Evolution of Time Periodic Perturbations on Films Falling Down Walls

Abstract

The research on the stability of films falling down walls has recently been the attraction of many scientists due to its practical importance and because of the many challenging problems it still presents not only from the theoretical but also from the experimental point of view. A model non-linear evolution equation which describes the film stability is the Benney equation (BEQ) Benney (1966). The BEQ has been investigated theoretically by Gjevik (1970), Nakaya (1975), Krishna and Lin (1977), Pumir et al. (1983), Chang (1989), Nakaya (1989), Joo et al. (1991a,b), Joo and Davis (1992a,b) and Liu and Gollub (1994). In all these papers the temporal growth of the perturbations is examined in the reference frame of the laboratory. A different point of view was presented by Deissler et al. (1991) for waves of the Kuramoto-Sivashinsky equation (KSEQ). Making a distinction between convective and absolute instability they solved numerically the KSEQ. The problem of convective and absolute instability for falling films from the point of view of the BEQ has been discussed in the paper by Joo and Davis (1992a) for falling films.