Modeling the Internal Flow of a Droplet

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Modeling the Internal Flow of a Droplet

• Craig Ferguson

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Table of Contents

• Problem Definition
• Applications
• Physical Background
• Program Design
• Algorithm Used
• User Interface
• Current Progress
• Future Work

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Electrowetting
1
4
Electrowetting Applications
2 3
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Problem Definition

• Model the flow inside a droplet moving between
  two infinite plates

Actual Situation (Droplet)
Current Model (Pipe Flow)
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Physical Background

• Navier Stokes Equations 4
• Computational Fluid Dynamics

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Program Design

• Inputs Wall Velocities, Droplet Shape,
  Viscosity, Density, Droplet Size
• Algorithm Variation on SIMPLE
• Outputs Graphical Representations of Fluid
  Flows and Pressures Vector Plots, Topographical
  Plots

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Considered Algorithm

• SIMPLE Semi-Implicit Method for Pressure-Linked
  Equations

• Guess P
• Calculate (u, v) for surrounding nodes
• Correct the guessed pressures and velocities
• Repeat until convergence

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Coordinate Transformations
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Program Design
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Results
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Results
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Results
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Future Work

• Finish coordinate transformations
• Set up boundary conditions for desired problem
• Obtain results
• Test results against laboratory data, to be
  gathered
• Modify program to be more general or more
  efficient

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References

• 1 Duke University. (June 2004). Digital
  Microfluidics by Electrowetting, Duke
  University. http//www.ee.duke.edu/research/micro
  fluidics/.
• 2 http//www.answers.com/topic/e-ink-flex-tablet
  -display-jpg
• 3 Liquavista http//www.liquavista.com/files/LQV
  060828XYR-15.pdf
• 4 Weisstein, Eric. (2005) Navier-Stokes
  Equations From Eric Weissteins World of
  Physics. http//scienceworld.wolfram.com/physics/
  Navier-StokesEquations.html.

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Questions? Comments?