Spatial patterns and double diffusion in

Spatial ordering has been observed recently during various photochemical reactions. Convoluted concentration bands first appear near the surface of shallow irradiated solutions. They thereafter extend into the bulk, and finger-like structures spontaneously develop. We discuss here the possible role of double-diffusion effects in the onset of this phenomenon. Indeed, chemical reactions occurring near the surface or evaporation of the solvent, or both, induce in the bulk adverse gradients of a pair of properties (concentrations of solute or concentration and temperature) having different diffusivities. This difference can then destabilize the homogeneous solution and trigger the observed patterns. The competition between nonlinear chemical kinetics and diffusion (Turing mechanism) or other hydrodynamical processes can lead to coherent macroscopic structures in open chemical systems driven far from thermal equilibrium (1). Unfortunately experimental examples of such stationary chemical dissipative structures are scarce and not well characterized (2-5; for a recent review, see ref. 6). Furthermore the detailed mechanism of these complex reactions are still not completely elucidated. However, recently the formation of spatial structures have been reported in a large class of photochemical reactions not only in complex systems such as the photolysis of halogen compounds but also in photosystems exhibiting simple reaction kinetics (79) (firstor second-order return reaction). It follows that these patterns are not generated by the Turing mechanism. Furthermore, as the characteristic wavelength is not intrinsic and depends on the thickness of the solution (3), one must therefore search for the origin of these structures in the coupling of the chemical processes with hydrodynamics. We want to stress here the importance of double diffusive convection in systems where chemical reactions occur near the surface. Double diffusion mechanisms have indeed been recognized as leading effects inducing instabilities in multicomponent systems (10-12). For the sake of clarity, we consider the following model. A shallow layer of solution (of thickness L) of a chromogenic compound A of concentration 'A is irradiated. The photochromic k reaction A + h v B takes place near the surface in the absorbing layer. This reaction induces in the solution time-dependent nonlinear concentration gradients of A and B, the Laplace transforms of which are of the form: AO sinh(w/DA)'2z zA0(zaw) = (cDA)j2 cosh(co/DA)Y/L