560:
555:
552:
546:
540:
532:
511:
510:
509:
507:
502:
488:
481:
478:
475:
470:
462:
459:
454:
441:
422:
419:
416:
413:
406:
403:
400:
394:
384:
380:
376:
373:
370:
363:
360:
357:
351:
341:
337:
329:
328:
327:
324:
310:
303:
299:
283:
263:
255:
250:
236:
229:
213:
193:
185:
181:
174:
167:
160:
156:
152:
146:Distributions
143:
141:
137:
133:
129:
125:
121:
111:
109:
105:
101:
97:
96:
91:
87:
83:
78:
76:
72:
68:
64:
60:
56:
52:
48:
44:
40:
33:
19:
18:Flushing time
5421:Geochemistry
5351:
5347:
5328:
5309:
5290:
5281:
5277:
5258:
5241:
5237:
5218:
5199:
5189:
5162:
5158:
5100:
5096:
5045:
5041:
5035:
5016:
4969:(2): 87–95.
4966:
4962:
4956:
4937:
4909:
4881:
4853:
4847:
4814:
4810:
4803:
4778:
4758:
4731:. Retrieved
4729:. 2020-06-22
4726:
4717:
4690:
4686:
4680:
4661:
4655:
4628:
4624:
4578:
4559:
4507:
4503:
4463:
4459:
4420:(1): 58–62.
4417:
4413:
4373:
4369:
4262:
4251:
4219:
4213:
4202:binding site
4182:
4179:Pharmacology
4173:
4165:
4146:
4120:
4026:gas constant
4003:
3891:
3856:Disinfection
3854:
3839:
3808:
3773:
3756:
3747:
3745:
3629:
3623:
3621:
3430:
3355:
3339:Applications
3333:
3206:
3054:
2864:
2850:
2846:
2843:hydrodynamic
2835:
2826:
2448:
2364:
2354:
2350:
2346:
2342:
2310:
2208:
2199:
2062:
1968:
1965:
1960:
1958:
1875:In an ideal
1874:
1771:
1678:
1669:
1666:
1661:
1660:The mean is
1659:
1600:
1592:
1588:
1584:
1580:
1575:In an ideal
1574:
1565:
1556:Little's Law
1543:
1539:
1509:
1501:
1496:
1492:
1488:
1484:
1480:
1476:
1472:
1470:
1314:conservative
1307:
1234:
1230:
1177:stratosphere
1127:
987:
983:
979:
977:
883:
879:
877:
756:
674:
506:conservative
503:
437:
325:
301:
297:
253:
251:
227:
183:
177:
172:
165:
158:
135:
119:
117:
100:waiting time
99:
93:
90:pharmacology
79:
74:
70:
43:fluid parcel
38:
36:
4817:: 250–261.
4708:11336/74207
4646:11336/45663
4631:: 463–471.
4326:Micromixing
4248:Biochemical
4235:bioadhesive
4168:contaminate
3788:water table
3776:groundwater
3625:micromixing
2855:deconvolute
1599:delayed by
1297:water vapor
1185:troposphere
440:steady flow
5390:Categories
5382:(Lenntech)
5097:Biosensors
4733:2020-07-23
4343:References
4141:See also:
4127:outgassing
4118:seconds).
3894:adsorption
3886:See also:
3830:See also:
1544:on average
1540:on average
1497:space time
59:human body
4983:1474-1776
4206:half-life
4101:−
4070:τ
3954:
3942:τ
3935:τ
3819:Aquitards
3674:∞
3665:∫
3574:−
3566:
3558:∞
3549:∫
3499:¯
3405:−
3397:
3234:∫
3011:∞
3002:∫
2917:τ
2787:δ
2783:−
2761:−
2753: out
2741:−
2717:τ
2653:δ
2649:−
2627:−
2615:∫
2596:τ
2532:δ
2528:−
2496:−
2484:∫
2465:τ
2415:δ
2411:−
2319:−
2266:−
2254:∫
2220:τ
2164:τ
2149:τ
2113:≤
2110:τ
2088:τ
2027:−
2019: out
2007:−
1983:τ
1931:τ
1928:−
1918:
1896:τ
1815:−
1803:∫
1784:τ
1722:−
1710:∫
1691:τ
1638:−
1635:τ
1629:δ
1620:τ
1437:τ
1432:⟹
1346:∂
1338:∂
1277:τ
1264:τ
1211:τ
1198:τ
1153:τ
1140:τ
1107:τ
1094:τ
1063:τ
1047:τ
1038:τ
1033:∞
1024:∫
1002:τ
963:τ
947:τ
938:τ
933:∞
924:∫
902:τ
826:τ
817:∫
813:−
795:τ
743:τ
657:τ
654:∂
646:∂
637:−
624:⟹
538:∂
530:∂
486:∀
467:∂
451:∂
417:τ
401:τ
390:∞
381:∫
374:τ
358:τ
347:∞
338:∫
264:τ
194:τ
95:lead time
82:chemistry
49:(e.g.: a
5181:99856827
5129:26193327
5070:19954225
4999:22955177
4991:26678621
4839:29128774
4534:11505988
4299:See also
4242:lozenges
4240:, gums,
4238:polymers
4198:kinetics
4157:aquifers
4149:glaciers
3872:protozoa
3864:bacteria
3784:Porosity
3273:′
3258:′
2735: in
2001: in
1251:reactant
880:mean age
869:Averages
130:and the
5411:Ecology
5120:4600167
5050:Bibcode
4819:Bibcode
4785:165–167
4727:CEMF.ir
4512:Bibcode
4468:Bibcode
4422:Bibcode
4276:cathode
4208:of the
4193:enzymes
4024:is the
3868:viruses
3794:versus
