Phase-field Navier–Stokes model for vesicle doublets hydrodynamics in incompressible fluid flow

Abstract

In this paper, we study the hydrodynamics of a vesicle doublet suspended in an external viscous fluid flow. Vesicles in this study are modeled using the phase-field model. The bending energy and energies associated with enforcing the global volume and area are considered. In addition, the local inextensibility condition is ensured by introducing an additional equation to the system. To prevent the vesicles from overlapping, we deploy an interaction energy definition to maintain a short-range repulsion between the vesicles. The fluid flow is modeled using Navier–Stokes equations under the assumption of incompressible flows, and the vesicle evolution in time is modeled using two advection equations describing the process of advecting each vesicle by the fluid flow. Rather than solving the velocity–pressure saddle point system, we apply the Residual-Based Variational MultiScale (RBVMS) method to Navier–Stokes equations and solve the coupled systems monolithically using isogeometric analysis. We study vesicle doublet hydrodynamics in shear flow, planar extensional flow, and parabolic flow under various configurations and boundary conditions. Based on the fluid flow profile and domain configuration, we have observed various dynamics like tank-threading, locking, doublet separation, sliding, and shape transformation in tubular channels.