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 [formula presented] and g, respectively. From liquid conservation, the early time behavior of the average interface position follows [formula presented] until a crossover time [formula presented] After that the pinning height [formula presented] is approached exponentially in time, in accordance with mean field theory. The statistical roughness of the interface is described by an exponent [formula presented] at all stages of the rise, but the dynamic length scale controlling roughness crosses over from [formula presented] to a time independent pinning length scale [formula presented] © 2001 The American Physical Society.