Non-equilibrium molecular dynamics simulation of electrokinetic effects on heterogeneous ionic transport in nano-channel

The presence of the electric double layer (EDL) near the solid/liquid interface has a great impact on the liquid flowing through nano channels. In this paper, a non-equilibrium molecular dynamics method (NEMD) model is developed to investigate the transport characteristics of the heterogeneous ionic fluid flowing in a 4.672 nm-depth channel due to the electrokinetic effect induced by the EDL. An external perturbing velocity is introduced on the liquid instead of a constant force to study the electrokinetic effects on the flow. The effect of charges adsorbed on channel surfaces on flow resistance is especially considered. Two different charged surfaces with discrete or uniform charge distributions are compared, respectively. Besides Lennard-Jones (L-J) potential energy and Coulomb force, the ion–dipole interaction between the charged particle and the water molecule in the liquid is especially taken into account. According to the simulation results, the liquid density reaches the peak value in the EDL. However, unlike that predicted by the Poisson–Boltzmann theory, the liquid density profile is not exactly an anti-parabola curve, which has a significant fall before the density reaching the peak value in the EDL. It is shown that the charges absorbed on the channel surface have little influence on the liquid density distribution, but they play an important role in the fluid velocity distribution. Meanwhile, the liquid velocity slippage in the EDL emerges, which is well in agreement with the prior experimental data available. Moreover, though the non-dimensional velocities are nearly the same under different external velocity fields, the velocity slippage for the uniformly charged wall is much larger than that for the discretely charged wall. All of these results provide a probable reason why the flow behavior in a nano-channel is particularly different from that in a macro duct.     

The effect of a concentration‐dependent viscosity on particle transport in a channel flow with porous walls

The transport of a dilute suspension of particles through a channel with porous walls, accounting for the concentration dependence of the viscosity, is analyzed. In particular, we study two cases of fluid permeation through the porous channel walls: (1) at a constant flux and (2) dependent on the pressure drop across the wall. We also consider the effect of mixing the suspension first compared with point injection by considering inlet concentration distributions of different widths. We find that a pessimal inlet distribution width exists that maximizes the required hydrodynamic pressure for a constant fluid influx. The effect of an external hydrodynamic pressure, to compensate for the reduced transmembrane pressure difference due to osmotic pressure, is investigated. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1891–1904, 2014     

RO membrane solute rejection behavior at the initial stage ofcolloidal fouling

This study investigated the rejection of salt and inert organic compounds by reverse osmosis membranes during the initial stage of colloidal fouling. Results of laboratory-scale experiments showed that colloidal fouling caused a marked decrease in flux, salt rejection and rejection of organics with molecular weight (MW) smaller than about 100 g/mol. Removal of neutrally charged organics was mainly by size or steric exclusion. Rejection of xylose, which has MW >100 g/mol, was not affected much by colloidal fouling. The decrease in salt and low MW organic rejections during the initial stage of colloidal fouling was attributed to cake-enhanced concentration polarization, whereby the colloidal cake layer hindered back diffusion of solutes from the membrane surface to the bulk solution, resulting in higher solute concentration gradient across the membrane. At higher channel wall shear rate, the rates of colloidal deposition, flux decline, decrease in salt rejection, and decrease in low MW organic rejection were lower.     

Numerical study of a permeable capsule under Stokes flows by the immersed interface method

A two-dimensional model to simulate the mass transfer of a permeable, deformable, and adhesive capsule flowing in a binary solution of a vessel is proposed using the immersed interface method (IIM). The fluid flow is governed by the full Navier–Stokes equations and the solute distribution is governed by the advection–diffusion equation. Mass transport across the capsule membrane is computed using the Kedem–Katchalsky equations while the adhesion between the capsule and the walls is introduced via a potential function. The model is first validated for the simple shear flow away from the substrate walls and then for capsule adhesion and deformation next to a substrate wall. It is next used to study solute transfer between the capsule and the vessel walls with and without a flow field. In the absence of a flow field, the results show that the transient of the solute transfer between the capsule and the vessel walls depends on the membrane diffusive permeability. In the presence of a Stokes flow field, behavior of the solute transfer seems to be fairly similar to that found for the stationary capsule for the same physical parameters. Moreover, the results suggest that the total solute transfer between the capsule and the vessel walls is enhanced when the capsule moves near to one wall. The increased adhesion strength between the capsule and walls would further increase the total solute transfer to the vessel walls although quite marginal.     

