Fluid Coupling in Cross-Membrane Ion Transport
DescriptionWe propose to study ion transport between two flow regions separated by a porous membrane for arbitrary numbers of ions with arbitrary valences. This will serve as a model problem for numerous engineering and biological applications where cross-flow filtration is important. A major challenge in working on these types of problem is that there is a typically a huge discrepancy between the width of the bulk flow region and the width of the Debye layers. To avoid this problem we will use formal long-wavelength asymptotics to derive a one-dimensional system of equations that describe the flow and ionic concentrations in the bulk regions. We then plan to use matched asymptotic analysis to determine the solutions inside the porous membrane, and the Debye layers adjacent to the membrane. We thereby will obtain an effective macro-scale description of this challenging multi-scale problem. We expect that the macro-scale equations will be of mixed type, in which ion concentration, electric potential and fluid motions are fully-coupled. To examine the behaviour of these equations we will perform numerical simulations. In particular, we will determine the effects of the electric field on the ion transport between the two flow regions. Of particular interest to applications will be how an electric potential between two regions can enhance the cross-flow filtration. We will also determine how the effects of multiple ionic species, nonlinear active pumps across the membrane, and membrane curvature modify the dynamics.
|Effective start/end date||1/01/22 → …|