Electroosmotic Fluid Motion and Late-Time Solute Transport for Large Zeta Potentials

2000 ◽  
Vol 72 (20) ◽  
pp. 4767-4777 ◽  
Author(s):  
Stewart K. Griffiths ◽  
Robert H. Nilson
Keyword(s):  
Solute Transport ◽  
Fluid Motion ◽  
Late Time ◽  
Zeta Potentials

Tuning the dispersion of reactive solute by steady and oscillatory electroosmotic–Poiseuille flows in polyelectrolyte-grafted micro/nanotubes

2019 ◽  
Vol 880 ◽  
pp. 73-112
Author(s):  
Milad Reshadi ◽  
Mohammad Hassan Saidi
Keyword(s):  
Hydrodynamic Dispersion ◽  
Asymptotic State ◽  
Late Time ◽  
Band Broadening ◽  
Zeta Potentials ◽  
Tracer Particles ◽  
Ion Partitioning ◽  
Analytical Approaches ◽  
Benchmark Solutions ◽  
Poiseuille Flows

This paper extends the analysis of solute dispersion in electrohydrodynamic flows to the case of band broadening in polyelectrolyte-grafted (soft) capillaries by accounting for the effects of ion partitioning, irreversible catalytic reaction and pulsatile flow actuation. In the Debye–Hückel limit, we present the benchmark solutions of electric potential and velocity distribution pertinent to steady and oscillatory mixed electroosmotic–pressure-driven flows in soft capillaries. Afterwards, the mathematical models of band broadening based on the Taylor–Aris theory and generalized dispersion method are presented to investigate the late-time asymptotic state and all-time evolution of hydrodynamic dispersion, respectively. Also, to determine the heterogeneous dispersion behaviour of solute through all spatiotemporal stages and to relax the constraint of small zeta potentials, a full-scale numerical simulation of time-dependent solute transport in soft capillaries is presented by employing the second-order-accurate finite difference method. Then, by inspecting the dispersion of passive tracer particles in Poiseuille flows, we examine the accuracy of two analytical approaches against the simulation results of a custom-built numerical algorithm. Our findings from hydrodynamic dispersion in Poiseuille flows reveal that, compared to rigid capillaries, more time is required to approach the longitudinal normality and transverse uniformity of injected solute in soft capillaries. For the case of dispersion in mixed electrohydrodynamic flows, it is found that the characteristics of the soft interface, including the thickness, permittivity, fixed charge density and friction coefficient of the polymer coating layer, play a significant role in determining the Taylor diffusion coefficient, advection speed and dispersion rate of solutes in soft capillaries.

scholarly journals Transient solute transport with sorption in Poiseuille flow

2017 ◽  
Vol 828 ◽  
pp. 733-752 ◽  
Author(s):  
Li Zhang ◽  
Marc A. Hesse ◽  
Moran Wang
Keyword(s):  
Partition Coefficient ◽  
Solute Transport ◽  
Poiseuille Flow ◽  
Reaction Rates ◽  
Late Time ◽  
Sorption Model ◽  
Transport Velocity ◽  
Transport Behaviour ◽  
Kinetic Sorption ◽  
Limiting Case

Previous work on solute transport with sorption in Poiseuille flow has reached contradictory conclusions. Some have concluded that sorption increases mean solute transport velocity and decreases dispersion relative to a tracer, while others have concluded the opposite. Here we resolve this contradiction by deriving a series solution for the transient evolution that recovers previous results in the appropriate limits. This solution shows a transition in solute transport behaviour from early to late time that is captured by the first- and zeroth-order terms. Mean solute transport velocity is increased at early times and reduced at late times, while solute dispersion is initially reduced, but shows a complex dependence on the partition coefficient $k$ at late times. In the equilibrium sorption model, the time scale of the early regime and the duration of the transition to the late regime both increase with $\ln k$ for large $k$. The early regime is pronounced in strongly sorbing systems ($k\gg 1$). The kinetic sorption model shows a similar transition from the early to the late transport regime and recovers the equilibrium results when adsorption and desorption rates are large. As the reaction rates slow down, the duration of the early regime increases, but the changes in transport velocity and dispersion relative to a tracer diminish. In general, if the partition coefficient $k$ is large, the early regime is well developed and the behaviour is well characterized by the analysis of the limiting case without desorption.

