Transcript Slide 1 - Union College

Computational Model of a Fluid Undergoing Electrocapillary Propulsion
by: Craig Ferguson
Union College Mechanical Engineering and Computer Science 2007
Advisors: Brad Bruno and Chris Fernandes
ABSTRACT
Many new devices and applications are being created that involve transporting droplets from one place to another. A common method of achieving this is through electrocapillary
effects, a process through which a surface is electrowetted in such a way that it will cause a droplet to be pulled forward. Because this is a relatively new field, not much is known
about the flows within droplets while they are undergoing this electrocapillary propulsion. However, much of the droplet’s behavior, such as its internal mixing and drag, are
dictated by its internal flow pattern. In order to determine these and other characteristics, the flow pattern must be fully understood.
For this reason, a computational fluid dynamics program has been created that uses a semi-implicit finite difference method to predict the flow within droplets of varying size,
shape, and fluid. The program allows for the user to dictate all important parameters and outputs the pressure and velocity throughout the droplet as well as a velocity vector
diagram. It also supports custom coordinate transformations so the droplet may be any shape desired.
USER INTERFACE
BACKGROUND
Electrowetting is a process through which the contact angle of a fluid on a surface
may be changed by applying a voltage to it. By applying a voltage to one side of a
droplet, the difference in contract angles will cause it to move in what is known as
The user interface is designed
electrocapillary motion. The fluid within the droplet must be flowing during this
so the user may input all
motion, and that flow pattern dictates certain properties of the droplet, such as the
analysis criteria then run the
drag or internal mixing.
analysis, the results of which
Because these flows are very difficult to experimentally measure, a computational
are displayed both graphically
model would greatly increase the ease with which electrocapillary flows may be
as a vector plot. Any values are
studied and predicted as well as greatly decrease the cost of these studies. It is for
also listed in a text box beneath.
this reason that a computational model has been created of a droplet undergoing
electrocapillary flow.
PROBLEM SPECIFICATIONS
RESULTS
The goal of the project is to create a two dimensional computational fluid dynamics
A Java applet has been created that will calculate the internal flow of a droplet
program that will calculate the velocities of the flow within an incompressible,
qualitatively well. It is capable of modelling the flow patterns of both a lid-driven
Newtonian droplet that is moving at steady state through a channel.
cavity flow as well as the flow that would be experienced by a droplet travelling
through a channel. The results of the program were compared qualitatively to
experimental PIV results for a droplet as it travels through a tube. An overlay of the
experimental and computational results are shown below.
This droplet may have any type of constant shear on its side walls to simulate air, oil,
or any other substance next to it. The modelled droplet must be shaped exactly as it
would be in the real world, so the curvature of the sides must be changeable to fit
real world examples.
ALGORITHM
The algorithm that was used was a modification of the SIMPLE algorithm, or SemiImplicit Method for Pressure-Linked Equations. This is an iterative method in which
The blue lines originating from the red circles are the computational velocities at that
point, while the fainter lines are the PIV flow results. Though the magnitudes cannot
be compared, the flow pattern itself is fairly identical between the two.
the droplet is divided into a grid of nodes, which are either flagged as Pressure
Nodes or Velocity Nodes, in the pattern shown.
CONCLUSIONS
In conclusion, a Java applet has been created that qualitatively predicts flow patterns
for many different droplet types and shapes. Because the program includes
coordinate transformations, it is capable of calculating flow fields within droplet
The Navier-Stokes equations are solved for either the vertical or horizontal velocity
with curved sides, as a real droplet would have.
at each Velocity Node using all adjacent nodes. These new velocities are then in turn
Though the computational program is currently only known to be qualitatively
used to calculate the pressures at each Pressure Node. Then, These new pressures are
correct, it is a powerful tool in predicting the traits of many different types of
used to recalculate velocities. This process repeats until both the pressures and
droplets travelling through channels. This program may be used quickly and easily
velocities stop changing, at which point convergence has been reached.
by future researchers to study electrocapillary flows as well as any flow involving
liquid travelling through a channel.