Viscous drops in emulsion flows can deform and break or coalesce upon encounter. Drop breakup and coalescence result in the evolution of drop distribution, and drop deformation results in a complex emulsion rheology. Thus, studies of the dynamics on the drop scale are important for understanding macroscopic properties of emulsions.

In our recent investigations, we focused on drop behavior in external creeping flows. Under creeping-flow conditions, drop dynamics is characterized by the capillary number Ca (strength of the flow normalized by drop relaxation time) and the form of the external flow. Drop deformation becomes significant for Ca=O(1); for large capillary numbers interfacial tension is too weak to withstand flow-induced stresses and the drop breaks.

Our study of drop dynamics near critical capillary number above which no stationary drop shapes exist revealed that drop evolution in the near-critical regime exhibits universal features, characteristic of saddle-node bifurcation at the critical point. We also showed that drops in two-dimensional linear flow have two branches of stationary states that correspond to two stabilizing mechanisms--capillary relaxation and rotation by the vorticity component of the flow. Multiple branches of stationary states were not expected and thus were unnoticed in previous experiments and computer simulations.

Another unexpected feature of drop dynamics was found in our study of coalescence of drops pushed together by an external flow. Our computer simulations and asymptotic analysis revealed that external flow can stabilize drops to coalescence by pumping fluid back into the gap separating drop interfaces; external flow can also accelerate drop coalescence by pumping fluid out.

You will find details on the above phenomena as well as results of our study of the rheology of an emulsion of surfactant-covered drops in the publications listed below.

Related Publications
 
"Hindered and accelerated coalescence of drops in Stokes flow," M. B. Nemer, X. Chen., D. P. Papadopoulos, J. Blawzdziewicz, and M. Loewenberg, Phys. Rev. Lett., 92, 114501 (2004). pdf

"Multiple stationary drop shapes in strain-dominated linear Stokes flows," J. Blawzdziewicz, V. Cristini, and M. Loewenberg, Phys. Fluids, 15, L37 (2003). pdf

"Nonlinear rheology of a dilute emulsion of surfactant-covered spherical drops in time-dependent flows," J. Blawzdziewicz, P.M. Vlahovska, and M. Loewenberg, J. Fluid Mech., 463, 1 (2002). pdf

"Critical behavior of drops in linear flows: I. Phenomenological theory for drop dynamics near critical stationary states," J. Blawzdziewicz, V. Cristini, and M. Loewenberg, Phys. Fluids, 14, 2709 (2002). pdf

"The effect of flow on drop coalescence," M. B. Nemer, X. Chen, J. Blawzdziewicz, and M. Loewenberg, Sixth Microgravity Fluid Physics and Transport Phenomena Conference, Cleveland, August 14-16 (2002). 

"An adaptive mesh algorithm for evolving surfaces: simulations of drop breakup and coalescence," V. Cristini, J. Blawzdziewicz, and M. Loewenberg, J. Comput. Phys., 168, 445 (2001). pdf

"Rheology of a dilute emulsion of surfactant-covered spherical drops," J. Blawzdziewicz, P.M. Vlahovska, and M. Loewenberg,  Physica A, 276, 50 (2000). pdf

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