scholarly journals On the reliability of analytical models to predict solute transport in a fracture network

2014 ◽  
Vol 18 (6) ◽  
pp. 2359-2374 ◽  
Author(s):  
C. Cherubini ◽  
C. I. Giasi ◽  
N. Pastore
Keyword(s):  
Solute Transport ◽  
Transport Model ◽  
Fractured Rock ◽  
Early Time ◽  
Taylor Dispersion ◽  
Breakthrough Curves ◽  
Nonlinear Flow ◽  
Analytical Models ◽  
Late Time ◽  
Tracer Transport

Abstract. In hydrogeology, the application of reliable tracer transport model approaches is a key issue to derive the hydrodynamic properties of aquifers. Laboratory- and field-scale tracer dispersion breakthrough curves (BTC) in fractured media are notorious for exhibiting early time arrivals and late time tailing that are not captured by the classical advection–dispersion equation (ADE). These "non-Fickian" features are proven to be better explained by a mobile–immobile (MIM) approach. In this conceptualization the fractured rock system is schematized as a continuous medium in which the liquid phase is separated into flowing and stagnant regions. The present study compares the performances and reliabilities of the classical MIM and the explicit network model (ENM), taking expressly into account the network geometry for describing tracer transport behavior in a fractured sample at bench scale. Though ENM shows better fitting results than MIM, the latter remains still valid as it proves to describe the observed curves quite well. The results show that the presence of nonlinear flow plays an important role in the behavior of solute transport. First, the distribution of solute according to different pathways is not constant, but it is related to the flow rate. Second, nonlinear flow influences advection in that it leads to a delay in solute transport respect to the linear flow assumption. However, nonlinear flow is not shown to be related with dispersion. The experimental results show that in the study case the geometrical dispersion dominates the Taylor dispersion. However, the interpretation with the ENM shows a weak transitional regime from geometrical dispersion to Taylor dispersion for high flow rates. Incorporating the description of the flow paths in the analytical modeling has proven to better fit the curves and to give a more robust interpretation of the solute transport.

scholarly journals Steric Effects on Electroosmotic Nano-Thrusters under High Zeta Potentials

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3222
Author(s):  
Jiaxuan Zheng ◽  
Siyi An ◽  
Yongjun Jian
Keyword(s):  
Electric Potential ◽  
Steric Effect ◽  
Specific Impulse ◽  
Fluid Motion ◽  
Finite Size ◽  
Numerical Algorithms ◽  
Ionic Species ◽  
Double Layers ◽  
Power Ratio ◽  
Zeta Potentials

Here, space electroosmotic thrusters in a rigid nanochannel with high wall zeta potentials are investigated numerically, for the first time, considering the effect of finite size of the ionic species. The effect, which is called a steric effect, is often neglected in research about micro/nano thrusters. However, it has vital influences on the electric potential and flow velocity in electric double layers, so that the thruster performances generated by the fluid motion are further affected. These performances, including thrust, specific impulse, thruster efficiency, and the thrust-to-power ratio, are described by using numerical algorithms, after obtaining the electric potential and velocity distributions under high wall zeta potentials ranging from −25.7 mV to −128.5 mV. As expected, the zeta potential can promote the development of thruster performances so as to satisfy the requirement of space missions. Moreover, for real situation with consideration of the steric effect, the thruster thrust and efficiency significantly decrease to 5–30 micro Newtons and 80–90%, respectively, but the thrust-to-power ratio is opposite, and expends a short specific impulse of about 50–110 s.

scholarly journals An Experimental Study on Solute Transport in One-Dimensional Clay Soil Columns

