Mathematical modelling of a dip coating process using a generalised newtonian fluid I. Model development

PERALTA, J. M.; MEZA, B. E.; ZORRILLA, S. E.

INDUSTRIAL & ENGINEERING CHEMICAL RESEARCH

AMER CHEMICAL SOC

Lugar: Washington; Año: 2014 vol. 53 p. 6521 - 6532

0888-5885

Dip coating consists in the immersion of a substrate into a reservoir containing a film-forming fluid and then, the withdrawing from the bath to produce the film. The objective of this work was to develop a mathematical model of the fluid dynamic variables in a dip coating process, considering that the film-forming fluid behaves as a generalised Newtonian fluid. An analytical and simple mathematical model that relates the main fluid parameters using a generalised Herschel-Bulkley model was proposed. This model was obtained based upon rigorous mass and momentum balances applied to a monophasic and non-evaporative system, where the main forces are viscous and gravitational. The parameters that can be estimated are: velocity profile, average velocity, flow rate, local thickness, and average thickness of the coating film. Finally, the sufficient conditions for the model were obtained. The experimental validation and sensitivity analysis are presented in a complementary paper as Part II.