Capillary rise in a packing of glass spheres

Abstract

A series of experiments are performed to give insight into the mechanisms of liquid rise in a 3D dense random packing of glass spheres. A sharp knee in the log-log plot of water height h versus time t curve is observed, with an attendant change in h(t) characteristic from $h\propto t^{0.5}$ to $h\propto t^{0.05}$. This behaviour is observed for 5 choices of diameter distribution of spheres, such that the mean diameter is in the range of 0.22 mm to 1.20 mm, and the ratio of standard deviation to mean diameter lies between 0.014 and 0.157. Immediate arrest in water rise occurs when the water reservoir is removed from the bottom of the column, in support of the conclusion that water rise is by capillary action. In the post-knee regime of the h(t) response, water rise occurs in a jerky manner by a series of jumps, involving transverse jumps and more occasional vertical jumps in water ingress; each jump is by an increment of sphere diameter. The incubation time for each vertical jump is sensitive to height of meniscus and dictates the overall rate of water rise. Pendular-rings at the junctions between glass spheres are not observed above the meniscus; this casts doubt upon the notion that the jerky motion of the meniscus is due to the incubation time for a vapour-fed pendular-ring to grow and coalesce with the meniscus. Possible sources of the height-dependent incubation time for each vertical jump are discussed, including a time-dependent increase in surface tension. Additional insight is obtained by observing water rise, and glycerol rise in (i) a monolayer of glass spheres, (ii) in a capillary tube of diameter slightly greater than that of the glass beads and filled with a single column of glass spheres and (iii) an empty capillary tube. Continued liquid rise beyond the knee in the h(t) curve is noted in all cases except for that of an empty capillary tube.