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We report on a novel formulation of a phase-field model which incorporates order parameters with preserved volume representing cells and particles evolving in a system such that the interfacial energy decreases. In our model, an anti-forcing free energy density is defined to fulfill constraints on selected volume fractions by counterbalancing phase changes. Cells are defined as regions with energy bearing boundaries that may differ in their physical states. The model is coupled with a Lattice-Boltzmann method to describe the motion of cells in a flow field. We show 2D and 3D simulation results of equilibrium shapes, of the dynamics of cells in a flow field and study the interaction of cells among each other and of cells with the vein wall for different types of wall bifurcations. Based on the results the coupled phase-field and Lattice Boltzmann model may serve as a framework to investigate phenomena such as the merging and agglomeration of cells in veins. |
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