Mathematical Modeling of a Dip-Coating Process Using a Generalized Newtonian Fluid. 1. Model Development

Abstract

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 fluiddynamic variables in a dip-coating process, considering that the film-forming fluid behaves as a generalized Newtonian fluid. An analytical and simple mathematical model that relates the main fluid parameters using a generalized Herschel−Bulkley model was proposed. This model was obtained on the basis of rigorous mass and momentum balances applied to a monophasic and nonevaporative 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 2.

Rheological Properties of a Commercial Food Glaze Material and Their Effect on the Film Thickness Obtained by Dip Coating

“…Theoretical average film thickness values were estimated using the phenomenological mathematical model proposed by Peralta et al . () for a dip‐coating process of a plate during the draining stage based on Eq. (1): where < h > is the theoretical average film thickness (m), h is the film thickness at the x position of the plate (m), g x is the gravity acceleration (m/s 2 ), 2 F 1 [ a , b ; c ; z ] is the Gauss hypergeometric function (Aomoto and Kita ), is the ratio of the yield stress to the maximum stress and t is the time (s).…”

“…Recently, Peralta et al . () performed a theoretical study of the fluid dynamic phenomena in a dip‐coating process, considering the withdrawal and draining steps and that the film‐forming fluid behaved as a generalized Newtonian fluid (Reiner ; Bird et al . ).…”

“…In addition, this study provides new experimental data to validate the mathematical modeling of the dip‐coating process developed in our research group, considering the temperature dependence of the rheological parameters of a commercial food glaze material (Peralta et al . 2014a,b).…”

Draining of films on a quasivertical plate using viscous dissipation

“…In this sense, efforts in previous works have been made in order to obtain analytical expressions for the main outputs (velocity, flow rate, and film thickness) that describe the film draining flow on regular geometries, such as vertical plates. [2][3][4][5] During free draining, the shear flow of the film-forming material is due mainly to gravity forces that generate the movement of the film. The energy that must be supplied to maintain the relative motion of a fluid under simple shear, and that is often considered to be a dissipated power, is usually referred to as viscous dissipation.…”

Numerical simulation and experimental validation of liquid‐film‐flow characteristics in dip coating for non‐Newtonian fluids

“…Free surface profiles and flow field patterns of dip coating with Newtonian and Bingham fluids were analyzed by Hurez and Tanguy , with the purpose of finding the location of the free surface and investigating flow characteristics at equilibrium. Peralta et al developed a mathematical model of the fluid dynamic variables in a dip‐coating process. To sum up, previous investigations of film flow are simple, either experimentally or numerically.…”