By Patrick Bennett, Manhasset High School, Manhasset, NY; Chris Wiggins, Columbia University, New York, NY; and Marc Horner, Fluent Inc.

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Microchannels can be used to transport, mix, and process fluids such as DNA. By using these small channels, hand held devices can be created that perform the same task as entire laboratories in a space one-thousand times smaller and with an accuracy one-million times greater. Due to the small dimensions of microchannels (diameters on the order of 200 microns), their Reynolds numbers are always low - often approaching zero - resulting in Stokes flow and poor mixing.

Species contour map computed using CFD is in good agreement with experiment¹

A particular geometry that has sparked interest for its potential for chaotic and improved mixing1 utilizes an array of asymmetric chevron grooves etched onto the floor of a microchannel to promote transverse components in the fluid flow. CFD models for a number of microchannel designs of this type have been created in GAMBIT and solved in FLUENT. Using periodic boundary conditions and pressure-driven flow, the steady-state velocity field was computed for each, and a series of species advection calculations were run using a user-defined scalar (UDS) to simulate the transport and mixing of two distinct fluids. Contour plots of this scalar are in good qualitative agreement with experimental findings.¹

Species contours on the boundaries of the mixing device illustrate "ditch mixing" or mixing inside the grooves

Based on the UDS results, the degree of mixing was calculated through a standard deviation function that associates complete mixing with a value of 0 and complete segregation with a value of 0.5. These values were plotted against downstream length or converted into a "percent mixed" function for comparison with other geometries.

A nice benefit of using CFD for such a study is the flexibility that it yields in terms of visualization. Traditional empirical methods typically make use of confocal microscopy, which is difficult to do and only planar in nature. FLUENT allows for 3D continuum images to be rendered, displaying such things as the development of a transverse component to the flow, the creation of counter swirls, and the effectiveness of the "ditch mixing" process in the mixer (mixing inside the grooves). FLUENT has allowed for a much more robust exploration of the 3D, chaotic flow patterns in the system.

One geometric parameter of interest was the groove depth. Through the optimization trials, where different groove depths were analyzed and compared, it was shown that increasing the depth of the grooves both decreases pressure drop and increases effective mixing. This leads to the conclusion that the added volume of the grooves acts as a "buffer" to the no-slip condition on the walls of the channel and grooves and allows for stronger transverse components to be added to the flow, promoting the stretching and folding actions that are required for mixing.

Reference:

1 Stroock A.D., Dertinger S.K.W., Ajdari A., Mezic I., Stone H.A., and Whitesides G.M., "Chaotic Mixer for Microchannels." Science Magazine, 295, January 2002.

Editor's Note:

Pat Bennett presented this work at the American Physical Society, Division of Fluid Dynamics Meeting last November, and entered the 2002 Intel Science Talent Search and Siemens Westinghouse competitions. He was recognized as a semi-finalist at both events. A FLUENT user for three years, he will enter Stanford University in September.

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