Dynamics of free liquid films

Abstract

i. We will term a layer of viscous incompressible liquid moving in another liquid or gas a free film if its thickness h measured along the normal n to the mean surface F Ss small in comparison to the characteristic scale of motion while the gradients of velocity v and temperature 8 within the layer are finite as h + 0. The latter will be true if the viscosity and thermal conductivity coefficients of the external liquid do not exceed the corresponding characteristics of the film material. Then, in the first approximation, the position of the film may be specified by a two-dimensional surface F and its dynamics may be described by parameters distributed over F, assuming v and 8 to be continuous functions of the point in space x and time t everywhere (local thermodynamic equilibrium principle). In particular, Lagrangian coordinates for the film and enveloping phase can be defined, permitting use of a phenomenological approach to derivation of the equations of motion of r [i]. The basic principles of thermodynamics and theological relationships lead to a closed problem in dynamics of thin liquid films, containing within itself at h = 0 the problem of thermocapillary convection [2], while the thermodynamic relationships transform to the classical Gibbs conditions on an interphase boundary. The equations of motion of isothermal free films of viscous and elastoviscous liquids were derived in [3].