Dynamics of a reactive falling film at large Péclet numbers. II. Nonlinear waves far from criticality: Integral-boundary-layer approximation

We consider the dynamics of a reactive falling film far from criticality. Our analysis is based on the integral-boundary-layer (IBL) approximation of the equations of motion, energy and concentration, and associated free-surface boundary conditions. We develop a hierarchy of IBL models starting from a simplified Shkadov approach to large IBL systems based on high-order Galerkin projections.
We show that these high-order models correct the deficiencies of Shkadov’s approach and predict correctly all relevant quantities including the critical Reynolds number. We also numerically construct nonlinear solutions of the solitary wave type for a simplified Shkadov approximation and we show that unlike the long-wave theory in Paper I which leads to branch multiplicity and limit
points as well as points where the solitary wave solution branches terminate, the IBL model predicts the existence of solitary waves for all Reynolds numbers