Drainage and rupture of a Newtonian film between two power-law liquid drops interacting under a constant force

Abstract

The deformation, drainage and rupture of the film of a Newtonian fluid between colliding drops of a power-law liquid is studied numerically for gentle constant-force collisions at small Reynolds numbers. The whole shear-thinning range of the power-law parameter, n, is investigated, together with a range of transformed dispersed to continuous-phase viscosity ratios, λ *, covering the transition from partially mobile to immobile interfaces. The problem is solved numerically by means of a finite-difference method for the equations in the continuous phase and a finite-element method for the non-Newtonian flow in the drops. The final stage of drainage is well described by a power-law empirical dependence of the minimum film thickness on time for the whole range of ( λ *; n) values investigated. The boundaries of the partially mobile, transitional and immobile drainage region in ( λ *; n) plane as well as the coefficients of the empirical dependence are obtained. The application of the results for power-law drops to practically more relevant general viscous dispersed phases is discussed. The rupture of the film due to van der Waals forces is studied for a wide range of the transformed Hamaker constant, A *, including both ‘rim’ and ‘nose’ rupture modes. The results indicate that the transformed critical rupture thickness, h c ∗ , is only weakly dependent on the non-Newtonian flow in the drops, being primarily determined by A *, as predicted by the approximate relation given in [A.K. Chesters, Trans. Inst. Chem. Engrs. Part A 69 (1991) 259–270].