Photo-Marangoni convection in a thin liquid film?

Marangoni convection caused by a photochemical reaction of the type A^hv⇌B in a thin liquid film with deformable interface is studied. A system of two coupled nonlinear evolution equations for the film thickness and the reactant concentration is derived in the long-wave approximation. Linear stability analysis is performed and the conditions for Marangoni convection to occur are obtained. It is shown that the type of instability depends on the ratio of diffusivities of the reactant and the product of the photochemical reaction: If the diffusivities are equal, the instability is always monotonic, while when they are significantly different the instability can be oscillatory. Numerical simulations of the derived system of equations are performed. It is shown that in the case of the monotonic instability, the system develops a spotty pattern that ultimately leads to the film rupture. In the case of oscillatory instability, it is shown that photo-Marangoni convection can result in sustained wavy patterns with a square symmetry.