Abstract
Flows of a viscous incompressible liquid with a thermocapillary boundary are investigated numerically on the basis of the mathematical model that consists of the Oberbeck-Boussinesq approximation of the Navier-Stokes equations, kinematic and dynamic conditions at the free boundary and of the slip boundary conditions at solid walls. We assume that the constant temperature is kept on the solid walls. On the thermocapillary gas-liquid interface the condition of the third order for temperature is imposed. The numerical algorithm based on a finite-difference scheme of the second order approximation on space and time has been constructed. The numerical experiments are performed for water under conditions of normal and low gravity for different friction coefficients and different values of the interphase heat transfer coefficient.
Highlights
The problems of the fluid flows with a dynamic contact angle are very important at present
Flows of a viscous incompressible liquid with a thermocapillary boundary are investigated numerically on the basis of the mathematical model that consists of the OberbeckBoussinesq approximation of the Navier-Stokes equations, kinematic and dynamic conditions at the free boundary and of the slip boundary conditions at solid walls
We assume that the constant temperature is kept on the solid walls
Summary
The problems of the fluid flows with a dynamic contact angle are very important at present. The main question of such types of the problems relates to a non-consistency of the condition on the free boundary and the classical no-slip boundary condition on the solid wall in a neighborhood of the contact point. If the boundary walls of a liquid containing domain are moving with a constant speed, the contact angle is changing with the velocity [4, 5, 9]. Changing of this angle will depend on a character of thermal regimes on the free and solid boundaries. Interaction of the gravitational and thermocapillary convection and their influence on behavior of the contact angle and shape of the free boundary should be investigated
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