The point ion modified Poisson–Boltzmann theory for a planar electric double layer with different permittivities for the electrode,inner layer and diffuse layer

The planar electric double layer is modelled by an electrode, inner layer and diffuse layer whose constant permittivities differ. A point ion modified Poisson–Boltzmann analysis is made of the model with the ions in the diffuse layer having a distance of closest approach to the electrode, which is greater than the inner layer thickness and mimics the ion radius of a primitive model electrolyte. Comparisons are made with existing Monte Carlo simulations for uncharged and charged electrodes. For 1:1 and 2:1 electrolytes with a charged electrode, the modified Poisson–Boltzmann theory successfully predicts the singlet ion normalised density functions and the mean electrostatic potential. With the uncharged electrode, the neglect of ion size is more critical and the theoretical predictions are now poor at the higher concentrations.     

Density functional theory study on ion adsorption and electroosmotic flow in a membrane with charged cylindrical pores†

ABSTRACT

Ion adsorption and electroosmotic flow induced by an external electric field have a variety of practical applications, especially for membrane technology. In this work, a partially perturbative density functional theory (DFT) based on the modified fundamental measure theory was applied to investigate the ion density distributions and partitions in a charged cylindrical pore. Different types of electrolyte solutions, including both charge symmetric and asymmetric, were examined using the proposed theory with various pore diameters, bulk densities, ion valencies and surface charge densities. The ion concentration profiles calculated with the theory exhibit good agreements with the results of the Monte Carlo simulations, while the results of the Poisson–Boltzmann equation deviate greatly especially for the high valence electrolytes in narrow cylindrical pores. Some interesting phenomena discovered in both experiments and simulations, such as the reverse distribution of the ions and charge inversion, can be well reproduced with the DFT. Based on the ion concentration distributions obtained from the DFT, the transient velocity profiles of the electroosmotic flow in the charged cylindrical nanopores were calculated with the Navier–Stokes (NS) equation. The characteristics of the electroosmotic flow were discussed under the different bulk electrolyte concentrations and thickness of the electric double layer inside the nanopore. The enhancement of the velocity near the pore wall, which cannot be described by the traditional theory, was well characterised by the DFT combined with the NS equation.     

Structure of a planar electric double layer containing size-asymmetric ions: density functional approach

We have studied the structure of the electrolytes with asymmetries in charge and size near a charged planar electric double layer by a density functional theory. In the present theory, the hard-sphere contribution has been approximated as the direct pair correlation function with the coupling parameter, whereas the electronic contribution has been approximated as the mean-spherical approximation in the bulk phase. This theoretical approach for the size-symmetric and size-asymmetric electrolytes displays a good agreement with the simulation results over a wide range of surface charge densities and electrolyte concentrations. However, the accuracy between the present theory and the simulation results slightly deteriorates for the highly size-asymmetric electrolytes and the multivalent electrolytes. In these cases, the performance of the present theory is comparable to those of the simplified extension of the Poisson–Boltzmann theory and the modified Poisson–Boltzmann theory. The calculated result indicates that the surface charge distribution function, which was introduced as an indicator for studying the charge reversal, layering effect, and surface charge amplification in a planar electric double layer, describes the electronic properties of a planar electric double layer well.     

Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation

~~Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation1. Feynman, R., There's plenty of room at the bottom, Journal of Microelectromechanical Systems, 1992, 1: 60 -66. 2. Piekos, E. S., Breuer, K. S., Numerical modeling of micromechanical devices using the direct simulation Monte Carlo method, Transactions of the ASME, Journal of Fluids Engineering, 1996, 118: 464-469. 3. Beskok, A., Karniadakis, G. E., Trimmer, W., Rarefaction and …     

Hydrodynamics within the electric double layer on slipping surfaces

We show, using extensive molecular dynamics simulations, that the dynamics of the electric double layer (EDL) is very much dependent on the wettability of the charged surface on which the EDL develops. For a wetting surface, the dynamics, characterized by the so-called zeta potential, is mainly controlled by the electric properties of the surface, and our work provides a clear interpretation for the traditionally introduced immobile Stern layer. In contrast, the immobile layer disappears for nonwetting surfaces, and the zeta potential deduced from electrokinetic effects is considerably amplified by the existence of a slippage at the solid substrate.     

