Interface pinning in spontaneous imbibition

Abstract

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(t)similar tot(1/2) until a crossover time t*(g, epsilon). 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 similar or equal to 1.25 at all stages of the rise, but the dynamic length scale controlling roughness crosses over from xi (x)similar toH(1/2) to a time independent pinning length scale xi (p)(epsilon ,g).