Marangoni convection in a photo-chemically reacting liquid

Marangoni convection caused by a photochemical reaction of the type A hν B in a deep liquid layer is studied. Linear stability analysis is performed and the conditions for Marangoni convection to occur are obtained. It is shown that increasing the rate of the direct reaction, for example, by increasing the light intensity, destabilizes the steady state and causes convective motion of the fluid, whereas increasing the rate of the inverse reaction stabilizes the steady state. A weakly nonlinear analysis of the problem is performed that gives conditions for hexagonal convective patters to occur. It is shown that, in the case of small light absorption length, the hexagonal cells correspond to "down"-hexagons.