Theoretical analysis of roll-over-web coating of a micropolar fluid under lubrication approximation theory

摘要

The theoretical model of roll coating onto a moving sheet is developed based on micropolar fluid constitutive equations and lubrication approximation. Closed form expressions for velocity, microrotation and pressure gradient are obtained. Runge-Kutta method is used to calculate the engineering quantities of interest such as, pressure, roll-separating (load-carrying) force and power input. The separation point is numerically calculated using Newton's iterative method together with generalized Leibniz rule. The effects of involved parameters on the pressure gradient, velocity, pressure and other mechanical quantities are displayed through various graphs. Extreme pressure is observed in the nip region for larger coupling numbers and microrotation parameters. This leads to increased load-carrying force and power input for micropolar fluid when compared to a Newtonian fluid. Moreover, the separation point decreases from its Newtonian value with increasing N.