C. Gao et al., MENISCUS FORCES AND PROFILES - THEORY AND ITS APPLICATIONS TO LIQUID-MEDIATED INTERFACES, Journal of tribology, 120(2), 1998, pp. 358-368
A theory for obtaining meniscus forces and profiles for any given liqu
id-mediated interface is presented that includes the effects of surfac
e interactions, adsorption and evaporation of liquid films. The menisc
us force is obtained from the derivative of the total free energy of l
iquid-mediated interface, which requires the meniscus profile to be kn
own. The meniscus profile is the solution of a second-order differenti
al equation, as derived from Pascal's law for static incompressible li
quids with inclusion of surface interactions. For nonvolatile liquid f
ilms, the total liquid amount at the interface is a conserved quantity
, whereas for volatile liquids, the liquid films are in thermodynamic
equilibrium with their respective vapor phase. Two typical types of in
itial liquid conditions are considered. Type I represents the case in
which one surface is wet and the other is initially dry, having a fini
te contact angle with the liquid. Type II represents the situation in
which both surfaces are wet by either a liquid or by two different liq
uids before making contact. If two or more types of liquids are involv
ed at the interface, miscibility of the liquids and interactions due t
o other liquid(s) have to be also considered. For contacts with azimut
hal geometry, which is merely a mathematical convenience, such as elli
psoidal/spherical, conical or crater, the theory generates several ana
lytical formulae for calculating meniscus forces without involving men
iscus profiles. The formulae can be handily applied to various surface
probes techniques such as Scanning Probe Microscopy or Surface Force
Apparatus. The proposed theory is also applicable to ''meniscus rings'
' formed around crater geometry, such as encountered in laser-textured
magnetic disks. In this case, the outer meniscus ring can be asymmetr
ic to the inner meniscus ring if no liquid passage exists between the
inner and outer meniscus ring. Even for the case of spherical contact
geometry, the calculated meniscus profile is very nonspherical with a
much larger volume than that of the widely assumed spherical meniscus
profile for Type I conditions, leading to an under-estimation of the m
eniscus force in the previous models. It is found that for a spherical
or a crater contact geometry, the surface interactions have little ef
fect on the meniscus force provided the lateral meniscus dimension is
much smaller than the radius of the sphere or of the crater. However t
he surface interactions have a large effect on the meniscus force for
other contact geometries, such as conical contact geometry. The calcul
ated meniscus forces are compared with the normal component of the sti
ction force measured at the laser textured surfaced and good agreement
is found. The calculated meniscus profiles are also found in good agr
eement with that measured using light interferometer technique between
two cross cylinders. One very interesting finding of our theory is th
at the meniscus volume grows first and may then shrink, as observed ex
perimentally by others, because the initially dry surface become wette
d and the boundary conditions change over from Type I to Type II.