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Numerical modeling of the dynamics of soft particles in microchannel flows

Abstract : Vesicles are a model system for understanding the dynamical behavior of a closed soft particle such as red blood cells (RBCs) in flows. The inextensible lipid bilayer membrane of a vesicle admits resistance to the bending elasticity, and its large surface-area-to-volume ratio allows the vesicle to exhibit remarkable shape changes in the dynamics even in a simple flow. Significant progress has been made over the past decades in understanding vesicle dynamics in unbounded Stokes flows. This manuscript deals with the numerical investigation of shape transition and lateral migration of 3D vesicles in wall-bounded Stokes flows by means of an isogeometric finite-element method (FEM) and boundary-element method (BEM). Starting from a previously reported isogeometric FEM-BEM simulations of the dynamics of soft particles (drops, capsule, and vesicle) in Stokes flows in free space, the original code is developed to account for microchannel walls of arbitrary cross-section. The present work focuses on the dynamics of a vesicle that is transported through a circular tube in a pressure-driven flow. First, we investigate typical vesicle shapes, different lateral migration modes, and flow structure onto vesicle membrane versus three independent dimensionless parameters, namely, the reduced volume, the confinement, and the (bending) capillary number. Shape transitions and the phase diagram of stable shapes for several reduced volumes are obtained in the (confinement, capillary number) space, showing an extension of the set of vesicle morphologies and rich vesicle dynamics owing to the intricate interplay among the tube wall, hydrodynamic stresses, and membrane bending. Secondly, we study, via an axisymmetric BEM, the hydrodynamics under high confinements in which the shape of the vesicle is expected to maintain axisymmetry. A particular emphasis is given to the prediction of the vesicle mobility and the extra pressure drop caused due to the presence of the vesicle, the latter having implications in the rheology of a dilute suspension. In addition, based on the numerical results of limiting behavior of quantities of interest near maximal confinement, we give various scaling laws to infer, for example, the vesicle velocity, its length, and the thickness of lubrication film. Finally, we present a coupled, hybrid continuum–coarse-grained model for the study of RBCs in fluid flows. This model is based on a combination of the vesicle model with a network of springs with fixed connectivity, representing the cytoskeleton. Numerical results show that this two-component vesicle–cytoskeleton model isable to extract the mechanical properties of RBCs and predict its dynamics in fluid flows.
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Jinming Lyu. Numerical modeling of the dynamics of soft particles in microchannel flows. Mechanics of the fluids [physics.class-ph]. Ecole Centrale Marseille, 2019. English. ⟨NNT : 2019ECDM0002⟩. ⟨tel-02519793⟩

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