Drainage of Foam Films

Abstract

A brief review of the classical theory of foam film drainage is presented as well as a new theory accounting for the effect of thickness non-homogeneities in the film developed by the film drainage. The science of foams is as old as classical mechanics since the first systematic study in this area has been carried out by Newton [1]. He has noticed that soap films, losing liquid in time, pass through various thicknesses with characteristic colors. When the thinning process advances black spots appear which are sometimes unstable and the film ruptures at their place. These structures are nowadays known as Newton's black films. During the next centuries the interest to thin liquid films (TLFs) has increased [2-4] due to their importance for disperse systems such as foams, emulsions and suspensions widely employed in technology. The stability of dispersions is directly related to the process of thinning and rupture of TLFs dividing bubbles, droplets and particles [5]. At present, intensive investigations are performed on foam films formed from aqueous solutions of surfactants with biological origin. Special attention [6] is paid to TLFs stabilized by phospholipides because of the important role of these substances in the structure of biological membranes and metabolism of the living cells. The simplest TLF system, a single microscopic foam film, has proven to be a useful tool for model investigations. In many aspects the results of such a study are applicable to other types of TLFs as well, e.g. emulsion films, films on solid and liquid substrata. The contemporary versions of the interferomertic method proposed by Scheludko and Exerowa [7] enable measurement of the local kinematics in time of the film thickness. It is a challenge presently for theoreticians to supply a detailed theory of the TLF drainage. Scheludko [8] has also proposed a formula for the thinning rate of horizontal microscopic films formed in the center of a double concave drop 3 Re 2 2 3 h p V V R     (1) where V is drainage velocity, h and R are the thickness and radius of the film, respectively,  is the dynamic viscosity and p  is the difference between the capillary and disjoining pressures. Equation (1) is analogous to an expression known as the Reynolds law [9] for the velocity