Solitary waves and solitons in liquid films

Abstract

We consider weakly dispersive and weakly nonlinear surface waves on liquid films in which long-range interaction forces are operative. As a first approximation, disturbances on both interfaces of the film can be described as a superposition of symmetrical and antisymmetrical waves even when considering nonlinearities. For small, but finite amplitudes, the antisymmetrical waves are free of nonlinearities, whereas for the symmetrical ones a Korteweg–de Vries equation can be derived. Depending on the particular thickness dependence of the long-range interaction forces the symmetrical disturbances lead to solitary waves with negative amplitudes (holes) or with positive amplitudes (intumescences). Taking as an example a soap film, with electrical double layer and London–van der Waals forces as interaction phenomenon, it is shown that observable solitons can be expected. It is put forward that the theory, presented here, is a contribution towards framing more sophisticated theories of liquid film (in)stability.