Magnetohydrodynamic slip flow and diffusion of a reactive solute past a permeable flat plate with suction/injection

The magnetohydrodynamic (MHD) boundary layer slip flow and solute transfer over a porous plate in the presence of a chemical reaction are investigated. The governing equations were transformed into self-similar ordinary differential equations by adopting the similarity transformation technique. Then the numerical solutions are obtained by a shooting technique using the fourth order Runge-Kutta method. The study reveals that due to the increase in the boundary slip, the concentration decreases and the velocity increases. On the other hand, with an increase in the magnetic field and mass suction, both boundary layer thicknesses decreased. As the Schmidt number and the reaction rate parameter increases, the concentration decreases and the mass transfer increases.     

EFFECTS OF SOLUTE ADSORPTION ON HINDERED DIFFUSION UPTAKE RATES IN FINITE BATH EXPERIMENTS

This work investigates the effects of solute adsorption on hindered diffusion behavior in porous catalysts. A mathematical model describing the adsorptive diffusion process is developed. The model, termed the shrinking pore model, incorporates the local reduction in catalyst pore diameter due to the adsorption of solute molecules on the pore walls. The influence of the adsorbed solute layer is found to depend on two additional parameters, reflecting the relative degree of adsorption and molecule/pore size ratio. Hindered diffusion experiments are performed for diffusion controlled adsorptive uptakes of two solute molecules, quinoline and polystyrene, from cyclohexane on a porous catalyst. Comparison of the experimental data and model simulation results shows that for the larger polystyrene solute the shrinking pore model better represents the uptake behavior than the conventional model which assumes constant catalyst properties, e.g. pore diameter, during the uptake process. Experimental measurements were found to be in good agreement with model simulations after accounting for additional hindered diffusional effects due to an adsorbed solute layer on the pore walls. The additional hindrance due to the adsorbed solute was found to be very significant for the uptake of the larger polystyrene solute, whereas it was not significant for the smaller quinoline solute.     

Fluid Flow Characteristics of Forced Flow Electrophoresis

Abstract

Fluid flow in forced flow electrophoresis has not been previously analyzed, even though it presents some interesting aspects. The effectiveness of this method for biological separations is due to a superimposition of an electric field on filtration. A mathematical model is presented, describing fluid flow and mass transfer for dilute solutions at electrical potentials less than the critical one. The calculated solute trajectories in a channel are determined by the ratio of the electrophoretic velocity to the withdrawal velocity through the permeable wall. The stationary layer and the layer in which all the solutes arrive at the permeable membrane at the end of the channel are also calculated. The concentration of the filtrate through the permeable membrane is obtained from the material balance of the solute entering the channel. Increased performance is obtained by means of a double-stage forced flow electrophoresis, where the ratio of final filtered solute concentration to inlet concentration is shown to be the square of the same ratio at the first stage.     

Diffusiophoresis of a colloidal sphere in nonelectrolyte gradients parallel to one or two plane walls

The quasisteady diffusiophoretic motion of a spherical particle in a fluid solution of a nonionic solute located between two infinite parallel plane walls is studied theoretically in the absence of fluid inertia and solute convection. The imposed solute concentration gradient is constant and parallel to the two plane walls, which may be either impermeable to the solute molecules or prescribed with the far-field concentration distribution. The particle-solute interaction layer at the particle surface is assumed to be thin relative to the particle radius and to the particle-wall gap widths, but the polarization effect of the diffuse solute in the thin interfacial layer caused by the strong adsorption of the solute is incorporated. The presence of the neighboring walls causes two basic effects on the particle velocity: first, the local solute concentration gradient on the particle surface is enhanced or reduced by the walls, thereby speeding up or slowing down the particle; secondly, the walls increase viscous retardation of the moving particle. To solve the continuity and momentum equations, the general solutions are constructed from the fundamental solutions in both the rectangular and the spherical coordinate systems. The boundary conditions are enforced first at the plane walls by the Fourier transforms and then on the particle surface by a collocation technique. Numerical results for the diffusiophoretic velocity of the particle relative to that under identical conditions in an unbounded fluid solution are presented for various values of the relaxation parameter of the particle as well as the relative separation distances between the particle and the two plates. For the special case of diffusiophoretic motions of a spherical particle parallel to a single plate and on the central plane of a slit, the collocation results agree well with the approximate analytical solutions obtained by using a method of reflections. The presence of the lateral walls can reduce or enhance the particle velocity, depending on the surface properties of the particle, the relative particle-wall separation distances, and the solutal boundary condition at the walls. In general, the boundary effect on diffusiophoresis is quite complicated and relatively weak in comparison with that on sedimentation.     

