An exact solution for blade coating of a second-grade fluid on a porous substrate

Abstract

This study explores the blade coating process with a simple fixed blade for a second-grade fluid over a moving porous substrate. The article investigates both plane and exponential blade coating. The analysis simplifies the governing equations via lubrication approximation theory by assuming that blade length is much larger than the coating layer thickness. Suitable scales normalize the governing equations. The expressions for pressure gradient and velocity are analytically obtained whereas pressure is attained using a so-called “shooting method” numerical technique. How the Reynolds number $R_e$ , suction velocity $v_0$ and non-Newtonian second-grade parameter $ϵ$ affect the velocity, pressure gradient, pressure, coating layer thickness and load on the blade are observed and displayed graphically and as tables. Interesting engineering quantities like velocity, pressure gradient and pressure are highlighted in graphical form whereas load and thickness are presented as tables. It is observed that the pressure gradient, pressure, velocity, load and thickness decrease as the parameters $\in$ and $R_e$ and $v_0$ icrease for the cases of both plane and exponential coaters while all these physical quantities are observed to increase when the parameter $\in$ increases. The most important physical quantity is the load for it is responsible in maintaining the coating quality and thickness. Moreover, it is perceived that the load decreases as the Reynolds number $R_e$ and $v_0$ increases get accelerated and it increases when parameter $ϵ$ is increased.