Wetting of fibers : theory and experiments

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Abstract
We first present a digest of a previous theoretical study of one of us (F. B.) about the static aspects of wetting of thin fibers. This study includes the effects of long range Van der Waals interactions. Two points merit special attention : (i) the threshold value Sc of the spreading parameter for complete wetting is greater than zero (Sc = 3/2 γ (a/b)2/3 with γ the liquid surface tension, b the fiber radius and a = (A/6 π γ)1/2 where A is a Hamaker constant (A = ASL - ALL)) ; and (ii) when S > Sc and when the liquid is in contact with a reservoir of zero-curvature, the thickness of this wetting film is locked to ec = a2/3 b1/3, i.e. the thickness for S = S c. A recent study about the dynamics of such a microscopic film is then presented : the situation of upward creeping of a liquid on a fiber is specially studied. As for the planar geometry two regimes can be distinguished : a static regime, defined by the equilibrium between disjoining pressure, Laplace pressure and gravity : e(h) ∼ (h + K -2/b)-1/3 and a dynamic regime where viscous terms have to be considered while gravity can be neglected : e(h, t) ∼ t/h2. These two profiles first creep with diffusion equations. After a characteristic time, the static profile then follows a h s ∼ t 3/5 — law and catches the diffusive tongue up at the final equilibrium height H. These theoretical predictions are tested by a new set of experiments using spin labels and electron spin resonance (ESR). Not all our results are understood via our theory. Particularly the creeping velocity is too large when compared to theory. The explanation of this discrepancy is due to surface roughness. Nevertheless we believe that Van der Waals interactions are relevant in our problem : the final state seems to involve a static wetting film along the fiber