Impact of the interface heat defect on the thermocapillary response of the phase boundary in a liquid–gas system upon local heating from below

Abstract

The problem of thermocapillary convection induced by local boundary heating in a closed cell filled with a volatile liquid and an overlying gas–vapor mixture is studied. The mathematical model is based on the Boussinesq approximation of the nonstationary Navier – Stokes equations for a viscous incompressible fluid. It includes the heat balance condition on the liquid–gas contact boundary in a generalized form to correctly take into account effects of thermodiffusion and evaporation as well as energy characteristics of the surface which govern the thermocapillary response of the interface. Numerical simulation is carried out in order to ascertain the influence of the heat defect on the amplitude of interface deformations and evolution of convective regimes upon heating by thermal sources embedded in the cuvette substrate. A comparative analysis of the results obtained within the frame of classical and generalized problem statements enables to estimate the impact of energy spent by the Marangoni force to deform the interface: the effect results in a decrease in the depth of a thermocapillary dimple in the zone of thermal load and in the amplitude of phase boundary oscillations.