Geofluids ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-17 ◽  
Author(s):  
Muhammad Zaheer ◽  
Zhang Wen ◽  
Hongbin Zhan ◽  
Xiaolian Chen ◽  
Menggui Jin
Keyword(s):  
Solute Transport ◽  
Dispersion Equation ◽  
Transport Process ◽  
Breakthrough Curve ◽  
Small Scale ◽  
Low Permeability ◽  
Late Time ◽  
Time Behavior ◽  
One Dimensional ◽  
Advection Dispersion

Solute transport in low-permeability media such as clay has not been studied carefully up to present, and we are often unclear what the proper governing law is for describing the transport process in such media. In this study, we composed and analyzed the breakthrough curve (BTC) data and the development of leaching in one-dimensional solute transport experiments in low-permeability homogeneous and saturated media at small scale, to identify key parameters controlling the transport process. Sodium chloride (NaCl) was chosen to be the tracer. A number of tracer tests were conducted to inspect the transport process under different conditions. The observed velocity-time behavior for different columns indicated the decline of soil permeability when switching from tracer introducing to tracer flushing. The modeling approaches considered were the Advection-Dispersion Equation (ADE), Two-Region Model (TRM), Continuous Time Random Walk (CTRW), and Fractional Advection-Dispersion Equation (FADE). It was found that all the models can fit the transport process very well; however, ADE and TRM were somewhat unable to characterize the transport behavior in leaching. The CTRW and FADE models were better in capturing the full evaluation of tracer-breakthrough curve and late-time tailing in leaching.

scholarly journals On the reliability of analytical models to predict solute transport in a fracture network

2013 ◽  
Vol 10 (12) ◽  
pp. 14905-14948
Author(s):  
C. Cherubini ◽  
C. I. Giasi ◽  
N. Pastore
Keyword(s):  
Solute Transport ◽  
Transport Model ◽  
Fractured Rock ◽  
Early Time ◽  
Taylor Dispersion ◽  
Breakthrough Curves ◽  
Nonlinear Flow ◽  
Analytical Models ◽  
Late Time ◽  
Tracer Transport

Abstract. In hydrogeology, the application of reliable tracer transport model approaches is a key issue to derive the hydrodynamic properties of aquifers. Laboratory and field-scale tracer dispersion breakthrough curves (BTC) in fractured media are notorious for exhibiting early time arrivals and late-time tailing that are not captured by the classical advection–dispersion equation (ADE). These "non-Fickian" features are proved to be better explained by a mobile–immobile (MIM) approach. In this conceptualization the fractured rock system is schematized as a continuous medium in which the liquid phase is separated into flowing and stagnant regions. The present study compares the performances and reliabilities of classical Mobile–Immobile Model (MIM) and the Explicit Network Model (ENM) that takes expressly into account the network geometry for describing tracer transport behavior in a fractured sample at bench scale. Though ENM shows better fitting results than MIM, the latter remains still valid as it proves to describe the observed curves quite well. The results show that the presence of nonlinear flow plays an important role in the behaviour of solute transport. Firstly the distribution of solute according to different pathways is not constant but it is related to the flow rate. Secondly nonlinear flow influences advection, in that it leads to a delay in solute transport respect to the linear flow assumption. Whereas nonlinear flow does not show to be related with dispersion. However the interpretation with the ENM model shows a weak transitional regime from geometrical dispersion to Taylor dispersion for high flow rates. The experimental results show that in the study case the geometrical dispersion dominates the Taylor dispersion. Incorporating the description of the flowpaths in the analytical modeling has proved to better fit the curves and to give a more robust interpretation of the solute transport.

Control of Rate of Solute Transport in Newly Developed Portable Agar Gel Blood Purification System

1998 ◽  
Vol 2 (1) ◽  
pp. 67-70
Author(s):  
Akihiro C. Yamashita ◽  
Ryoichi Sakiyama ◽  
Hiroyuki Hamada ◽  
Kakuji J. Tojo
Keyword(s):  
Solute Transport ◽  
Blood Purification ◽  
Agar Gel ◽  
Purification System
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