Simulation of Osmotic Swelling by the Stochastic Immersed Boundary Method

We develop computational methods for the simulation of osmotic swelling phenomenarelevant to microscopic vesicles containing transformable solute molecules. We introduce StochasticImmersed Boundary Methods (SIBM) that can capture osmotically driven fluid transport throughsemi-permeable elastic membranes subject to thermal fluctuations. We also develop numerical meth-ods to handle within SIBM an elastic shell model for a Neo-Hookean material. Our extended SIBMallows for capturing osmotic swelling phenomena driven by concentration changes and interactionsbetween a discrete collection of confined particles while accounting for the thermal fluctuations of thesemi-permeable membrane and the hydrodynamic transport of solvent. We use our computationalmethods to investigate osmotic phenomena in regimes that go beyond the classical van’t Hoff theory.We develop statistical mechanics theories for osmotic swelling of vesicles when there are significant in-teractions between particles that can transform over time. We validate our theoretical results againstdetailed computational simulations. Our methods are expected to be useful for a wide class of appli-cations allowing for the simulation of osmotically driven flows, thermally fluctuating semi-permeableelastic structures, and solute interactions.