Effects of non-linear slip and magnetohydrodynamics (MHD) on the coating thickness of web using viscoplastic nanofluid model in the blade coating process

Blade coating involves applying a fluid to a surface with a fixed blade, offering economic benefits compared to other coating technologies. It’s widely used in producing paper, preserving information, applying coloring agents, and manufacturing photographic films and magnetic storage devices. This article presents a theoretical two-dimensional study of the blade coating process using a viscoplastic material with slip and magnetohydrodynamics (MHD). The viscoplastic material’s rheology is characterized by the Bingham plastic model. The fundamental fluid dynamics equations are used to model the problem mathematically. These nonlinear partial differential equations are then transformed into ordinary differential equations using lubrication approximation theory and normalized variables. The simplified equations are solved using Matlab’s built-in function “bvp4c” in conjunction with the Regula-Falsi Method. Through graphical analysis, the effects of various parameters on physical quantities are investigated. The theoretical results indicate that, with a fixed MHD parameter value ( M = 4 ), the coating thickness and blade load increase by 57% and 594% , respectively, for plane coaters. For exponential coaters, these values are 55% and 592% higher than those for Newtonian fluid.