Stokes oscillating boundary layer

At this point we digress slightly to recall the classic Stokes oscillating boundary layer problem (Lighthill 1978, Landau c Lifshitz 1987). In this problem a large volume of fluid, say in the region z<0, is bounded by a solid... 

From the description of the Stokes problem, we conclude that the incompressible surfactant film causes an oscillating Stokes-type boundary layer to develop, which is the predominant damping mechanism. By the same argument as before, the amplitude of the wave solution satisfying Laplace s equation is modified by an exponential attenuation exp(-)3 Here, however, we take the attenuation length to be given by the viscous boundary layer thickness of Eq. (10.5.34), from which, by comparison with Eq. (10.5.32),... 

Both the Stokes flow solutions and the large Reynolds number boundary layer solutions assume that the flow around the bubble is axisymmetric. This assumption fails for some situations at large Reynolds numbers. Saflinan [20] and Hartunian and Sears [21] performed experiments on bubbles at large Reynolds numbers. For bubbles in distilled water, they found that bubbles larger than a critical size tend to spiral or zigzag. Hartunian and Sears reported the critical value of the equivalent spherical diameter to be 1.7 mm. Later, Duineveld [15] found that the critical value was 1.9 mm. In tap water, the critical value is smaller. Hartunian and Sears reported the value to be 1.3 mm. Table 1 summarizes experimental results for the onset of oscillations. 

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