This instability apear when we heat the botom side of liquid film wich have a free top surface. the instability is due to the superficiel tension gradients. this phenmena has been studied by Benard at the begining of the century and has been considered for a long time as a Raleigh -Benard instability.
this instability apear when there is a temperature vibration. the interface forces introduce a volume motion. if we put a soap drop at the surface of dusty watter we see that the dusty go in the radial direction to the outside of the flow. this produce , indirectely the apparition of a superficiel layerin the watter. the forces make the particals attracted by the zones of the less concetration and the most superficiel tension.
above a precise value of DTc , a he xagonal cellules apear between the bottom side and the top side of the liquid film.
the variation of superficiel superficiel tension the fluid is dropt to the outsid of the cell. for reasons of mass continuity the hot fluid from the bottom move to the top. this heat transfer sincrease the initial perturbation.
the instability is structured into hexagonal cells as is shown in the folloween figure.
as for the Rayleigh-Benard instability, the stabilisator process come from the viscous forces and the heat diffusion. this two process tend to transform the velocity field and the temperature field as a homogeniouse one.
the Marangoni number is adimentional number witch control the apparition of instability.
some significant adimentional values :