Implementation of a flexible and modular multiphase framework for the analysis of surface-tension driven flows based on a L-S VOF approach

The mathematical modelling and numerical simulation of multi-phase flows are both a demanding and highly complex exercise. In typical problems with industrial relevance, the fluids are often in non-isothermal conditions and interfacial phenomena are a relevant part of the problem. A number of effects due to the presence of temperature differences must be adequately taken into account to make the results of numerical simulations consistent and realistic. Moreover, in general, gradients of surface tension at the interface separating two liquids are a source of numerical issues that can delay (and even prevent completely in some circumstances) the convergence of the solution algorithm. Here, we propose a fundamental and concerted approach for the simulation of the typical dynamics resulting from the presence of a dispersed phase in an external matrix in nonisothermal conditions based on the modular computer-aided design, modelling, and simulations capabilities of the OpenFOAM environment. The resulting framework is tested against the migration of a droplet induced by thermocapillary effects in the absence of gravity. The simulations are fully three-dimensional and based on an adaptive mesh refinement (AMR) strategy. We describe in detail the countermeasures taken to circumvent the problematic issues associated with the simulation of this kind of flows.