Physica B 284}288 (2000) 145}146 Dynamics of the contact line on rough substrates A. Prevost*, E. Rolley, C. Guthmann, M. Poujade Laboratoire de Physique Statistique, de l 'Ecole Normale Supe & rieure 24, Rue Lhomond 75231 Paris, Ce & dex 05, France Abstract We have studied the spreading of a liquid He meniscus on two di!erent cesium substrates with a controlled random roughness. The mean distance between the `mesaa defects is of the order of 20 m. In the case of strong pinning, we "nd that the roughness of the contact line scales as ¸. Close to the wetting temperature, the liquid invades channels between the defects; this leads to a change in the scaling behavior of the roughness of the contact line. 2000 Elsevier Science B.V. All rights reserved. Keywords: Cesium; Contact line; He liquid; Surface roughness; Wetting Solid surfaces are usually rather disordered, being either rough or chemically heterogeneous, and there is yet no complete understanding on how this disorder a!ects the wetting properties of a liquid. We investigated this situation using liquid He on two di!erent rough cesium substrates. The substrates are prepared on optical mirrors (optical #atness /20, rms roughness 3 A s , diameter 30 mm) [1,2]. Using standard photo-lithographic techniques, 10 `mesaa defects are randomly distributed over the mirrors, covering 15% of the whole area. A 100 layers of cesium is then evaporated in situ at low temperature. For substrates S1, S2, respectively, the defects have a typical lateral size of 7, 10 m and are 10, 1 m high. The substrates are tilted by 43 with respect to the horizon, therefore specifying the average direction of the contact line (CL hereafter). We studied the motion of the CL on the dry substrates S1 and S2. On S1, we have also "lled with liquid helium the channels between the defects, to obtain a binary substrate (S1B hereafter): 85% of S1B is "lled with He and 15% is composed of disconnected dry Cs patches. Surprisingly, the mean contact angle of the He meniscus is non-zero on S1B and the CL is still well de"ned up to the wetting temperature ¹ . For all substrates, ¹ is * Corresponding author. E-mail address: prevost@physique.ens.fr (A. Prevost) We acknowledge F.R. Ladan for preparing the substrates. 1.95 K. In all the situations described here, defects are very strong, corresponding to a strong pinning of the CL. Let us call (x) the displacement of the CL relative to its average position. The CL roughness is characterized by =(x)"(((x#x )!(x ))), where the bar is an average on x along the CL and the brackets an average over all successive con"gurations of the CL. Fig. 1 shows =(x) obtained on S1, for various temper- atures ¹. The #uctuations of the CL are very large. Each single defect acts as a strong pinning center which de- forms the CL. =(x) increases with ¹: indeed, as pointed out in Ref. [3], the shape of the CL depends on the competition between the pinning potential of the dis- order and the CL elastic energy, which for a given defor- mation varies like sin ( is the contact angle, and is the surface tension of the liquid}vapor interface). Therefore, as ¹ increases, decreases and so does the elastic energy of the CL. We expect that, closer to ¹ , the pinning potential distorts more e!ectively the CL. At ¹"0.86 K, =(x) scales reasonably well as x but de- viates from any scaling law at higher ¹. Fig. 2 shows =(x) as measured on S2 and on S1B. On S2 (lower curves), the general behavior of =(x) resembles that is observed on S1. =(x) is however one order of magnitude lower, showing smaller #uctuations of the CL. =(x) scales always as x for ¹ ranging from 1.1 K to 0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 1 8 5 - 7