Long cross-over dynamics in capillary imbibition

We present new experimental and theoretical results of the spontaneous capillary invasion of dry capillary tubes by viscous liquids. We show how deviations from Washburn’s law, which predicts a diffusive-like growth of the advancing meniscus, persist for much of the invasion process–if not all. We identify two sources of hydro- dynamic resistance that account for this effect: the difference in velocity between the fluid reservoir and the fluid within the capillary, and the motion of the meniscus itself. Both contributions give rise to power-law terms in the force balance, which introduce a long cross-over from the initial acceleration of the liquid to the asymptotic limit of Washburn’s law. Such long cross-over dynamics, which we call slowly-slowing-down dynamics, is likely to govern other systems in spontaneous capillary flow where a persistent resistance to growth is present.