Numerical investigation of a dependence of the dynamic contact angle on the contact point velocity in a problem of the convective fluid flow

A two-dimensional problem of the fluid flows with a dynamic contact angle is studied in the case of an uniformly moving contact point. Mathematical modeling of the flows is carried out with the help of the Oberbeck–Boussinesq approximation of the Navier–Stokes equations. On the thermocapillary free boundary the kinematic, dynamic conditions and the heat exchange condition of third order are fulfilled. The slip conditions (conditions of proportionality of the tangential stresses to the difference of the tangential velocities of liquid and wall) are prescribed on the solid boundaries of the channel supporting by constant temperature. The dependence of the dynamic contact angle on the contact point velocity is investigated numerically. The results demonstrate the contact angle behavior and the different flow characteristics with respect to the various values of the contact point velocity, friction coefficients, gravity acceleration and an intensity of the thermal boundary regimes.