1. Modeling the Internal Flow of a Droplet Craig Ferguson

2. Table of Contents Problem Definition Applications Physical Background Program Design Algorithm Used User Interface Current Progress Future Work

3. Electrowetting [1]

4. Electrowetting Applications [2] [3]

5. Problem Definition Model the flow inside a droplet moving between two infinite plates Actual Situation (Droplet) Current Model (Pipe Flow)

6. Physical Background Navier Stokes Equations [4] Computational Fluid Dynamics

7. 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

8. 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

9. Coordinate Transformations

10. Program Design

11. Results

14. 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

15. 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.

16. Questions? Comments?