GRAVITY-DRIVEN REACTIVE COATING FLOW DOWN AN INCLINED PLANE

The coating flow of a reactive fluid on an inclined plane is studied. The fluid viscosity steadily increases due to a sustained cross-linkin g reaction. Using well-known long wave approximations and a simple kin etic relation, we find that the linear stability of a uniform coating is affected not only by the inclination angle but also by the reaction order. In the weakly nonlinear limit, a generalized Kuramoto-Sivashin sky (K-S) equation is derived. Two interesting cases are identified in the limit of creeping flow. One is when surface tension is moderate a nd a generalized Burger's equation results, and the other is when the surface tension is large and the traditional K-S equation is recovered when the inclination angle is greater than 90-degrees. The solution i n this case represents a shock-like traveling wave down the incline an d it appears to be unique for reacting coating flows.