A discrete-forcing immersed boundary method with permeable membranes is developed to investigate the effect of lubrication on the permeations of solute and solvent through membrane. The permeation models are incorporated into the discretisation at the fluid cells including the membrane, and discretised equations for the pressure Poisson equation and convection–diffusion equation for the solute are represented with the discontinuities at the membrane. The validity of the proposed method is established by the convergence of the numerical results of the permeate fluxes (solute and solvent) to higher-order analytical models in a lubrication-dominated flow field. As a model of the mass exchange between inside and outside of a biological cell flowing in a capillary, a circular membrane is placed between parallel flat plates, and the effect of lubrication is investigated by varying the distance between the membrane and the walls. The pressure discontinuity near the wall is larger than that at the stagnation point, which is a highlighted effect of lubrication. In the case of a small gap, the solute transport is dominated by convection inside the circular membrane and by diffusion outside. Through the time variation of the concentration in the circular membrane, lubrication is shown to enhance mass transport from/to inside and outside the membrane.

开发了一种具有渗透膜的离散强迫浸入边界方法，以研究润滑对溶质和溶剂通过膜渗透的影响。渗透模型被纳入包括膜在内的流体单元的离散化中，压力泊松方程和溶质对流扩散方程的离散方程用膜处的不连续性表示。所提出方法的有效性是通过渗透通量（溶质和溶剂）的数值结果收敛到润滑主导流场中的高阶分析模型而建立的。作为在毛细管中流动的生物细胞内外质量交换的模型，圆形膜被放置在平行平板之间，通过改变膜和壁之间的距离来研究润滑效果。壁面附近的压力不连续性大于驻点处的压力不连续性，这是润滑作用的突出表现。在小间隙的情况下，溶质传输主要由圆形膜内部的对流和外部的扩散主导。通过圆形膜中浓度的时间变化，显示润滑增强了从/到膜内部和外部的质量传输。溶质运输主要由圆形膜内部的对流和外部的扩散主导。通过圆形膜中浓度的时间变化，显示润滑增强了从/到膜内部和外部的质量传输。溶质运输主要由圆形膜内部的对流和外部的扩散主导。通过圆形膜中浓度的时间变化，显示润滑增强了从/到膜内部和外部的质量传输。