Oscillation of a Liquid Column in an Eccentric Annulus

The velocity distribution of flow in an eccentric cylindrical annulus is determined in an attempt to investigate the vertical capillary rise in the channel. The critical values of the radii ratio and the eccentricity at which the capillary rise changes from oscillatory to monotone or vice versa are determined. For a particular aspect ratio, the rise becomes monotonic as the eccentricity increases. The oscillations are also dampened as the annulus becomes thinner. These critical values depend on Galileo and Bond numbers as well as the contact angle. The results reduce to the limiting cases of concentric and fully eccentric annuli. The critical values are also calculated for the special arrangements when the radii ratios are 1 and 0. The latter limit is in perfect agreement with the conditions found in the literature for the classical circular channel.