Levelling of surface undulations

The rate at which the amplitude a of a sinusoidal undulation on the stuface of a liquid decreases with time as it is pulled out by surface tension forces is given by [10] 

The height H that a liquid rises in a capillary tube of radius a, in time t, (compared to the ultimate height Ho) is given by 

9 is the contact angle (this means that the height will decrease for mercury, since 9 = 140 °). 

The approximate thickness of a Newtonian liquid layer trapped at the tube wall by a large flattened bubble moving at a velocity U up/ along a tube of radius a is given by 

Exercise Calculate the rate of seepage of water through a crack 10 micron by 2 mm 

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Figure 10 Definition diagram for the levelling of surface undulations on a liquid.

Levelling of surface undulations under the action of surface tension... 

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