Response surface-based sensitivity analysis and mathematical modeling of Williamson fluid model (WFM) in coating process

Purpose This study investigates the flow of non-Newtonian fluids for the fixed constraining boundary in order to construct a mathematical model for an incompressible, non-Newtonian fluid that passes through a little gap between a roll and substrate. By considering suitable dimensionless parameters, the dimensionless form of the governing equations is produced. Design/methodology/approach The fluid flow governing equations have been made simpler with the application of lubrication approximation theory (LAT). The expression for velocity profile, coating thickness, separation force, pressure distribution, roll power input, pressure gradient, and separation point are obtained with the implementation of the perturbation technique. To investigate the impacts of different physical parameters such as Wiesenberger number, force and the dependence of the response factors coating thickness, power input, and roll separation force, sensitivity analysis and an experimental design based on response surface methodology (RSM) are employed. Findings The correlation equation derived from the RSM demonstrates the relationship between the output and input parameters. The high values of coefficient of determination for output responses coating thickness, power input and roll separation force are 99.90, 99.91 and 97.16%, respectively, which demonstrates the validity of our analysis. Moreover, the impacts of involved parameters on the quantities of interest are displayed through various graphs and in tabular form. Moreover, it has been established that an increase in the Weissenberg number correlates with a drop in velocity; conversely, an increase in the embedding factor F is associated with an increase in velocity. Both the factors leads to decreasing the pressure gradient but an increasing for pressure distribution. The coating thickness and separation point diminish as power input and separation force escalate with increasing F. On the other hand, a larger Weissenberg number lowers the separation force while raising the coating thickness, power input, and separation point. Finally, we assure our results by comparing to previously published research. Originality/value This study addresses a gap in the existing literature by exploring the rheological properties of the Williamson fluid model and integrating numerical methods along with response surface techniques in the coating process.