TY - JOUR
T1 - A boundary-integral model for drop deformation between two parallel plates with non-unit viscosity ratio drops
AU - Janssen, P.J.A.
AU - Anderson, P.D.
PY - 2008
Y1 - 2008
N2 - A boundary integral method is presented for drop deformation between two parallel walls for non-unit viscosity ratio systems. To account for the effect of the walls the Green's functions are modified and all terms for the double-layer potential are derived. The full three-dimensional implementation is validated, and the model is shown to be accurate and consistent. The method is applied to study drop deformation in shear flow. An excellent match with small-deformation theory is found at low capillary numbers, and our results match with other BIM simulations for pressure-driven flows. For shear flow with moderate capillary numbers, we see that the behavior of a low-viscosity drop is similar to that of drop with a viscosity ratio of unity. High-viscosity drops, on the other hand, are prevented from rotating in shear flow, which results in a larger deformation, but less overshoot in the drop axes is observed. In contrast with unconfined flow, high-viscosity drops can be broken in shear flow between parallel plates; for low-viscosity drops the critical capillary number is higher in confined situations.
AB - A boundary integral method is presented for drop deformation between two parallel walls for non-unit viscosity ratio systems. To account for the effect of the walls the Green's functions are modified and all terms for the double-layer potential are derived. The full three-dimensional implementation is validated, and the model is shown to be accurate and consistent. The method is applied to study drop deformation in shear flow. An excellent match with small-deformation theory is found at low capillary numbers, and our results match with other BIM simulations for pressure-driven flows. For shear flow with moderate capillary numbers, we see that the behavior of a low-viscosity drop is similar to that of drop with a viscosity ratio of unity. High-viscosity drops, on the other hand, are prevented from rotating in shear flow, which results in a larger deformation, but less overshoot in the drop axes is observed. In contrast with unconfined flow, high-viscosity drops can be broken in shear flow between parallel plates; for low-viscosity drops the critical capillary number is higher in confined situations.
U2 - 10.1016/j.jcp.2008.06.027
DO - 10.1016/j.jcp.2008.06.027
M3 - Article
SN - 0021-9991
VL - 227
SP - 8807
EP - 8819
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 20
ER -