A theoretical investigation of roll coating phenomena

This thesis is primarily concerned with the theoretical modelling of steady, forward roll coating systems under different degrees of starvation by the use of analytical and numerical techniques. The concept of ‘starvation’ in a two roll coater is introduced and three possibilities identified: the fully-flooded, moderately-starved and ultra-starved situations. An extensive literature survey of work related to the fully-flooded case is given, together with a discussion of the difficulties associated with, and application of finite element methods to, free surface coating flows. Four models of ultra-starved roll coating are developed, the first of which neglects the flux between the rollers. The analytical solution of this first ‘Zero Flux’ model predicts streamlines and pressures that are in qualitative agreement with experiment. This model is refined further: first of all to allow a small, non-zero flux, then to enable prediction of the film thicknesses produced on the rollers during the forward case. The theoretical film thickness predictions agree well with Malone’s [1992] experimental data. The final model also allows a small flux between the rollers, but retains all other assumptions of the ‘Zero Flux’ model. Streamline predictions from this last model agree well with experiment. A FORTRAN finite element code is developed to solve free surface coating flows and is used to obtain film thickness ratio predictions in fully-flooded roll coating over a wider velocity ratio range than previously reported. These predictions agree reasonably well with Savage’s [1992] model. A numerical model of starvation in roll coating systems is developed and the predicted velocity and pressure fields are in qualitative agreement with both experimental observations and the analytical predictions for ultra-starved flow. Finally, numerical film thickness ratio predictions are obtained over the gamut of starvation: they are almost independent of the degree of starvation and are in good agreement with Malone’s [1992] experimental data.