An immersed boundary method for mass transfer through porous biomembranes under large deformations

In this paper, a novel immersed boundary method for modeling convection and diffusion of mass transfer through porous membranes under large deformations is proposed. An algebraic function consisted of transmembrane velocity and diffusion coefficient of membrane is derived for modeling local concentration jumps across porous membranes. An additional equation is introduced to describe the temporal evolution of diffusive flux. Numerical validations show that the present method is robust to predict the concentration field under various fluid-porous membrane coupling conditions such as membrane oscillations in an elastic force driven flow, tank-treading and swinging motion of red blood cells in simple shear flow, and parachuting motion when cells squeeze in narrow channels down to 4 micrometers. The conservations of mass and volume in single cell are examined, and the relative errors of mass conservation are negligible. Numerical results suggest that the proposed method is capable of predicting mass transfer through porous membranes while providing detailed hydrodynamics around cells in micro-circulatory systems. (C) 2020 Elsevier Inc. All rights reserved.