FLOW OF A LIQUID IN A NONUNIFORMLY HYDROPHOBIZED CAPILLARY

We investigate theoretically the flow of a liquid in a plane capillary whose walls are inhomogeneously hydrophobized. The role of hydrophobi city is revealed in the apparent slippage of a liquid over a solid. Th e origin of the slippage effect is probably linked to a decrease in vi scosity in a very thin layer adjacent to the wall. The solution is obt ained for a case where the size of the inhomogeneous sectors is much g reater than the capillary halfwidth. The formulae derived for a single inhomogeneous slippage region are generalized for several such sector s assuming weak overlapping. It is shown that the contribution to the flow from the inhomogeneously hydrophobized sectors substantially depe nds on their amplitudes, extents and conditions of the overlapping. It is also demonstrated that the problems in calculating an increase in the flow from the average (along the capillary axis) and from real var iable slip lengths may have different length scales. These observation s enable us to explain why an increase in the liquid flow through the hydrophobized capillary has been experimentally found only at a relati vely large contact angle, and why such a conventional criterion of sur face hydrophobicity as the average advancing contact angle cannot give a reliable prediction of the average value of slip length (and vice v ersa).