In this work, we contribute to the development of numerical algorithms for the direct simulation of three-dimensional incompressible multiphase flows in the presence of multiple fluids and solids. The volume of fluid method is used for interface tracking, and the Brinkman penalization method is used to treat solids; the latter is assumed to be perfectly superhydrophobic or perfectly superhydrophilic, to have an arbitrary shape, and to move with a prescribed velocity. The proposed algorithm is implemented in the open-source software Basilisk and is validated on a number of test cases, such as the Stokes flow between a periodic array of cylinders, vortex decay problem, and multiphase flow around moving solids.

We perform high-resolution numerical simulations of three-dimensional dynamics of an elongated bubble in a microchannel at moderate Reynolds numbers up to 1800. For this purpose, we use the coupled Brinkman penalization and volume of fluid methods implemented in the open-source framework Basilisk. The new results are validated with available experimental data and compared with previous numerical and theoretical predictions. We extend existing results to regimes with significant inertia, which are characterized by intense deformations of the bubble, including cases with azimuthal symmetry breaking. Various dynamical features are analyzed in terms of their spatiotemporal characteristics, such as frequencies and wavelengths of the bubble surface undulations and vortical structures in the flow.