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

[1]

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

1. Guess P

2. Calculate (u, v) for surrounding nodes

3. Correct the guessed pressures and velocities

4. Repeat until convergence

Coordinate Transformations

Program Design

Results

Results

Results

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.

Questions? Comments?