Effect of confinement on the steady-state behavior of single droplets during shear flow

The effect of geometrical confinement on the deformation and orientation of single droplets during steady-state shear flow is investigated microscopically in a counterrotating device. The model system consists of poly(dimethyl siloxane) droplets of varying sizes and viscosities in a poly(isobutylene) matrix. The experimental results are first compared with the predictions of the model by Maffettone and Minale [ J. Non-Newtonian Fluid Mech. 78, 227–241 (1998)] for bulk flow. For all viscosity ratios, deviations from the Maffettone and Minale model start to occur at a droplet diameter to gap spacing ratio of the order of 0.4. The droplet deformation increases and the droplets orient more towards the flow direction as a consequence of confinement. At low viscosity ratios, the deviations remain small, whereas at high viscosity ratios, larger deviations from bulk behavior are observed. The observations are also compared with the theory of Shapira and Haber [ Int. J. Multiphase Flow 16, 305–321 (1990)] which includes the influence of wall effects on deformation. The Shapira and Haber model is modified by replacing the Taylor model as bulk reference by the Maffettone and Minale model. Good agreement between theory and experimental results is found for a wide range of viscosity ratios.