Dc is the capillary, R = radius and is the same as the capillary Which way the b

Question

Dc is the capillary, R = radius and is the same as the capillary

Which way the bubble will move as it is observed at the location shown in the illustration below. Explain why!? from left to right from right to left What is the velocity of the bubble at the location shown in the illustration? Assume that frictional losses in the Mechanical Energy Balance equation are given by: F = 32u-mu L/ rho where u- is the bubble velocity. Illustration Data dc = 500 [mu m]; R = 250 [mu m]; L = 0.004 [m]; mu water = 0.001 [Pa s]; rho water = 1000 [kg/m3]; sigma water-air = 0.072 [N/m].

Explanation / Answer

a)

The bubble moves from left to right.
Logic:
Inside the bubble the pressure will be

P = Patm + 2/R

where is the surface tension of the fluid.

So, just inside the liquid layer on the left end the pressure is more than Patm and just inside the liquid layer on the right end the pressure is equal to Patm. So the positive pressure gradient is rightward wich will drive the fluid rightward as pressure is more on left.

b)

Work done by internal pressures in moving the fluid= W =(P-Patm)*R2*V

where V is the velocity of bubble.

By conservation of energy

Work done by pressures = Wrk done by friction

Solving both equations u get V.

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