Analytical models for predicting penetration depth during slot die coating onto porous media

A series of analytical models have been developed to predict the penetration depth during slot die coating on porous media. Analytical models for both Newtonian and non-Newtonian fluids were derived based on Lubrication Theory, Darcy's law, and a modified Blake-Kozeny equation. Using these models, the penetration depth can be quickly solved and the effects of material properties and processing conditions on penetration depth can be easily investigated. Experiments of coating Newtonian glycerin and non-Newtonian blackstrap molasses onto Toray series carbon paper were conducted to validate developed models. The overall relative error between the predicted and measured penetration depth was found to be typically lower than 20%, which demonstrates the relative accuracy of developed models. Furthermore, based on a parametric study, it was found that the effect of capillary pressure on penetration depth is less than 10% when the ratio of coating bead pressure and capillary pressure is larger than 10.