ACROSS MASS TRANSFER PHENOMENON IN A CHANNEL OF LOWER STRETCHING WALL

This study aims to investigate the effect of across mass transfer (AMT) phenomenon on a three-dimensional steady viscous flow in a channel of lower stretching wall. The phenomenon of AMT is established by imposing suction at one plate and injection at the other plate of the channel simultaneously. Both the walls are assumed to be porous so that suction/injection can take place. Interesting observations regarding viscous drag at the stretching plate have been recorded in the presence of AMT phenomenon at the twin walls. A highly accurate purely analytic solution has been obtained for the governing nonlinear equations. The issue of convergence and accuracy of the analytic solution has been discussed in detail. Results are discussed through graphs.     

Diffusiophoresis of a colloidal sphere in nonelectrolyte gradients perpendicular to two plane walls

The problem of the diffusiophoretic motion of a spherical particle in a fluid solution of a nonionic solute situated at an arbitrary position between two infinite parallel plane walls is studied theoretically in the quasisteady limit of negligible Peclet and Reynolds numbers. The applied solute concentration gradient is uniform and perpendicular to the plane walls. The particle-solute interaction layer at the particle surface is assumed to be thin relative to the particle radius and to the particle-wall gap widths, but the polarization effect of the diffuse solute in the thin interfacial layer caused by the strong adsorption of the solute is incorporated. The presence of the walls causes two basic effects on the particle velocity: first, the local solute concentration gradient on the particle surface is altered by the walls, thereby speeding up or slowing down the moving particle; second, the walls enhance the viscous retardation of the particle. A boundary-collocation method is used to semianalytically solve the solutal and hydrodynamic governing equations of the system. Numerical results for the diffusiophoretic velocity of the particle relative to that under identical conditions in an unbounded fluid solution are presented for various cases. The collocation results agree well with the approximate analytical solutions obtained by using a method of reflections. The net effect of the confining walls is always to reduce the particle velocity, irrespective of the surface properties of the particle or the relative particle-wall separation distances. The boundary effect on diffusiophoresis of a particle normal to two plane walls is found to be quite significant and generally stronger than that parallel to the walls.     

Wall-flow filters with wall-integrated oxidation catalyst: A simulation study

Diesel soot abatement via diesel particulate filters composed of so-called wall-flow monoliths is well established. Today, due to recent improvements in the production technology full-featured catalyst functionality can be implemented in the filter walls.

This work focuses on a comparison of the reactor performance of the wall-flow filter and the conventional flow-through monolith. To this end a two-dimensional numerical model is set up for each of the two reactor configurations.

Concentration profiles in the wall-flow filter systematically change as a function of flow velocity.

At high flow velocities transport from the inlet channel into the porous wall is nearly entirely dominated by convection. This leads to uniform axial concentration profiles in the inlet and outlet channel and a steep gradient in the porous wall.

At low velocities radial transport into the porous wall is dominated by diffusive transport. This leads to a negligible radial concentration gradient between the inlet and the outlet channel.

Under most operating conditions relevant for an automotive exhaust catalyst the flow velocity is in an intermediate range with contributions of diffusive and convective transport.

The transition from entirely convection dominated transport at high space velocities to increasingly diffusion dominated transport at lower flow velocities is similarly found for first order kinetics and a generalized Langmuir–Hinshelwood–Hougen–Watson (LHHW) rate law.

Wall-flow filters show systematic conversion advantages over the conventional monolith for a first order reaction. For a reaction with LHHW-type kinetics this effect is not generally observed. It is one major result of this work that the relative performance of the two reactor configurations depends on the kinetics of the catalyzed reaction.     

