thin film nonlinear differential equations linear stability non-linear stability
Issue Date:
2015
Publisher:
Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Citation:
Pliska Studia Mathematica Bulgarica, Vol. 25, No 1, (2015), 41p-54p
Abstract:
In this work the special case of free films of liquid (bounded by two interfaces between liquid and gas or liquid and two other liquids) is considered. The films are assumed to be viscous (Newtonian or non-Newtonian), with fully mobile interfaces (with unknown velocity, but with given shear stresses on the interfaces), laterally bounded (with fixed film thickness or fixed thickness gradient on the lateral boundaries), with planar located midsurface (symmetric interfaces with respect to the middle plane). Additional action of different forces on the interfaces is applied, such as capillary forces (through a constant or temperature/surfactant dependent surface tension), van der Waals forces, etc. Typical solutions of the nonlinear evolution equations are discussed. In the cases when the film static shapes exist (which depends on the combination of the different parameters), a linear and nonlinear stability analysis is also presented for them, when squeezing perturbations are applied on the shape itself, on the velocity or on the temperature, etc. 2010 Mathematics Subject Classification: 76E30, 76E17, 76A05, 76A20.
