Drop deformation in two-roll mills considering wall effects

Experimental, theoretical and numerical results of dynamics of drop deformation in strong flows generated by a co-rotating two-roll mill and considering the influence of near rigid walls are presented. The drop dynamics is altered, with respect to a drop free of wall effects, by the proximity of the rigid boundaries as well as caused by a non-linear and non-uniform flow due to gradients of flow-type parameter and shear rate. Simulations were carried out using the Boundary Element Method (BEM). Since the inclusion of the whole boundaries (drop and rollers surfaces) is not an easy and trivial task, bi-dimensional numerical simulations was performed as a first approach. The experimental and numerical results were obtained for a flow type of a = 0.03 and two values of viscosity ratio lambda = 0.012 and 16. In general, numerical results for the stationary deformation parameters, up to intermediate confinements, are in agreement with the experiments, with and without wall effects. Since the case of drops with a high viscosity ratio did not match existing theoretical models, the wall-effect theory of Shapira and Haber was modified, considering Cox's second-order theory as the converging theory without wall effects. From low to intermediate confinements, the new Cox-Shapira-Haber model fitted the observed experimental deformations.