A Method for Calculation of Final Film Thickness in Free Coating of Viscoelastic Fluids onto a Vertical Surface

Abstract

A method for the calculation of the final film thickness in free coating of a viscoelastic fluid onto a vertical surface withdrawn from its vessel is developed. The method is based on the definition of an objective function, the minimization of which guarantees that the kinematic as well as the dynamic conditions at the lower boundary of the dynamic meniscus region are simultaneously satisfied. A systematic approach is provided in order to localize the optimum value of the final film thickness within the optimization interval. It was observed that there was a clear relationship between the estimated final film thickness and the value of a parameter A. The closeness of this parameter to zero corresponds to the dynamic constraint being fulfilled at the lower boundary of the dynamic meniscus region. This relationship is used as an objective means of determining the direction to update the interval of optimization to obtain the final thickness of the film. The results of the proposed method are compared to the previous works on the free coating of viscoelastic fluids, which are based on a trial‐and‐error method. The performance of the previously applied rheological models to the formulation of the free coating process, mainly the modified Oldroyd models, is also compared by introducing the present method.