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 ε and g, respectively. From liquid conservation, the early time behavior of the average interface position follows H(t)∼t1/2 until a crossover time t*(g,ε). After that the pinning height Hp(g,ε) is approached exponentially in time, in accordance with mean field theory. The statistical roughness of the interface is described by an exponent χ≃1.25 at all stages of the rise, but the dynamic length scale controlling roughness crosses over from ξ×∼H1/2 to a time independent pinning length scale ξp(ε,g).