Modeling electrokinetic flows by the smoothed profile method

We propose an efficient modeling method for electrokinetic flows based on the smoothed profile method (SPM) 1, 2, 3 and 4 and spectral element discretizations. The new method allows for arbitrary differences in the electrical conductivities between the charged surfaces and the surrounding electrolyte solution. The electrokinetic forces are included into the flow equations so that the Poisson–Boltzmann and electric charge continuity equations are cast into forms suitable for SPM. The method is validated by benchmark problems of electroosmotic flow in straight channels and electrophoresis of charged cylinders. We also present simulation results of electrophoresis of charged microtubules, and show that the simulated electrophoretic mobility and anisotropy agree with the experimental values.     

微尺度振荡Couette流的格子Boltzmann模拟

采用有效多松弛时间-格子Boltzmann方法(Effective MRT-LBM)数值模拟了微尺度条件下的振荡Couette和Poiseuille流动. 在微流动LBM中引入Knudsen边界层模型,对松弛时间进行修正. 模拟时平板或外力以正弦周期振动,Couette流中考虑了单平板振动、上下板同相振动这两类情况. 研究结果表明,修正后的MRT-LBM模型能有效用于这类非平衡的微尺度流动模拟;对于Couette流,随着Kn数的增大,壁面滑移效应变得越明显. St越大,板间速度剖面的非线性特性越剧烈;两板同相振荡时,若Kn,St均较小,板间流体受到平板拖动剪切的影响很小,板间速度几乎重叠在一起;在振荡Poiseuille流动中,St数增大到一定值时,相位滞后现象减弱;相对于Kn数,St数对振荡Couette 和Poiseuille流中不同位置处速度相位差的产生有较大影响. 关键词： 格子Boltzmann方法 有效MRT模型 Knudsen层 振荡流     

Local Well-Posedness of Vlasov–Poisson–Boltzmann Equation with Generalized Diffuse Boundary Condition

Journal of Statistical Physics - The Vlasov–Poisson–Boltzmann equation is a classical equation governing the dynamics of charged particles with the electric force being self-imposed. We...     

Lattice-Boltzmann Simulations of Fluid Flows in MEMS

The lattice Boltzmann model is a simplified kinetic method based on the particle distribution function. We use this method to simulate problems in MEMS, in which the velocity slip near the wall plays an important role. It is demonstrated that the lattice Boltzmann method can capture the fundamental behaviors in micro-channel flow, including velocity slip, nonlinear pressure drop along the channel and mass flow rate variation with Knudsen number. The Knudsen number dependence of the position of the vortex center and the pressure contour in micro-cavity flows is also demonstrated.     

Dynamics of a self-propelled particle under different driving modes in a channel flow

In this paper, a model that combines the lattice Boltzmann method with the singularity distribution method is proposed to simulate a self-propelled particle swimming(exhibiting translation and rotation) in a channel flow. The results show that the velocity distribution for a self-propelled particle swimming deviates from a Maxwellian distribution and exhibits highvelocity tails. The influence of an eccentric potential doublet on the translation velocity of the particle is significant. The velocity decay process can be described using a double exponential model form. No large differences in the velocity distribution were observed for different translation Reynolds numbers, rotation Reynolds numbers, or regular intervals.     

Liquid Flow in a Porous Channel with Electrokinetic Effects

In this paper, a fully developed laminar flow in a porous channel between two paralleled flat plates in the presence of a double layer electric field is analyzed. The linear Poisson-Boltzmann equation is suggested to model the double layer electric field near the solid-liquid interface. The equation of motion is extended by including the electrical body force generating from the double layer field and then solved analytically. Different from previous models, our proposed one is continuous in the whole flow field and matches commonly-accepted models in the field of fluid mechanics. Besides, the effects of various physical parameters such as the zeta potential, the electrokinetic separation distance, and the ratio of the streaming current to conduction current on the velocity, the pressure, the apparent viscosity of the fluid, as well as the streaming potential are discussed. Physical explanations on the changing trends of those physical quantities with various parameters are given.     

