Dynamics of wetting with nonideal surfaces. The single defect problem

摘要

Under static conditions, the macroscopic contact angle thgr; between a (partially wetting) liquid, a solid, and air, lies between two limiting values thgr;r(receding) and thgr;a(advancing). If we go beyond these limits (e.g., thgr;=thgr;a+egr;, egr;0) the contact line moves with a certain macroscopic velocityU(egr;). In the present paper, we discussU(egr;) (at small egr;) for a very special situation where the contact line interacts only with one defect at a time. (This could be achieved inside a very thin capillary, of radius smaller than the average distance between defects.) Using earlier results on the elasticity and dynamics of the contact line in ideal conditions, we can describe the motions around lsquo;lsquo;smoothrsquo;rsquo; defects (where the local wettability does not change abruptly from point to point). For the single defect problem in a capillary, two nonequivalent experiments can be performed: (a) theforceFis imposed (e.g., by the weight of the liquid column in the capillary). Here we define egr;=(Fminus;Fm)/Fm, whereFmis the maximum pinning force which one defect can provide. We are led to a time averaged velocityUmacr;sim;egr;1/2. (b) ThevelocityUis imposed (e.g., by moving a horizontal column with a piston). Here the threshold force is not atF=Fm, but at a lower valueF=FUmdash;obtained when the contact line, after moving through the defect, leaves it abruptly. Defining egr;macr;=(Fmacr;minus;FU)/FU, whereFmacr; is the time average of the force, we find hereUsim;egr;macr;3/2. These conclusions are strictly restricted to the single defect problem (and to smooth defects). In practical situations, the contact line couples simultaneously to many defects: the resulting averages probably suppress the distinction between fixed force and fixed velocity.