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Accurate Analytical Models of Fluid Friction in Rectangular Microchannels

S. W. Tchikanda, R. H. Nilson and S. K. Griffiths
Sandia National Laboratories, US

Keywords: Numerical Methods, Microfluidics Systems, Mathematical Modeling and Scaling Laws

Liquid flow in microchannels is important to a number of technologies including cooling of microelectronics by heat pipes and capillary pumped loops as well as capillary wetting of channels in molding processes and in chip-based devices for identification of chemical and biological species. Since channel lengths in these applications greatly exceed lateral channel dimensions, such flows can be accurately and efficiently modeled using one dimensional analyses in which the frictional flow resistance is described in terms of a friction coefficient that depends on the channel geometry, the fraction of the channel depth that is filled with liquid, and the wetting angle between the meniscus and the solid channels walls. Although a number of previous numerical studies have provided friction coefficients for some subsets of the important parameter range, they generally do not span a wide range of channel aspect ratios and wetting angles and rarely do they provide simple analytical approximations needed for application by others. Here we use numerical solutions of the Navier Stokes equations to guide the construction of analytical approximations by blending three asymptotic solutions that apply in different ranges of the ratio of channel width to fluid depth. The approximations are easily applied and are accurate within a few percent over the full range of parameters.

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