Isogeometric Analysis of Vesicle Hydrodynamics: A Study on Single Vesicles and Vesicle-Vesicle Interactions using Phase-Field Models
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This talk explores isogeometric analyses of vesicle hydrodynamics, focusing on single-vesicle hydrodynamics and vesicle-vesicle interactions using phase-field models. In the first study, the focus is on inextensible vesicles subjected to external fluid flow with inertial forces. Adopting the phase-field model introduced by Aland et al. (2014), the coupled fluid-vesicle problem is addressed with the enforcement of global area and volume constraints using a Lagrange multiplier method. A specialized equation ensures the local inextensibility condition. The full Navier-Stokes equations are considered, and a finite element formulation is introduced through a residual-based variational multiscale method, while standard Galerkin finite elements are applied to other partial differential equations in the model. A monolithic solution scheme based on the generalized-α time integration method is employed, leveraging the high continuity of NURBS functions to reduce the equation-solving complexity. The algorithm is extended to three-dimensional problems, and various two-dimensional scenarios, including vesicle dynamics in quiescent fluid, shear flow, and plane Poiseuille flow with and without obstructions, are investigated. In the second study, the hydrodynamics of vesicle doublets suspended in an external viscous fluid flow are examined. Short-range repulsion between vesicles is maintained through an interaction energy functional to prevent overlap. Vesicle evolution is captured through two advection equations. The study explores vesicle doublet hydrodynamics in various flow scenarios, revealing dynamic phenomena such as tank-threading, locking, doublet separation, sliding, and shape transformation in tubular channels based on fluid flow profiles and domain configurations.