Physica D 61 (1992) 166-182 North-Holland Gravitational instabilities of thin liquid layers: dynamics of pattern selection L. Limat, P. Jenffer 1, B. Dagens, E. Touron, M. Fermigier and J.E. Wesfreid Laboratoire de Physique et de M~canique des Milieux H~t&og~nes, URA CNRS 857, ESPCI, 10 rue Vauquelin, 75231 Paris Cedex 05, France We present recent results obtained in the study of the instabilities induced by gravity on liquid layers hanging below solid surfaces, in situation of perfect wetting (without contact lines). Two cases are discussed: two-dimensional films of constant volume, and films continuously supplied with "fresh" liquid by an external source. In the first case, we show experimental evidences suggesting that the formation of a two-dimensional structure within the film arises by means of front propagation mechanisms. In the simplest situation, propagation of a one-dimensional structure ("roll" formation), the measured front speed is close to that deduced from the linear marginal stability theory. In the second case, the liquid film is hanging below an horizontal overflowing half-cylinder. Depending on the rate of supply, different regimes are observed (dripping, arrays of parallel jets, triangular sheets). The arrays of drops and jets exhibit interesting spatio- temporal phase dynamics: oscillations, pairing or nucleation of cells, forced tilt waves. 1. Introduction Gravitational instabilities (or Rayleigh-Taylor instabilities) of thin films [1-5] occur in many practical situations: coating of a solid surface with paint or lubricating agent, formation of aerosols by centrifugal effects [6], boiling of liquids with formation of vapor films [7]. These instabilities also raise fundamental issues regard- ing the selection of patterns in the non-linear growth regime, and the stability of these patterns with respect to secondary instabilities. In a recent experiment [4,5], we studied pat- tern selection in the case of a two-dimensional film first spread by a stabilizing gravity on a solid 1Also: Laboratoire de Physique PCEM M2D, Universit6 Paris Sud, Batiment 336, 91405 Orsay, France. plate (situation of perfect wetting, the selected fluid being a silicon oil) and then placed in an unstable situation by flipping the plate upside- down. Complex dynamics were observed in this case, different patterns associated to different symmetry orders being formed (see fig. 1): one- dimensional undulations parallel to the bound- aries (called lines or "rolls" in analogy with convective instabilities), axisymmetric patterns [5] nucleated by the initial perturbation associ- ated to the presence of dust failing on the inter- face, axisymmetric patterns breaking in fivefold, sixfold and even sevenfold geometry, hexagonal patterns often obtained by non-linear interac- tions between the previous ones. After a more or less complicated history, the whole structure evolves towards an hexagonal symmetry. An ex- ample of the final array of pendant drops is 0167-2789/92/$05.00 ~ 1992- Elsevier Science Publishers B.V. All rights reserved