Coaxial disk devices are widely used at low Reynolds numbers to simulate cellular shear loading. Here, we develop a mathematical theory for analyzing fluid behavior in these instruments. It improves upon classical results by accounting for both unsteady dynamics and wall drag effects. All previous models are shown to be special cases of the present one. Most devices utilize a low aspect ratio, for which we find wall effects to be limited to small regions near the periphery. In these cases, classical theory yields acceptable precision over most of the domain. Investigators commonly simulate pulsatile effects using low-frequency sinusoidal forcing. Results indicate that fluid motion remains essentially harmonic, permitting the exact solution to be approximated by a simple separable expression. This approximation should be useful in analyzing specific configurations. A wavelike flow mode conjectured to exist at high Strouhal numbers is also discussed.
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Research Article| November 01 2001
Mathematical analysis of coaxial disk cellular shear loading devices
Michael C. Wendl; Mathematical analysis of coaxial disk cellular shear loading devices. Rev. Sci. Instrum. 1 November 2001; 72 (11): 4212–4217. https://doi.org/10.1063/1.1409569
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