Aa. Alexeyev et Oi. Vinogradova, FLOW OF A LIQUID IN A NONUNIFORMLY HYDROPHOBIZED CAPILLARY, Colloids and surfaces. A, Physicochemical and engineering aspects, 108(2-3), 1996, pp. 173-179
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).