Electron transfer across a conducting nanowire (nanotube)/electrolyte solution interface

The reduction of anions (considering hexacyanoferrate (III) as example) at charged conducting cylinders of nano-size, i.e., metal wires or carbon tubes, in contact with electrolyte solution is explored over a wide range of overpotentials. Two key parameters contributing to the current (solvent reorganization energy and work terms) are addressed in the framework of a quantum mechanical theory of electron transfer. It is argued that double layer effects play a crucial role and entail a significant rise of the current density as compared with plain metal electrodes. The stationary diffusion to a nanocylinder was found to proceed much faster, which results in an additional enhancement of the current. Some qualitative effects of the electron transfer across a conducting nanocylinder are discussed (in part, the appearance of an inverted Arrhenius plot).     

反渗透、纳滤过程的物理化学研究（Ⅱ） 多孔荷电膜的溶质分离规律

在多孔膜溶质的脱除率方程和溶液渗透通量方程的基础上由溶液电中性条件导出了荷电膜的单价电解质、中性分子混合溶液体系离子的脱除率方程,中性分子的脱除率方程,溶液渗透体积通量方程和离子、中性分子的浓缩比表达式。由方程的函数性质讨论了荷电膜的单价电解质、中性分子混合溶液的溶质组分脱除率和溶液渗透体积通量随离子浓度、pH值的变化规律。预测了盐和中性分子的脱除率和溶液渗透体积通量随浓度变化曲线出现极大和极小值的现象,由此得出了下列结果：随pH值的增加,单价电解质溶液的阳离子、阴离子和氢离子的脱除率变化顺序为由 R _M⁺ > R _X^- > R _H⁺变化到R _M⁺ =R _X^-> R _H⁺再变化到R _X^->R _M⁺> R _H⁺,离子脱除率变化曲线将出现极大和极小值;有机酸的总脱除率表达式阐明了文献中的可电离有机分子与pH值的关系式中参数的物理意义,解释了该关系式的对氨基苯甲酸水溶液的脱除率随pH值变化的拟合曲线高于脱除率实验值的原因,解释了对氨基苯甲酸的甲醇溶液的溶质脱除规律;离子的浓缩比依赖于料液中离子组成和离子所对应盐的浓缩比。     

Shear-induced transport of a particle layer along a porous wall

A theory is presented which describes the transport of a concentrated layer of particles along a porous wall under laminar flow conditions. A shear-induced hydrodynamic diffusion mechanism is proposed to describe the lateral migration of particles away from the porous wall as the layer is sheared. At steady state, the particle diffusion within the layer is balanced by the convective flux of particles toward the porous wall due to the fluid flow into the wall. This model predicts the nonlinear velocity and concentration profiles within the sheared particle layer, as well as the layer thickness and the wall concentration. In addition, a criterion is found for predicting whether or not a stagnant particle layer will form on the porous wall. The application of this theory to crossflow microfiltration is discussed.     

附加空气层的多层墙体热湿耦合非稳态传递模型及验证

为准确预测附加空气层的多层墙体内的温湿度分布和动态变化,研究多孔介质墙体内的热湿耦合非稳态传递规律,基于Luikov、Fick定律等基础传递理论,推导出热湿空气在墙体内部的瞬态耦合传递控制方程。通过对控制方程驱动势、方程项系数的改进,以空气含湿量和温度为驱动势,建立了建筑多孔介质墙体热湿耦合传递非稳态模型。采用有限容积法隐式差分格式设计了MATLAB模拟计算程序,设置相应的初始条件和边界条件,计算附加空气层的多层墙体内温度、湿度、传热和传湿量随时间变化的分布规律。最后,通过对比新建模型模拟结果与WUFI软件的模拟计算结果,验证了模型的准确性和可行性。     

Diffusiophoresis of a colloidal sphere in nonelectrolyte gradients in a circular cylindrical pore

