DRAINAGE OF A THIN LIQUID-FILM CONFINED BETWEEN HYDROPHOBIC SURFACES

We investigate theoretically the drainage of a thin liquid film betwee n two undeformed hydrophobic spheres. The role of hydrophobicity is re vealed in the apparent slippage of liquid over the solid. The Origin o f the slippage effect is probably linked with a decrease in viscosity in the very thin near-to-wall layer. The solution is obtained for arbi trary values of slip lengths (from zero to infinity) as well as for ar bitrary radii of curvature of approaching surfaces. The main result co nsists in that the pressure and the drag force yield the product of co rresponding expressions for similar hydrophilic spheres and some corre ctions for slippage. These corrections depend only on the relationship s between the gap and the slip lengths. As a result, at distances that are much greater than both slip lengths of approaching surfaces, the liquid Row is the same as that for hydrophilic surfaces. If the gap wi dth exceeds considerably only one of the slip lengths then the pressur e and the resistance will be equal to those experienced by hydrophilic sphere moving toward the free bubble surface. If the gap is much smal ler than both slip lengths, the flow will be like that which arises wh en two bubbles approach each other. In the latter case, the hydrodynam ic drag is not inversely dependent on the gap but is inversely proport ional to the slip lengths and only logarithmically dependent on the ga p. The correction for slippage plays a dramatic role in the coagulatio n processes. The main result for coagulation consists in the possibili ty for collision to occur at a finite time. Also, this correction need s to be taken into account when the various properties of confined liq uids (first of all the hydrophobic attractive force) are investigated with the drainage technique.