Breakup of drops in simple shear flows with high-confinement geometry

- The define donating region (DDR) algorithm introduced by Harvie and Fletcher (2001) is developed in 3D.
- An analytical formulation for a zeroth-to-first-order fluxing algorithm based on the normal vector and the plane constant is presented (BDR).
- Convergence rates and features of the DDR method are addressed in 3D.
- The problem of a drop sheared by two closely-located walls is solved numerically using a PLIC-DDR-VOF method for low and moderate Reynolds, several capillary numbers and three viscosity ratios.
- Interface contours, conditions for stability and breakup are presented. The effects of the wall on the drop at low Re for two viscosity ratios are addressed.
- Wall migration of the interface is observed for a drop sheared at Re=110.
- The drops is shown to oscillate transversally at moderate Reynolds.
- Quantitative description of the stresses and velocity during breakup.

The problem of a drop subject to a simple shear flow in high constriction geometry is addressed numerically for different flow conditions. Wall effect on the critical capillary number and drop deformation is analyzed. Under uniform condition, drops in low and moderate Reynolds flows are more stable when the confinement is increased. The critical capillary number is shown to increase for drops more viscous than the medium (viscosity ratio λ=0.3) and decreases when the medium is more viscous (λ=1.9) or when Reynolds number is increased. A discussion on the accuracy of the numerical method and solutions to typical problems are included for comparison. The drop interface is reconstructed using the piecewise linear interface calculation (PLIC) and transported with the volume-of-fluid (VOF) method, which follows unsplit case-by-case schemes based on the basic donating region (BDR) or the defined donating region (DDR). Surface tension is included with the continuum-surface-force (CSF) model. A high-resolution (SMART) semi-implicit finite-volume discretization is employed in the linear momentum equations. Mass is conserved by following an implicit pressure-correction method (SIMPLEC). The normal vector of the interface is computed from height functions using least squares fitting. The advantage of the DDR scheme lies in its volume-conserving capabilities which have not been exploited in recent investigations.