Lubricated Immersed Boundary Method in Two Dimensions

Abstract

Many biological examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen and the intracellular trafficking of vesicles into dendritic spines, involve the near-contact of elastic structures separated by thin layers of fluid. Motivated by such problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We demonstrate 2nd-order accurate convergence for simple two-dimensional flows with known exact solutions to showcase the increased accuracy of this method compared to the standard immersed boundary method. Motivated by the phenomenon of wall-induced migration, we apply the lubricated immersed boundary method to simulate an elastic vesicle near a wall in shear flow. We also simulate the dynamics of a vesicle traveling through a narrow channel and observe the ability of the lubricated method to capture the vesicle motion on relatively coarse fluid grids.

35 pages, 11 figures

References in corpus (4)

• Non-inertial lateral migration of vesicles in bounded Poiseuille flow
• Forced transport of deformable containers through narrow constrictions
• Simulating flexible fiber suspensions using a scalable immersed boundary algorithm
• Active elastohydrodynamics of vesicles in narrow, blind constrictions

Cited by in corpus (7)

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• A sharp interface Lagrangian-Eulerian method for rigid-body fluid-structure interaction
• Coarse-graining the dynamics of immersed and driven fiber assemblies
• Influence of the vessel wall geometry on the wall-induced migration of red blood cells
• Eulerian simulation of complex suspensions and biolocomotion in three dimensions
• Parallel three-dimensional simulations of quasi-static elastoplastic solids
• On the additive chromatic number of several families of graphs