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.