Anomalous dynamics of capillary rise in porous media

The anomalous dynamics of capillary rise in a porous medium discovered experimentally more than a decade ago [T. Delker et al., Phys. Rev. Lett. 76, 2902 (1996)] is described. The developed theory is based on considering the principal modes of motion of the menisci that collectively form the wetting front on the Darcy scale. These modes, which include (i) dynamic wetting mode, (ii) threshold mode, and (iii) interface depinning process, are incorporated into the boundary conditions for the bulk equations formulated in the regular framework of continuum mechanics of porous media, thus allowing one to consider a general case of three-dimensional flows. The developed theory makes it possible to describe all regimes observed in the experiment, with the time spanning more than four orders of magnitude, and highlights the dominant physical mechanisms at different stages of the process.

Figure 1

Time dependence of the imbibition height in one-dimensional capillary rise. Circles: experimental data from [15] for beads $253\mu$m in diameter; dashed line: fit considered in [15]; solid line: present theory.

Figure 2

All four experimental sets from [15] for beads' diameters 180 $\mu$m ($▿$), 253 $\mu$m ($\circ$), 359 $\mu$m ($▵$), and 510 $\mu$m ($\square$). The corresponding theoretical curves are given as solid lines for the first three sets of data and as a dashed line for the last.