Spontaneous penetration of liquids into capillaries and porous membranes revisited

A critical review of the problem of spontaneous penetration of a wetting li quid into pore channels shows that no theory exists to quantitatively predi ct the initial stage of imbibition. Since C, H, Bosanquet (1923, Phil, Mag. 45, 525), the theory operates with an universal velocity U-Bosanquet = (2 gamma cos theta/rhor)(1/2), with gamma being the surface tension, theta the contact angle, r the capillary/pore radius, and rho the fluid density. It is assumed that the initial impulse of the liquid entering the pore is insi gnificant for the penetration dynamics. Though the importance of the outsid e flow pattern has been noted in many papers, a thorough mathematical analy sis of this effect is lacking in the literature, We derived a generalized e quation of the fluid front motion by averaging the Euler equations of flow inside and outside the pore space, This analysis shows the significance of the flow patterns at the pore entrance. The initial stage of liquid imbibit ion is studied in the inviscid approximation using the methods of dynamic s ystems. The phase portrait of the dynamic system reveals a multiplicity of penetration regimes, Remarkably, the Bosanquet solution represents a partic ular regime, with the apparent mass being set zero. The Bosanquet trajector y refers to a separatrix of the phase portrait. It is shown that the initia l conditions affect the rate of uptake significantly. The initial condition s stem from the prehistory of the fluid motion outside the pores prior to t he liquid-solid contact. The phase portrait method allows us to distinguish two groups of solutions for the capillary rise dynamics of an inviscid flu id, The first group of trajectories corresponds to the liquid front rebound ; the second group includes cyclic trajectories which correspond to the per iodic regimes with liquid front oscillations at the equilibrium position. T he upper estimate of the oscillation amplitude is found, (C)2001 Academic P ress.