Analytical and numerical evaluation of the forward roll-coating process using the Ellis fluid model

Forward roll coating is an industrial technique that is used to applies a thin protective liquid layer on a moving surface. The process of forward roll coating using the Ellis fluid is modeled in form of differential equations. These complex differential equations governing polymer motion are simplified using lubrication approximation theory due to the thin-film geometry. Both analytical and numerical methods are employed to determine the velocity field, pressure gradient, pressure distribution, and flow rate. Key coating features, such as film thickness and separation points, are also calculated. This study explores in detail how the inverse capillary number, Ellis fluid parameters, and power-law index affect the coating process. Results reveal that non-Newtonian effects significantly influence coating thickness and flow behavior. Shear-thinning behavior in the Ellis model reduces pressure and delays separation points, also enhancing coating smoothness. It is also noted that inverse capillary ( 1 N C a 2 ) number increases the separation point and coated thickness 12.80% and 20.26% as 1 N C a 2 increases from 0 to 2 for fixed α = 1 . For the same 1 N C a 2 and α = 2 the increased separation point and coated thickness are 6.99% and 10.99%. These effects for the pertinent parameters are shown through figures and tables, which illustrate how these parameters impact coating characteristics. Results confirm that Ellis’s fluid parameters play a crucial role in controlling coating thickness, separation points, and pressure distribution.