Describing the motion of a bubble through water

[ttja]

Homework Statement

A bubble of air which is 1 mm in diameter is released without initial velocity in the
volume of glycerol at room temperature. Describe the motion of the bubble as a
function of time assuming that its diameter remains unchanged. Note that friction
force acting on the bubble is given by

Drag Force = -4$$\pi$$$$\eta$$Rv

where h is the viscosity of the liquid, R is the radius of the bubble, and v is its
velocity. Note that the numerical coefficient in this formula is different from that for a
solid sphere moving in the liquid (which is 6π). Explain qualitatively why the
numerical coefficients in tbubble are different.

Homework Equations

F=ma
F=$$\rho$$Vg

The Attempt at a Solution

Tell me if I'm going about this the wrong way. To describe the motion of the bubble, which is essentially finding the function of position with respect to time, I equated F = ma = Fb - Ff. Then integrating knowing that the initial conditions for velocity and position are 0, perhaps this could be it?

As I researched, however, I had found that the initial acceleration for the bubble starting at rest to be 2g, whereas, by my method, i would only get 1g.

Other considerations I had heard from discussion are that the mass of the air inside the bubble is negligible, so am i supposed to use the mass of water in contact to the surface when calculating "m" ? In addition I had also heard something about work, but i have no idea how that plays in this problem.

As for the second part, I thought about how...since the bubble is not a rigid body, the molecules themselves are in a circular flow that ultimately act as a .. buffer of some sort? i know I am not making sense but i know there should be a difference between fluid in contact with fluid and fluid in contact with a solid.

 

[ehild]

Do not forget about Archimedes' principle when counting forces.

ehild