# ABSTRACT Many new devices and applications are being created that involve transporting droplets from one place to another. A common method of achieving.

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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. 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 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 electrocapillary motion. The fluid within the droplet must be flowing during this motion, and that flow pattern dictates certain properties of the droplet, such as the drag or internal mixing. Because these flows are very difficult to experimentally measure, a computational model would greatly increase the ease with which electrocapillary flows may be studied and predicted as well as greatly decrease the cost of these studies. It is for this reason that a computational model has been created of a droplet undergoing electrocapillary flow. PROBLEM SPECIFICATIONS The goal of the project is to create a two dimensional computational fluid dynamics program that will calculate the velocities of the flow within an incompressible, Newtonian droplet that is moving at steady state through a channel. 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 Semi- Implicit Method for Pressure-Linked Equations. This is an iterative method in which the droplet is divided into a grid of nodes, which are either flagged as Pressure Nodes or Velocity Nodes, in the pattern shown. The Navier-Stokes equations are solved for either the vertical or horizontal velocity at each Velocity Node using all adjacent nodes. These new velocities are then in turn used to calculate the pressures at each Pressure Node. Then, These new pressures are used to recalculate velocities. This process repeats until both the pressures and velocities stop changing, at which point convergence has been reached. USER INTERFACE The user interface is designed so the user may input all analysis criteria then run the analysis, the results of which are displayed both graphically as a vector plot. Any values are also listed in a text box beneath. RESULTS A Java applet has been created that will calculate the internal flow of a droplet qualitatively well. It is capable of modelling the flow patterns of both a lid-driven 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. 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. 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 with curved sides, as a real droplet would have. Though the computational program is currently only known to be qualitatively correct, it is a powerful tool in predicting the traits of many different types of droplets travelling through channels. This program may be used quickly and easily by future researchers to study electrocapillary flows as well as any flow involving liquid travelling through a channel.

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