Transient electrokinetic (EK) flows involve the transport of conductivity gradients developed as a result of mixing of ionic species in the fluid, which in turn is affected by the electric field applied across the channel. The presence of three different coupled equations with corresponding different time scales makes it difficult to model the problem using the lattice Boltzmann method (LBM). The present work aims to develop a hybrid LBM and finite difference method (FDM)-based model which can be used to study the electro-osmotic flows (EOFs) and the onset of EK instabilities using an Ohmic model, where fluid and conductivity transport are solved using LBM and the electric field is solved using FDM. The model developed will be used to simulate three different problems: (i) EOF with varying zeta-potential on the wall, (ii) similitude in EOF, and (iii) EK instabilities due to the presence of conductivity gradients. Problems (i) and (ii) will be compared with the analytical results and problem (iii) will be compared with the simulations of a spectral method-based numerical model. The results obtained from the present simulations will show that the developed model is capable of studying transient EK flows and of predicting the onset of instability.

中文翻译：

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基于全耦合混合格子玻尔兹曼和有限差分法的瞬态动电流研究


瞬态动电 (EK) 流涉及由于流体中离子物质混合而产生的电导率梯度的传输，而电导率梯度又受到跨通道施加的电场的影响。具有相应不同时间尺度的三个不同耦合方程的存在使得很难使用格子玻尔兹曼方法（LBM）对问题进行建模。目前的工作旨在开发一种基于 LBM 和有限差分法 (FDM) 的混合模型，该模型可用于使用欧姆模型研究电渗流 (EOF) 和 EK 不稳定性的发生，其中流体和电导率传输是使用 LBM 求解，使用 FDM 求解电场。开发的模型将用于模拟三个不同的问题：（i）壁上具有不同 zeta 电位的 EOF，（ii）EOF 的相似性，以及（iii）由于电导率梯度的存在而导致的 EK 不稳定性。问题（i）和（ii）将与分析结果进行比较，问题（iii）将与基于光谱方法的数值模型的模拟进行比较。从目前的模拟中获得的结果将表明，所开发的模型能够研究瞬态 EK 流并预测不稳定的发生。