Liquid Flow in a Porous Channel with Electrokinetic Effects

In this paper, a fully developed laminar flow in a porous channel between two paralleled flat plates in the presence of a double layer electric field is analyzed. The linear Poisson-Boltzmann equation is suggested to model the double layer electric field near the solid-liquid interface. The equation of motion is extended by including the electrical body force generating from the double layer field and then solved analytically. Different from previous models, our proposed one is continuous in the whole flow field and matches commonly-accepted models in the field of fluid mechanics.Besides, the effects of various physical parameters such as the zeta potential, the electrokinetic separation distance, and the ratio of the streaming current to conduction current on the velocity, the pressure, the apparent viscosity of the fluid,as well as the streaming potential are discussed. Physical explanations on the changing trends of those physical quantities with various parameters are given.     

Effective charge of a macroparticle in a non‐isothermal plasma within the Poisson–Boltzmann model

The electrostatic potential distribution around a charged, spherical, finite‐size macroparticle in a non‐isothermal plasma‐like medium is studied numerically within the Poisson–Boltzmann model. It is assumed that plasma consists of electrons and one species of singly charged ions. The effective charge of a macroparticle is calculated and its dependence on the electron to ion temperature ratio as well as on the particle radius and bare charge is considered. Numerical results for the effective charge in an isothermal plasma are compared with known analytical expressions.     

The effect of surface roughness on rarefied gas flows by lattice Boltzmann method

This paper studies the roughness effect combining with effects of rarefaction and compressibility by a lattice Boltzmann model for rarefied gas flows at high Knudsen numbers. By discussing the effect of the tangential momentum accommodation coefficient on the rough boundary condition, the lattice Boltzmann simulations of nitrogen and helium flows are performed in a two-dimensional microchannel with rough boundaries. The surface roughness effects in the microchannel on the velocity field, the mass flow rate and the friction coefficient are studied and analysed. Numerical results for the two gases in micro scale show different characteristics from macroscopic flows and demonstrate the feasibility of the lattice Boltzmann model in rarefied gas dynamics.     

Consistent lattice Boltzmann method

Lack of energy conservation in lattice Boltzmann models leads to unrealistically high values of the bulk viscosity. For this reason, the lattice Boltzmann method remains a computational tool rather than a model of a fluid. A novel lattice Boltzmann model with energy conservation is derived from Boltzmann's kinetic theory. Simulations demonstrate that the new lattice Boltzmann model is the valid approximation of the Boltzmann equation for weakly compressible flows and microflows.     

变像管相机中空间电荷效应的统计动力学分析

 从Boltzmann积分微分方程出发推出了保守势场中电子数密度按势能的分布规律,即Boltzmann统计分布。以此为基础,从统计动力学的角度详细分析了变像管相机中超短电子脉冲内部的空间电荷效应,通过求解Poisson方程得出了表征空间电荷效应的两个特征参量：空间电荷密度分布函数和速度分布函数,并对其按电位的动态变化规律进行了定性讨论。结果表明,限制变像管中的低电位区域和其中光电子脉冲从高电位向低电位传输的区域都将有助于优化整个变像管的性能。同时也重新讨论了光电阴极附近强加速场对光电子脉冲时间弥散的抑制作用,最终确定了其物理机制为不等位区间中电子脉冲空间分布的高度集中性。     

Space charge generation in flows of weakly conductive media with large difference of charged particles' mobilities

Electrification in boundary domains of flows of partially ionized multicomponent gas mixtures through channels whose conducting walls are exposed to a constant potential is studied. In such media, in the absence of applied electric fields, electrification is due to significantly different values of mobility of charged particles of opposite signs. The influence of the interaction of electrons and gas ions with the walls of the channel on the value of the space electric charge, the thickness and structure of the charged boundary layer and the value of the convective electric current is analyzed.     

Nonextensive statistics in viscous fingering

Measurements in turbulent flows have revealed that the velocity field in nonequilibrium systems exhibits q-exponential or power-law distributions in agreement with theoretical arguments based on nonextensive statistical mechanics. Here we consider Hele–Shaw flow as simulated by the lattice Boltzmann method and find similar behavior from the analysis of velocity field measurements. For the transverse velocity, we obtain a spatial q-Gaussian profile and a power-law velocity distribution over all measured decades. To explain these results, we suggest theoretical arguments based on Darcy's law combined with the nonlinear advection–diffusion equation for the concentration field. Power-law and q-exponential distributions are the signature of nonequilibrium systems with long-range interactions and/or long-time correlations, and therefore provide insight to the mechanism of the onset of fingering processes.