Abstract
ABSTRACTTo understand the lubrication-dominated permeation through a membrane, numerical simulations of permeation through a moving corrugated permeable membrane is carried out with a fully validated numerical method. Through comparisons between the numerical results and the results of an asymptotic analysis of permeate flux (under an infinitesimal permeability condition) using Reynolds lubrication equation, the effect of permeation on lubrication and its inverse effect (i.e., the dependence of permeation on lubrication) are discussed. The linear and non-linear dependences of the relaxation of the lubrication pressure due to membrane permeation are identified. The effect of the tangential component of the permeate flux is evaluated by a linear analysis, and the limitation of Reynolds-type lubrication is discussed.
Highlights
Mass transfer through a selective permeable membrane is typically observed in biological environments, for example, oxygen transport by red blood cells (RBCs), gas exchange in the alveoli, and nutrient absorption
The above consistent direct discretisation for the DFIB method is a suitable approach for membrane permeation, as the pressure fields on both sides reflect the local incompressible conservation at a cell level, which results in a sharp representation of the interface
Observed from the frame on the membrane for two different non-dimensional permeabilities (L) and three different corrugation amplitude parameters (δ). For both L cases, the locally developed Couette flows for the smallest amplitude case (δ = 0.1) suggest that the Reynolds lubrication may hold reasonably in the regions away from the membrane
Summary
Mass transfer through a selective permeable membrane is typically observed in biological environments, for example, oxygen transport by red blood cells (RBCs), gas exchange in the alveoli, and nutrient absorption. In view of handling the relative motion of spherical membranes (equivalent diameter Dp), a fixed fluid mesh system that is non-conforming to the membrane surface is often employed, and the lubrication pressure in a narrow gap of arbitrary non-spherical geometry is described. Considering feasible computational mesh size, the above geometric and dynamic assumptions for the Reynolds lubrication equation strongly restricts the applicability of the equation to model particle-induced flows [11] in the inter-particle region, where non-Reynolds lubrication effect becomes predominant. Another reason may be the difficulty in performing numerical simulation of the trans-membrane flux. The dependence of permeate flux on the lubrication pressure as well as the effect of permeation on lubrication are discussed for several corrugation amplitudes and permeation coefficients
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