1505:uniform
114:History
5335:
5316:
5297:
5265:
5225:
5179:
5127:
5117:
5068:
5023:
4997:
4989:
4981:
4944:
4916:
4888:
4860:
4837:
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4607:
4586:
4566:
4532:
4460:Tellus
4414:Tellus
4274:and a
4231:saliva
4061:, and
4057:is an
4004:where
3811:mining
3796:gravel
3431:for a
2838:tracer
2812:
2043:
1423:
1310:steady
888:moment
615:
5177:S2CID
5093:(PDF)
4995:S2CID
4755:(PDF)
4530:S2CID
4272:anode
4185:drugs
3876:cysts
3362:yield
2849:or a
2847:pulse
2453:Batch
2063:In a
1179:by a
41:of a
5333:ISBN
5314:ISBN
5295:ISBN
5263:ISBN
5223:ISBN
5125:PMID
5066:PMID
5021:ISBN
4987:PMID
4979:ISSN
4942:ISBN
4914:ISBN
4886:ISBN
4858:ISBN
4835:PMID
4789:ISBN
4666:ISBN
4605:ISBN
4584:ISBN
4564:ISBN
4187:are
3902:heat
3874:and
3866:and
3834:and
3792:clay
2851:step
2167:>
1550:and
1312:and
1273:>
1245:and
1237:are
1233:and
1149:<
1103:>
978:The
878:The
695:and
106:and
88:and
57:, a
55:lake
53:, a
37:The
5356:doi
5246:doi
5167:doi
5163:164
5115:PMC
5105:doi
5058:doi
4971:doi
4827:doi
4815:618
4703:hdl
4695:doi
4641:hdl
4633:doi
4629:176
4520:doi
4476:doi
4430:doi
4378:doi
4252:In
4121:In
3951:exp
3759:CFD
3563:exp
3394:exp
3356:In
1915:exp
1491:or
1487:),
1485:HRT
1475:or
1407:out
982:or
599:out
184:age
169:out
122:by
98:or
63:set
5392::
5350:.
5282:31
5280:.
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5240:.
5198:.
5175:.
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5157:.
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4074:0
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3649:o
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2667:A
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2635:A
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2607:A
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2566:A
2562:f
2558:d
2551:)
2546:A
2542:f
2536:A
2525:1
2522:(
2517:R
2513:V
2509:)
2504:A
2500:r
2493:(
2489:1
2479:O
2476:A
2472:N
2468:=
2434:)
2429:A
2425:f
2419:A
2408:1
2405:(
2395:R
2391:V
2387:=
2382:R
2378:V
2355:k
2351:A
2347:A
2343:A
2327:A
2323:r
2294:A
2290:f
2286:d
2279:)
2274:A
2270:r
2263:(
2259:1
2251:)
2248:1
2245:+
2242:R
2239:(
2234:O
2231:A
2227:C
2223:=
2174:/
2170:T
2153:3
2145:2
2139:2
2135:T
2124:2
2120:/
2116:T
2105:0
2099:{
2094:=
2091:)
2085:(
2082:E
2035:A
2031:r
2015:A
2011:C
1997:A
1993:C
1986:=
1969:E
1961:T
1944:.
1940:)
1935:T
1922:(
1910:T
1907:1
1902:=
1899:)
1893:(
1890:E
1853:A
1849:f
1845:d
1836:R
1832:V
1828:)
1823:A
1819:r
1812:(
1808:1
1798:O
1795:A
1791:N
1787:=
1750:A
1746:f
1742:d
1735:)
1730:A
1726:r
1719:(
1715:1
1705:O
1702:A
1698:C
1694:=
1670:T
1662:T
1644:)
1641:T
1632:(
1626:=
1623:)
1617:(
1614:E
1601:T
1593:T
1589:T
1585:t
1581:t
1526:f
1522:/
1518:m
1483:(
1454:f
1451:m
1446:=
1441:t
1427:}
1415:f
1412:=
1403:f
1399:=
1390:f
1381:0
1378:=
1372:t
1369:d
1364:m
1361:d
1355:=
1349:t
1341:I
1281:t
1268:a
1235:I
1231:E
1215:t
1207:=
1202:a
1187:.
1157:t
1144:a
1111:t
1098:a
1066:.
1060:d
1056:)
1053:t
1050:,
1044:(
1041:E
1028:0
1020:=
1017:)
1014:t
1011:(
1006:t
988:t
960:d
956:)
953:t
950:,
944:(
941:I
928:0
920:=
917:)
914:t
911:(
906:a
884:t
853:s
850:d
846:)
843:t
840:,
837:s
834:(
831:E
821:0
810:1
807:=
804:)
801:t
798:,
792:(
789:W
766:W
723:t
703:I
683:E
649:I
640:m
634:=
631:E
628:f
619:}
607:f
604:=
595:f
591:=
582:f
573:0
570:=
564:t
561:d
556:m
553:d
547:=
541:t
533:I
489:t
482:0
479:=
476:I
471:t
463:=
460:E
455:t
423:1
420:=
414:d
410:)
407:t
404:,
398:(
395:I
385:0
377:=
371:d
367:)
364:t
361:,
355:(
352:E
342:0
311:E
284:t
237:I
214:t
173:m
166:f
159:f
34:.
20:)
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