(a) Use the velocity and pressure in Problem 8.7 to calculate the drag coefficient for a bubble in creeping flow. How do the pressure and viscous contributions compare?

(b) Derive an expression for the terminal velocity of the bubble.

Data from Problem 8.7:

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.]

Transcribed Image Text:

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