AIChE Journal, Vol.40, No.1, 2-10, 1994
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-linking reaction. Using well-known long wave approximations and a simple kinetic 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-Sivashinsky (K-S) equation is derived. Two interesting cases are identified in the limit of creeping flow. One is when surface tension is moderate and 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 in this case represents a shock-like traveling wave down the incline and it appears to be unique for reacting coating flows.
Keywords:KURAMOTO-SIVASHINSKY EQUATION;VISCOSITY VARIATION;WAVELENGTH ANALYSIS;FILM FLOW;STABILITY;SURFACES;WAVES