Numerical modeling of thermocapillary two-phase flows using a two-scalar approach for heat transfer

A one-field model is derived from the sharp interface continuum mechanical balances for two-phase evaporative and thermocapillary flows. Emphasis is put on a clear distinction of the different velocities at the interface which appear due to phase transfer. The one-field model is solved numerically within a Finite Volume scheme and the interface is captured using an extended Volume of Fluid method, where the interface is reconstructed linearly with the PLIC technique. The numerical heat transfer is based on a two-scalar approach where two separate temperature fields are used for the temperature inside the two phases. This results in an accurate treatment of the interfacial heat transfer, specifically the interface temperature which is crucial numerically, both for evaporation and thermocapillarity. The method is validated for two-phase heat conduction, with analytical solution in case of no evaporation and with experimental measurement in case of incorporated evaporation effect. The method is applied to realistic cases dealing with non-uniformly heated thin liquid films, i.e. liquid films on (i) structured heated substrates and (ii) locally heated substrates. The numerical predictions in terms of flow pattern, surface deformation, temperature and velocity are compared with experiments conducted at the Université Libre de Bruxelles for (i) and at the Technische Universität Darmstadt for (ii). Qualitative agreement is achieved and shows the potential of this approach to simulate thermocapillary flows with dynamically deformable interfaces combined with evaporation