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### Modeling the Internal Flow of a Droplet

Craig Ferguson

Table of Contents

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

Electrowetting Applications

[2] [3]

Problem Definition

Model the flow inside a droplet moving between two infinite plates

Actual Situation (Droplet)

Current Model (Pipe Flow)

Physical Background

- Navier Stokes Equations [4]
- Computational Fluid Dynamics

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

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

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

References

[1] Duke University. (June 2004). “Digital Microfluidics by Electrowetting, Duke University.” http://www.ee.duke.edu/research/microfluidics/.

[2] http://www.answers.com/topic/e-ink-flex-tablet-display-jpg

[3] Liquavista http://www.liquavista.com/files/LQV060828XYR-15.pdf

[4] Weisstein, Eric. (2005) “Navier-Stokes Equations – From Eric Weisstein’s World of Physics.” http://scienceworld.wolfram.com/physics/Navier-StokesEquations.html.

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