Consider creeping flow of a liquid at velocity U relative to a spherical bubble of radius R, with coordinates as in Fig. 8.7. Show that the velocity and pressure in the surrounding liquid are

where μ is the viscosity of the liquid. [The general solution given by Eqs. (8.3-28)–(8.3-30) is applicable again here.]

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v, (r, 0) = = Ucos 01 (1-4) == vo (r; 0) Usin 0 1 P(r, 0) = R (1-1/7/2) r MUR 1.2 COS (P8.7-1) (P8.7-2) (P8.7-3)