Abstract
In this paper, a mathematical model of forward roll for coating a thin viscoplastic fluid onto a moving porous web is developed when the web passes through a small gap between the two rigid rolls. The conservation equations in the light of lubrication approximation theory are non-dimensionalized and solutions for the velocity profile, flow rate, pressure distribution are calculated numerically by using Range-Kutta-Fehlberg's method. It is found that by changing (increasing/decreasing) the material parameters, one can really control the engineering quantities like velocity distribution, flow rate, pressure distribution, and penetration depth The velocity graphs show that the gap between the velocity curves decrease, as fluid moves toward the separation point. This has a significant effect on the final volume of fluid flowing as at the separation point the fluid splits evenly. It was also found that the degree of fluid penetration is affected by the web flexibility and permeability. It has also been found that viscoelastic parameter and ratio of viscous to elastic forces have great impact on the emerging parameters, furthermore, the pressure gradient has been significantly affected with the variation in permeability and deformability. It is worth mentioning that the present study is a quick reference for the engineer working in coating industries and to compare the results with experimental data. Some results are shown graphically.