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SUMMARY:A three-dimensional small-deformation theory for electrohydrodynam
 ics of dielectric drops - Debasish Das\, Straghclyde University\, UK
DTSTART:20210521T153000Z
DTEND:20210521T163000Z
UID:TALK160480@talks.cam.ac.uk
CONTACT:virginia mullins
DESCRIPTION:Electrohydrodynamics of drops is a classic fluid mechanical pr
 oblem where deformations and microscale flows are generated by application
  of an external electric field. In weak fields\, electric stresses acting 
 on the drop surface drive quadrupolar flows inside and outside and cause t
 he drop to adopt a steady axisymmetric shape. This phenomenon is best expl
 ained by the leaky-dielectric model under the premise that a net surface c
 harge is present at the interface while the bulk fluids are electroneutral
 . In the case of dielectric drops\, increasing the electric field beyond a
  critical value can cause the drop to start rotating spontaneously and ass
 ume a steady tilted shape. This symmetry-breaking phenomenon\, called Quin
 cke rotation\, arises due to the action of the interfacial electric torque
  countering the viscous torque on the drop\, giving rise to steady rotatio
 n in sufficiently strong fields. Here\, we present a small-deformation the
 ory for the electrohydrodynamics of dielectric drops for the complete Melc
 her–Taylor leaky-dielectric model in three dimensions. Our theory is val
 id in the limits of strong capillary forces and highly viscous drops and i
 s able to capture the transition to Quincke rotation. A coupled set of non
 linear ordinary differential equations for the induced dipole moments and 
 shape functions are derived whose solution matches well with experimental 
 results in the appropriate small-deformation regime. Retention of both the
  straining and rotational components of the flow in the governing equation
  for charge transport enables us to perform a linear stability analysis an
 d derive a criterion for the applied electric field strength that must be 
 overcome for the onset of Quincke rotation of a viscous drop. 
LOCATION:GKB 100 Fluid Mechanics Webinar Series
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