Enhanced modeling of roll coating with pressure-dependent couple stress fluids

This study explores the roll coating process involving a fluid with couple stresses whose viscosity varies with pressure, addressing the need for more accurate modeling of complex fluids in coating technologies. A mathematical framework based on lubrication approximation theory (LAT) is proposed and exact analytical expressions are derived for the velocity, pressure gradient and separation point, enabling the investigation of different flow characteristics. Numerical simulations are conducted to study how couple stresses and pressure viscosity coefficient influence the key flow characteristics such as pressure distribution, pressure gradient, velocity fields, power input, exit coating thickness and load bearing force. Results demonstrate that the inclusion of pressure-dependent viscosity leads to a remarkable increase in pressure within the nip region compared to a Newtonian fluid with constant viscosity. Meanwhile, the couple stress parameter moderates the flow by reducing velocity gradients and damping peak pressure. The study offers valuable insights for improving efficiency of industrial coating systems that utilize Newtonian fluids with variable viscosity as well as non-ewtonian fluids.