Breakup modes of fluid drops in confined shear flows.

Using a conservative level set method we investigate the deformation behavior of isolated spherical fluid drops in a fluid channel subjected to simple shear flows, accounting the following three non-dimensional parameters: (1) degree of confinement (Wc = 2a/h, where a is the drop radius and h is the channel thickness); (2) viscosity ratio between the two fluids (λ = μd/μm, where μd is the drop viscosity and μm is the matrix viscosity); and (3) capillary number (Ca). For a givenWc, a drop steadily deforms to attain a stable geometry (Taylor number and inclination of its long axis to the shear direction) when Ca < 0.3. For Ca > 0.3, the deformation behavior turns to be unsteady, leading to oscillatory variations of both its shape and orientation with progressive shear. This kind of unsteady deformation also occurs in a condition of high viscosity ratios (λ > 2). Here we present a detailed parametric analysis of the drop geometry with increasing shear as a function of Wc, Ca, and λ. Under a threshold condition, deforming drops become unstable, resulting in their breakup into smaller droplets. We recognize three principal modes of breakup: Mode I (mid-point pinching), Mode II (edge breakup), and Mode III (homogeneous breakup). Each of these modes is shown to be most effective in the specific field defined by Ca and λ. Our study also demonstrates the role of channel confinement (Wc) in controlling the transition of Mode I to III. Finally, we discuss implications of the three modes in determining characteristic drop size distributions in multiphase flows. [ABSTRACT FROM AUTHOR]