Linear stability analysis free surface

Pearson s theoretical treatment was based on a linear stability analysis of the type described in Section 10.4 in connection with jet stability to small disturbances and paralleled Rayleigh s analysis for buoyancy driven instability. He assumed an infinite homogeneous liquid film of uniform thickness h whose lower surface is in contact with a rigid heat conductor at a fixed temperature and whose upper surface is free. Gravity is neglected (Ra = 0) and a linear temperature distribution across the film is assumed, with the high temperature at the lower surface. The surface tension is a function of temperature alone, and the rate of heat loss from the free surface is also a function of temperature only. 

Perez- Garcia C. and Cameiro G. (1991). Linear stability analysis of B6nard-Marangoni convection in fluids with a deformable free surface. Phys. Fluids, A3, 292. ... 

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