Generalized behavior of the breakup of viscous drops in confinements

The breakup of confined drops in shear flow between parallel plates is investigated as a function of viscosity ratio and confinement ratio. Using a boundary-integral method for numerical simulations and a counter-rotating experimental device, critical capillary numbers in shear flow are obtained. It is observed that different viscosity ratios yield different trends with increasing confinement ratio: a low viscosity ratio drop shows an increase in critical capillary number, at a viscosity ratio of unity no major trend is seen, and the critical capillary number for a high viscosity ratio drop decreases significantly. A generalized explanation for all viscosity ratios is that confinement affects the orientation of the drop with respect to the direction of the local strain field. At moderate confinement ratios, the drop orients more towards the strain direction, where it experiences a stronger flow and hence, the critical capillary number is decreased. As the drop gets more confined, it aligns more in the flow direction. Hence, the drop experiences a weaker flow and thus, additionally stabilized by wall effects, it breaks at a higher critical capillary number. In principle, this behavior is the same for all viscosity ratios, but transitions occur at different confinement ratios. Most of the breakup is of a binary nature, but ternary breakup can occur if the drop length is larger than 6 undeformed drop radii, consistent with arguments based on the Rayleigh-Plateau instability