Meniscus Forces and Profiles: Theory and Its Applications to Liquid-Mediated Interfaces

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Abstract
A theory for obtaining meniscus forces and profiles for any given liquid-mediated interface is presented that includes the effects of surface interactions, adsorption and evaporation of liquid films. The meniscus force is obtained from the derivative of the total free energy of liquid-mediated interface, which requires the meniscus profile to be known. The meniscus profile is the solution of a second-order differential equation, as derived from Pascal’s law for static incompressible liquids with inclusion of surface interactions. For nonvolatile liquid films, 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 initial liquid conditions are considered. Type I represents the case in which one surface is wet and the other is initially dry, having a finite contact angle with the liquid. Type II represents the situation in which both surfaces are wet by either a liquid or by two different liquids before making contact. If two or more types of liquids are involved at the interface, miscibility of the liquids and interactions due to other liquid(s) have to be also considered. For contacts with azimuthal geometry, which is merely a mathematical convenience, such as ellipsoidal/spherical, conical or crater, the theory generates several analytical formulae for calculating meniscus forces without involving meniscus profiles. These 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 asymmetric 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 meniscus force in the previous models. It is found that for a spherical or a crater contact geometry, the surface interactions have little effect on the meniscus force provided the lateral meniscus dimension is much smaller than the radius of the sphere or of the crater. However the surface interactions have a large effect on the meniscus force for other contact geometries, such as conical contact geometry. The calculated meniscus forces are compared with the normal component of the stiction force measured at the laser textured surfaces and good agreement is found. The calculated meniscus profiles are also found in good agreement with that measured using light interferometer technique between two cross cylinders. One very interesting finding of our theory is that the meniscus volume grows first and may then shrink, as observed experimentally by others, because the initially dry surface become wetted and the boundary conditions change over from Type I to Type II.