The problem of the diffusiophoretic motion of a spherical particle in a fluid solution of a nonionic solute along the centerline of a circular cylindrical pore is studied theoretically in the quasisteady limit of negligible Reynolds and Peclet numbers. The imposed solute concentration gradient is uniform and parallel to the pore wall, which may be either impermeable to the solute molecules or prescribed with the far-field concentration distribution. The particle-solute interaction layer at the particle surface is assumed to be thin relative to the particle radius and to the particle-wall gap width, but the polarization effect of the diffuse solute in the thin interfacial layer caused by the strong adsorption of the solute is incorporated. The presence of the pore wall causes two basic effects on the particle velocity: first, the local solute concentration gradients on the particle surface are altered by the wall, thereby speeding up or slowing down the particle; secondly, the wall increases viscous retardation of the moving particle. To solve the equations of conservation of mass and momentum, the general solutions are constructed from the fundamental solutions in both cylindrical and spherical coordinates. The boundary conditions are enforced first at the pore wall by the Fourier transforms and then on the particle surface by a collocation technique. Numerical results for the diffusiophoretic velocity of the particle relative to that under identical conditions in an unbounded fluid solution are presented for various values of the relaxation parameter of the particle as well as the relative separation distance between the particle and the pore wall. The collocation results agree well with the approximate analytical solution obtained by using a method of reflections. The wall-corrected particle velocity depends on the surface properties of the particle, the ratio of particle-to-pore radii, and the solutal boundary condition at the wall. In general, the boundary effect on diffusiophoresis is quite significant and complicated.     

Numerical simulation of probing the electric double layer by scanning electrochemical potential microscopy

Computational modeling of probing the electric double layer (EDL) by scanning electrochemical potential microscopy (SECPM) was carried out in order to evaluate the applicability of this method. The modeling is based on a continuum approach for the electric double layer in dilute solution using the modified Poisson-Boltzmann equation. This model takes into account the finite ion size and prevents steric effects near the charged surface. The approach of the SECPM probe towards a charged electrode, immersed in electrolyte solution, is simulated obtaining the potential profile in the direction normal to the electrode. The effects of the shape and the size of the metallic protrusion at the apex of the probe were studied. A clear dependence of the probe potential on the apex geometry was observed, and correlated to the apex surface charge density distribution. The overlap of the EDLs located at the probe and the electrode is studied by setting different initial open circuit potentials, i.e., different charging, to the probe. We have found that the obtained potential profiles are consequences of the EDL overlap, characterized by an ionic distribution in the gap separating the probe and electrode. Depending on the strength of both EDLs and their polarity, the Debye screening effect severely influences the probe potential.     

Sherwood number in flow through parallel porous plates (Microchannel) due to pressure and electroosmotic flow

An expression for Sherwood number is developed from first principles for combined pressure‐driven and electroosmotic flow in a porous rectangular microchannel. This quantifies the mass transfer of an electrically neutral solute in the microchannel and is useful for designing microfluidic devices and porous media flows. The convective‐diffusive species balance equation, coupled with the velocity field, is solved within the mass transfer boundary layer utilizing similarity method. From the simulations, it is observed that the Sherwood number increases as the electric double layer near the channel wall becomes more compact (as manifested through a decrease in the Debye length), and it reaches a constant value around the scaled Debye length of 40. The Sherwood number becomes constant at higher Debye lengths as electrokinetic effects become negligible. A detailed analysis of dependence of Reynolds number, dimensionless permeation velocity, ratio of driving force and scaled Debye length on Sherwood number is presented. © 2011 American Institute of Chemical Engineers AIChE J, 58: 1693–1703, 2012     

Effect of mass transfer on the reaction rate in a monolithic catalyst with porous walls

The influence of reacting gas flow on the heterogeneous reaction in catalyst volume of honeycomb porous monolith with triangular channels was studied. The spatial distributions of the reacting gas flow, the rates of local mass transfer between channel walls and gas flow, as well as the interaction of transfer processes and a catalytic reaction were determined on the basis of the computational fluid dynamics. The reactions of deep oxidation and steam reforming of methane were considered as model reactions.It was shown that there is no stabilization of the reacting flow over the whole channel length under studied conditions. The most intensive changing of the gas streams appears near the channel inlet, which causes the highest local rates of interphase exchange processes, the rate difference is up to two orders of magnitude. A higher reaction rate exists in the initial part due to penetration of feed components into the catalyst volume through the frontal surface. This leads to increasing the effectiveness factor whose value is above unity near the channel inlet. The reaction rate limitation by the transport of reagents inside porous wall was observed along the monolith length.