Interdisciplinary Applied Mathematics

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flows.


(a) Dynamic response of medium



(b) Velocity histories at various points



(c) Phase variation throughout medium



(d) Log-plot of velocity amplitude


FIGURE 3.16. Details of the flow dynamics for Kn = 10 and в = 1.0. Shear Stress Variation


In Figure 3.19, we present the effects of Kn and в on the wall shear stress using the DSMC results. We plot the shear stress normalized with the free-molecular and continuum shear stress values, to show that the DSMC results uniformly approach the correct asymptotic limits. We also compare the DSMC results with our empirical model for quasi-steady oscillatory flows given by equation (3.27). Good agreement between the empirical model and the DSMC results are observed for quasi-steady flows (в < 0.25). Beyond the quasi-steady flow regime there is a significant increase in the shear stress magnitude, especially for low Kn values. This is expected, since the shear stress is proportional to the velocity gradient, which increases with в, especially due to the formation of bounded Stokes layers. In the free-molecular flow limit, the shear stress reaches the same asymptotic limit of the steady plane Couette flow regardless of the Stokes number, as shown in equation (3.37b). In Figure 3.19, we observed similar behavior in the DSMC results. Interestingly, the DSMC data reached the asymptotic    shear    stress    value    in    the    transition    flow regime    for    large


Stokes number cases. This behavior is a manifestation of our definition of


(a) Dynamic response of medium



(b) Velocity histories at various points



(c) Phasevariation throughout medium



(d) Log-plot of velocity amplitude

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