Added mass fluid spheres

As for steady motion, shape changes and oscillations may complicate the accelerated motion of bubbles and drops. Here we consider only acceleration of drops and bubbles which have already been formed formation processes are considered in Chapter 12. As for solid spheres, initial motion of fluid spheres is controlled by added mass, and the initial acceleration under gravity is g y - l)/ y + ) (El, H15, W2). Quantitative measurements beyond the initial stages are scant, and limited to falling drops with intermediate Re, and rising... 

The virtual mass coefficient for a sphere in an invicid fluid is thus Cy = The basic model (5.111) is often slightly extended to take into account the self-motion of the fluid. In general the added mass force is expressed in terms of the relative acceleration of the fluid with respect to the particle acceleration. 

Discuss the limit > ->- 0. Show that there is a contribution to F for o> 1 that is independent of the viscosity. This term is known as the added-mass contribution and is identical to the force on an accelerating sphere in an inviscid fluid (that is, a fluid with /x = 0). It predicts that there is a contribution to the force that has the effect of adding an additional mass to the sphere that is equal to 1 /2 of the sphere volume times the fluid density. 

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