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When immersed in solution, surface-active particles interact with solute molecules and migrate along gradients of solute concentration. Depending on the conditions, this phenomenon could arise from either diffusiophoresis or the Marangoni effect, both of which involve strong interactions between the fluid and the particle surface. We introduce here a numerical approach that can accurately capture these interactions, and thus provide an efficient tool to understand and characterize the phoresis of soft particles. The model is based on a combination of the extended finite element-that enable the consideration of various discontinuities across the particle surface-and the particle-based moving interface method-that is used to measure and update the interface deformation in time. In addition to validating the approach with analytical solutions, the model is used to study the motion of deformable vesicles in solutions with spatial variations in both solute concentration and temperature.

Phoretic motion of soft vesicles and droplets: an XFEM/particle-based numerical solution