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Deformation of a viscous droplet in an electric field
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When an electric field meets an interface separating two immiscible liquids, it undergoes a jump due to the change of physical properties from one medium to the next. One of the consequences of the field discontinuity is the presence of an electric stress on the interface. In the case of a suspended drop placed in an otherwise uniform electric field, the curvature of the interface creates surface gradients of electric field and stress which are likely to deform the drop.
We consider here a neutrally buoyant and initially uncharged drop in a second liquid subjected to a uniform electric field. Both liquids are taken to be leaky dielectrics, i.e. dielectrics with a small but non-zero conductivity. The latter property induces a charge distribution on the drop surface, resulting in an interfacial electric stress balanced by hydrodynamic and capillary stresses.
Assuming creeping flow conditions and axisymmetry of the problem, the electric and flow fields are solved numerically with boundary integral techniques. The system is characterized by the physical property ratios R (resistivities), Q (permitivities) and M (dynamic viscosities). Depending on these parameters, the drop deforms into a prolate or an oblate spheroid. The relative importance of the electric stress and of the drop/medium interfacial tension is measured by the dimensionless electric capillary number, Cae. When M=1, we present a survey of the various behaviours obtained for a wide range of R and Q. We delineate regions in the (R,Q) plane, in which the drop either attains a steady shape under any field strength or reaches a limit point past a critical Cae. We identify the latter with linear instability of the steady shape to axisymmetric disturbances. Various break-up modes are identified, as well as more complex behaviours such as bifurcations and transition from unstable to stable solution branches. We also show how the viscosity contrast can stabilize the drop or advance break-up in the different situations encountered for M=1.
This talk is part of the Monday Mechanics Seminars (DAMTP) series.
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