Numerical analysis of coating thickness and pressure distribution in blade coating flows of power-law fluids

Abstract

The shear stress of a power-law fluid is exponentially related to the shear rate. Thus, unlike for Newtonian fluids, the Reynolds lubrication equation in the simplified differential form is nonlinear and cannot be solved analytically. This paper investigates the flow of a power-law fluid in comma-roll coating and planar blade coating. We establish an intermediate function F(x), defined as the ratio of the shear force τ(X,0) in the X-direction on the edge of the blade coater to the pressure gradient G(x). Using various flow patterns, the signs of F and G are determined, and expressions for ∂U/∂Y are obtained in terms of F and G. Combined with the velocity boundary condition, ∂U/∂Y is integrated and the explicit relation between the coating thickness H∞ and F is established. The pressure gradient is also obtained. Finally, dP/dX is integrated and combined with the inlet and outlet pressure conditions, and the bisection method is used to determine H∞. The coating thickness and pressure given by the proposed method for both comma-roll coating and flat blade coating are highly consistent with the exact results for n = 1, 1/2, and 1/3 calculated by Dien and Elrod's method. We deduce that the limiting thickness of comma-roll coating is (n + 1)/(2n + 1), and the limit of the pressure gradient is −[n+1/n]n. Moreover, we construct a phase diagram of the relationship between the shape parameter k of the blade coater and the power-law exponent n. These results have instructive significance and application value for guiding coating operations and applicator design.