Asymptotic studies of gravity-driven reacting coating flows and pultrusion processes

Abstract

Coating flows have many very important applications in engineering. The first part of this thesis deals with gravity-driven reacting coating flows down an inclined plane. When the reaction activation energy is large and heat release is significant, long wave theory and large activation energy asymptotics are applied jointly to derive a consistent set of governing equations, which describe wave formation on the free surface and evolution of the reaction front. The key feature shown by the solution is the coupling of the free surface with the reaction front. When the reaction activation energy is small and heat release is insignificant, long wave theory leads to a single governing equation for wave formation on the free surface. Unlike its traditional counterpart, this equation has variable coefficients attributed to the effect of variable viscosity. The solution of this equation shows that linear, as well as, nonlinear wave formations differ appreciably from the constant viscosity coating flows.

Pultrusion is a composite manufacturing process. Issues such as variable viscosity resin flows through a collection of fibers, pressure distribution, pulling force, etc. are examined in the second part of this thesis. Large activation energy asymptotics is again applied so that polymerization can be assumed to take place in a thin reaction front. Solutions of pressure & temperature distributions, shape of the reaction front and relation between pulling force and other factors lead to a better understanding about pultrusion. The asymptotic results are simple and provide insight into the mechanisms that characterize a successful operation. Some of the results are simple enough to be used directly to guide the pultrusion operations.