Upward creep of a wetting fluid : a scaling analysis

Abstract

A Van der Waals fluid, climbing from a reservoir along a vertical wall, should display a remarkable cascade of events : i) A macroscopic meniscus is set up in a short time t1 and reaches the classical altitude hc∼ 1 mm. ii) A dynamic precursor film appears at a time t2 ∼ 10-2 s. The tip of the « tongue» advances fast up to a time t3 ∼ 1 s and then more slowly. iii) A portion of static film builds up (from hc, up to a certain altitude h1(t)) at times t > t4 (t4∼ 10 s). iv) A self-similar, slow, growth of both the « tongue» and the static portion is reached after a time t = t5 ∼ 10 days