Joseph Scott Tenny and Dr. Daniel Maynes, Mechanical Enineering
Introduction
Recent advancements in technology have created the need for increased understanding of fluid flow in microtubes with a diameter of a 100μm or less. These types of flows can occur in many practical applications, one of which is a concept proposed for DNA analysis called “lab on a chip.” At this physical scale, the pressures required to drive the flow of the fluid are often too large for any type of potential application. An alternative approach to driving the fluid through a microtube is to use electro-osmosis. This type of flow uses an applied voltage potential to drive the fluid through the microtube instead of a pressure gradient. The nature of electro-osmosis has raised many questions as to the characteristics of the fluid dynamics as the solution flows through the microtube. The purpose of this research is to numerically calculate and characterize the hydrodynamic development region (the region at the inlet where the flow is developing) of electro-osmotically driven flows in microtubes. For this study the commercial CFD code Fluent was utilized to enable numerical modeling of the developing flow field.
Numerical Modeling
The first step in this research was to study dual-wall driven flow. Dual-wall driven flow occurs when the fluid is driven by two moving walls with infinite width and finite length. This type of fluid flow is analogous to electro-osmosis and can be numerically predicted in a CFD software package without the need for user-defined functions. The following paragraph explains the comparison between electro-osmotic and dual-wall driven flows.
In electro-osmotic flow the movement of the fluid results from a nonuniform distribution of charge near the surface called the Electric Double Layer (or the Debye length). The Electric Double Layer (EDL) is created when the stationary surface acquires a relative charge. Thus, oppositely charged ions in the liquid are attracted to the surface and same charged ions are repelled from the surface.1 When the liquid is under the influence of an electric potential the EDL will migrate towards the cathode. The cations pull the rest of the fluid with it towards the cathode due to viscosity. Thus, one can see how wall driven flow is analogous to electroosmotic flow. The moving walls, like the EDL, are what drive the fluid. Therefore, extensive research can be done on dual wall-driven flow providing results that can be used in analyzing electro-osmotic flows. Subsequently true electro-osmotic flows can be modeled using the gridindependent meshes developed previously.
Results
Four different aspect ratios (L/ Dh) were studied and ten different plate velocities were studied for each aspect ratio. Each plate velocity corresponded to a specific Reynolds Number (Re). The Reynolds Number is defined for this flow as the plate velocity times the hydraulic diameter divided by the kinematic viscosity. Grid-independence was found for each aspect ratio by analyzing the highest plate velocity at various grid sizes. Once the refining of the grid size had less than a 1% difference in the solution and had similar velocity profiles along the channel then that grid could be used for all other plate velocities.
Grid-independence has been found for three of the four aspect ratios (5, 20, 40). For an aspect ratio of 5 all the ten plate velocities have been solved for and analyzed. For the other two aspect ratios numerical simulations are still being conducted for the different plate velocities. For each set of conditions a solution was found and the average velocity and the entrance length were determined. The ratio of the average velocity to the plate velocity increases as the Reynolds number or plate velocity decreases. This behavior is seen in Figure 1.
The lower plate velocities developed much quicker than the higher ones. The two highest plate velocities never developed along the 20-centimeter channel. As can be seen in Figure 2 an increase in the Reynolds number results in an increase in the ratio of entrance length to hydraulic diameter.
It is anticipated that as the aspect ratio increases the entrance region will be shorter. Thus with a decreasing diameter there is a decrease in the entrance length. Also it is anticipated that as the aspect ratio increases that the difference between the plate velocity and the average velocity will decrease.
Conclusion
The wall driven flow part of this project will be finished and published this coming semester. Then I will be continuing the study of the entrance region for electro-osmotic flow velocity profiles. This study will be my thesis research for my master’s degree.
Working on this project has increased my knowledge of electro-osmosis and of the CFD software package Fluent. I have also grown to understand how difficult and rewarding research can be. I feel better prepared for research in graduate school because of this opportunity.
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1 Probstein, R.F., 1994, Physicochemical Hydrodynamics, 2nd Ed., Wiley, New York.