A theoretical analysis of blade coating for third-grade fluid

Abstract

In this article, coating process for a third-grade fluid using a simple fixed blade on a moving substrate is discussed. The analysis is carried out for both exponential (flexible blade) and plane (stiff blade) coaters. Coupled partial differential equations are simplified by applying the lubrication approximation theory and assuming that the coating layer thickness is much less than the blade length. The obtained system is normalized using suitable scales. A numerical solution of the governing boundary value problem is developed for various third-grade parameters. In addition, a perturbation solution is also obtained for small third-grade parameters. Interesting quantities such as pressure, pressure gradient, velocity, and load are computed and shown graphically and in tables. How the involved parameters influence the results is examined. The load on the blade is the most important physical quantity in the present work as it controls the coating thickness and quality. We found that the blade load increases as the third-grade material parameter $\beta$ increases.