Effect of the evaporation action on the stability of a thin liquid layer in the Landau–Levich problem

Abstract

The stability of the liquid layer in the Landau–Levich problem is theoretically investigated in the presence of the evaporation effect from the free surface. The free energy of a thin layer of an incompressible fluid is the sum of the dispersion (van der Waals) interaction and the specific electrical interaction caused by the presence of double electric layers at both interphase boundaries. The stability of such a system with respect to perturbations is studied in the framework of the long – wave approximation in the system of Navier-Stokes equations. A stability map is provided for different values of the evaporation parameter. It is established that the stability of the system increases with an increase in the dimensionless number of evaporation.