RESONANCE OF A LIQUID COLUMN IN A CAPILLARY-TUBE

A liquid column with height H, trapped in a capillary tube of radius R , possesses a mechanical eigenfrequency. The axis of the capillary tub e is oriented parallel to the gravitational force, so that the lower m eniscus is fixed at the lower end of the tube, if the density rho of t he liquid is higher than that of the surrounding fluid. Basic assumpti ons of the linear theory are a pinned contact line, the spherical cap approximation and H much greater than R. The shape of the susceptibili ty function, the dimensionless ratio of the mean liquid displacement t o the driving pressure gradient plotted versus frequency, depends on t he parameter X-0 = omega(0)/omega(c) only, where omega(0) denotes the eigenfrequency of the undamped system and omega(c) = eta/(rho R-2) sta nds for the characteristic frequency with the viscosity eta. For X-0 > root 24 the system is underdamped and resonance occurs, while for X-0 < root 24 the system is overdamped and resonance cannot be observed. If one interpretes capillary tubes as a model of a porous medium, the present mechanism contributes to the damping of sound waves in porous media saturated by two immiscible fluids, one of them being trapped.