Roughness and dynamics of a contact line of a viscous fluid on a disordered substrate

We have studied the roughness and the dynamics of the contact line of a viscous liquid on a disordered substrate. We have used photolithographic techniques to obtain a controlled disorder with a correlation length ξ = 10μm. Liquids with different viscosity were used: water and aqueous glycerol solution. We have found that the roughness W of the contact line depends neither on the viscosity nor on the velocity v of the contact line for v in the range 0.2-20μm/s. W is found to scale with the length L of the line as L ^ζ with a roughness exponent ζ = 0.51±0.03. This value is similar to the one obtained with superfluid helium. In the present experiment, we have checked that the motion of the contact line is actually overdamped, so that the phenomenological equation first proposed by Ertas and Kardar should be relevant. However, our measurement of ζ is in disagreement with the predicted value ζ = 0.39. We have also analyzed the avalanche-like motion of the contact line. We find that the size distribution does not follow a power law dependence. Received 18 April 2002