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SUMMARY:Deformation of a viscous droplet in an electric field - Etienne La
 c\, Schlumberger Research\, Cambridge
DTSTART:20070219T131500Z
DTEND:20070219T141500Z
UID:TALK6152@talks.cam.ac.uk
CONTACT:jnm11
DESCRIPTION:When an electric field meets an interface separating two immis
 cible \nliquids\, it undergoes a jump due to the change of physical proper
 ties \nfrom one medium to the next. One of the consequences of the field \
 ndiscontinuity is the presence of an electric stress on the interface. \nI
 n the case of a suspended drop placed in an otherwise uniform \nelectric f
 ield\, the curvature of the interface creates surface \ngradients of elect
 ric field and stress which are likely to deform the drop.\n\nWe consider h
 ere a neutrally buoyant and initially uncharged drop in \na second liquid 
 subjected to a uniform electric field. Both liquids \nare taken to be leak
 y dielectrics\, i.e. dielectrics with a small but \nnon-zero conductivity.
  The latter property induces a charge \ndistribution on the drop surface\,
  resulting in an interfacial \nelectric stress balanced by\nhydrodynamic a
 nd capillary stresses.\n\nAssuming creeping flow conditions and axisymmetr
 y of the problem\, the \nelectric and flow fields are solved numerically w
 ith boundary \nintegral techniques. The system is characterized by the phy
 sical \nproperty ratios R (resistivities)\, Q (permitivities) and M (dynam
 ic \nviscosities). Depending on these parameters\, the drop deforms into a
  \nprolate or an\noblate spheroid. The relative importance of the electric
  stress and \nof the drop/medium interfacial tension is measured by the \n
 dimensionless electric capillary number\, Cae. When M=1\, we present a \ns
 urvey of the various behaviours obtained for a wide range of R and \nQ. We
  delineate regions in the (R\,Q) plane\, in which the drop either \nattain
 s a steady shape under any field strength or reaches a limit \npoint past 
 a critical Cae. We identify the latter with linear \ninstability of the st
 eady shape to axisymmetric disturbances. Various \nbreak-up modes are iden
 tified\, as well as more complex behaviours \nsuch as bifurcations and tra
 nsition from unstable to stable solution \nbranches. We also show how the 
 viscosity contrast can stabilize the \ndrop or advance break-up in the dif
 ferent situations encountered for M=1.\n
LOCATION:MR5\, DAMTP
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