Osmotic forces and solute diffusion are increasingly seen as playing a fundamental role in cell movement. Here, we present a numerical method that allows for studying the interplay between diffusive, osmotic and mechanical effects. An osmotically active solute obeys a advection–diffusion equation in a region demarcated by a deformable membrane. The interfacial membrane allows transmembrane water flow which is determined by osmotic and mechanical pressure differences across the membrane. The numerical method is based on an immersed boundary method for fluid–structure interaction and a Cartesian grid embedded boundary method for the solute. We demonstrate our numerical algorithm with the test case of an osmotic engine, a recently proposed mechanism for cell propulsion.
Bibliographical noteFunding Information:
We thank Sean Sun, Alex Mogilner and Aaron Fogelson for useful discussion. This work was supported by NSF DMS-1620198 to L.Y. and NSF DMS-1620316 to Y.M.
© 2017 Elsevier Inc.
- Advection diffusion
- Cartesian grid embedded boundary method
- Fluid structure interaction
- Immersed boundary method