Drop Deformation under Electric Field Presented by

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Drop Deformation under Electric Field
Presented by

• Mr. Sada Shankar Gautam

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Presentation Planning

• Introduction
• Literature survey
• Problem definition
• Mathematical formulations
• Governing equations
• Numerical schemes used solve the problem
• Current status and future work

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Introduction

• Electro-hydrodynamics
• Separation of the dispersed phase from the
  continuous phase
• Preventing catalyst deactivation and corrosion
  and reducing oil viscosity
• Electro-coalescence- smaller drops forming bigger
  drops
• Time dependent electric field- responsible for
• drops settling

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Literature survey

• Perfect dielectric electric force acting on the
  bound free charges normal to the drop.
• Leaky dielectric electric stresses acting on
  induced free charges have tangential part in
  addition to the normal part.
• Tangential part makes the liquid flow inside and
  outside the drop.
• Shear forces acting between the fluids layer
  and normal to the drop interface.
• Ultimately leading to the drop deformation.

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Problem definitions

• AC field effects on drop deformation
• RMS value linked to the DC- known to produce
  equivalent deformation
• Time dependent part- a time dependent deformation
  defined by asymptotic expression
• Deformation, dielectrophoresis, electro-rotation-
  in AC electric field- not been studied so far
• Will try to study all these phenomena-solving
  electro-hydrodynamic equations numerically

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Mathematical formulations

• Assumptions incompressible, Newtonian, Stokes
  regime- continuity and momentum equations

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Governing equation

• Bulk liquids- leaky as well as perfect dielectric
  fluids- neutral
• Gausss law

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Boundary conditions
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Numerical Schemes (fundamental solution)
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Numerical Scheme (fundamental solution)

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Numerical scheme (fundamental solution)
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Boundary element technique

• Weighted integral of Laplaces equation and
  Gausss-Greens
• theorem
• Dirac-Delta function property
• Note- domain integral replaced by a point value

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Conclusions

• perfect dielectric system
• at low electric field, the drop assumes
  a prolate shape with small deformation.
  Increasing strength of the electric field leads
  the drop to assume prolate shape with large
  deformation. Results are consistent with the
  theory.
• leaky dielectric system
• at low electric field, the drop assumes an
  oblate shape, and increase in the strength of the
  electric field leads to high deformation and
  subsequent necking can lead to drop break up.