Mathematical modeling and numerical simulation of surface tension-driven two-phase flows without and with evaporation

The thermal Marangoni effect is an efficient and ecological way of enhancing heat and mass transfer in two-phase flows. The hydrodynamics of the resulting thermocapillary flow exhibits sensitive dependence on the interfacial thermal condition and on the fluid properties, which is mostly expressed by the Marangoni number. As a result, the enhancement of heat and mass transfer is usually accompanied and affected by different phenomena, e.g. pattern formation in Bénard-Marangoni instability, rupture of thin non-uniformly heated liquid film etc. Due to the limitated insights from experimental results and due to the weaknesses in many theoretical models – such as the simplification of a fixed planar fluid interface in the thin-film model, for instance, which causes some scope of uncertainty regarding the conditions to apply – a DNS of thermocapillary flow with dynamically deformable interface is often desired.

A continuum mechanical sharp interface model containing the two-phase continuity, Navier-Stokes and energy equations with suitably formulated jump conditions at the phase interface for incompressible fluids is established for numerical solution using finite volume discretisation. The fluid interface is captured using an extended VOF method with additional piecewise linear interface reconstruction. For a high accuracy which is essential for simulation of thermocapillary flow the numerical Marangoni force is calculated from an additional interface-temperature field resulting from the energy jump condition at the interface. In order to take into account phase change, further refinement of the computation of interfacial thermal condition is under development. A two-scalar ghost-fluid heat transfer model is being developed to fulfill the requirement on accuracy.

The method is validated quantitatively for thermocapillary migration of a droplet and qualitatively for the Bénard-Marangoni instability w.r.t. number and form of cell formation. Film rupture of a non-uniformly heated thin liquid film and Marangoni convection in a thin film on structured substrate can be simulated using the single field approach and will be quantitatively investigated using the more accurate 2-scalar method.

Multi-Physics, thermocapillary flows, multiphase flows, DNS, Volumen of Fluid

Chen Ma

Dipl.-Tech.-Math.

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