Evaporation and gravity induced pinning in spontaneous imbibition are examined within a phase field formalism. Evaporation is introduced via a nonconserving term and gravity through a convective term that constrains the influx of liquid. Their effects are described by dimensionless coupling constants $\epsilon$ and g, respectively. From liquid conservation, the early time behavior of the average interface position follows $H\left(t\right)\mathrm{}\sim t^{1/2}$ until a crossover time $t^{*}(g,\epsilon ).\mathrm{}$ After that the pinning height $H_p(g,\epsilon )$ is approached exponentially in time, in accordance with mean field theory. The statistical roughness of the interface is described by an exponent $\chi \simeq 1.25$ at all stages of the rise, but the dynamic length scale controlling roughness crosses over from ${\xi }_{\times }\sim H^{1/2}$ to a time independent pinning length scale ${\xi }_p(\epsilon ,g).\mathrm{}$

• Received 1 May 2001

DOI:https://doi.org/10.1103/PhysRevE.64.051605