J. Gaydos et Aw. Neumann, THE SHAPES OF LIQUID MENISCI NEAR HETEROGENEOUS WALLS AND THE EFFECT OF LINE TENSION ON CONTACT-ANGLE HYSTERESIS, Advances in colloid and interface science, 49, 1994, pp. 197-248
According to the classical theory of capillarity, which does not consi
der the influence of line tension, the wetting behaviour of solids is
governed by the Young equation of capillarity and a unique contact ang
le. This approach assumes that the surface of the solid is ideal. Real
solids, however, are both rough and chemically heterogeneous and thes
e surface characteristics lead to non-uniform wetting. Non-uniform wet
ting of solids may be characterized in part by contact angle hysteresi
s or the difference in equilibrium contact angles which exists between
adjacent heterogeneous patches on a solid. The presence of these patc
hes, which vary in size, inhibits uniform spreading. In addition, the
line of contact between the liquid and the solid may experience large
contortions in the vicinity of the patch-patch boundary. Using these b
asic physical ideas, a strategy is proposed for using a stripwise, het
erogeneous wall to evaluate numerically the effect of line tension upo
n the magnitude of the contact line contortions and the degree of cont
act angle hysteresis..The strategy uses a combination of incremental l
oading coupled with the Newton-Raphson method to generate a series of
non-zero line tension solutions. One solution sequence begins from an
initial analytical solution that corresponds to the zero line tension
case while another solution sequence begins from the case of infinite
line tension. These two sequences, which correspond to the outer and i
nner solutions of the modified Young equation of capillarity, i.e. mod
ified to include a line tension term, are matched numerically to gener
ate a complete contact line profile for different line tension values.
The primary conclusion which results is that the critical patch size
for the generation of contact angle hysteresis can be significantly la
rger than the dimension connected with the thickness of the liquid-vap
our interface, of the order of one micron.