A boundary-integral model for drop deformation between two parallel plates with non-unit viscosity ratio drops

  • Authors:

  • P. J. A. Janssen;P. D. Anderson

  • Affiliations:

  • Materials Technology, Dutch Polymer Institute, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands;Materials Technology, Dutch Polymer Institute, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2008

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Abstract

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.