Meniscus formation

The term AFs2 accounts for the increase in the L/V area during meniscus formation and for a plate of unit width this can be related to the increase A1 in the length of the L/V line ... 

As already indicated, by applying the Kelvin equation (assuming hemispherical meniscus formation) and correcting for the adsorbed layer thickness, we are able to calculate the ranges of apparent pore width recorded in Table 12.5. The values of mean pore diameter, w, are obtained from the volume/surface ratio, i.e. by applying the principle of hydraulic radius (see Chapter 7) and assuming the pores to be non-intersecting cylindrical capillaries and that the BET area is confined to the pore walls. 

Fig. 2 Meniscus formation of a magnetic fluid by magnetic field.

Weeks BL, Vaughn MW et al (2005) Direct imaging of meniscus formation in atomic force microscopy using environmental scanning electron microscopy. Langmuir 21 8096... 

For nonvolatile liquids, meniscus formation is different 499,501]. The liquid layer is not formed by spontaneous adsorption from the vapor but by adding a certain amount of liquid to the system. For example, a lubricant is added to the surface of a hard disk. Assuming that the liquid spreads spontaneously, the layer thickness is simply the total amount added divided by the total surface area available. The fact that the liquid spreads spontaneously implies that we have a repulsive disjoining pressure between the solid-liquid and the liquid-gas interfaces. For layers bound by van der Waals forces, this pressure is given by... 

Let us turn to the general case of meniscus formation. We consider two surfaces that approach each other in an A-rich phase with a little dissolved B. We further assume that the surfaces attract B more than A. As a result, the contact angle of B on the surfaces in A, B(A). is lower than 90°. In this case, B will tend to form a meniscus of a B-rich phase between the two surfaces. To derive volume equation, we equate the chemical potential of molecules B in the A-rich phase to the chemical potential of molecules B in the meniscus. The chemical potential of molecules B in the A-rich phase is gg + J rin(cB/cg). Here, Cb is the concentration of molecules B in the A-rich phase and gg is the standard chemical potential of B at saturation concentration Cg. The saturation concentration is the concentration of molecules B in the A-rich phase in contact and in equilibrium with a B-rich phase with a planar interface. The chemical potential of molecules Bin the B-rich phase is pg + + V 2)> where Yab i ... 

The influence of interconnection effects is diagrammatically illustrated on the example of a simple system consisting of one wide capillary of radius pj and two capillaries of radius pj (see Fig. 1). Capillary condensation in cylindrical capillary of radius p occurs at one value of relative pressure x+ (X=P/Ps) and desorption at another value of relative pressure x- The values x+ and X- depend on pore radius p, moreover X-(p)>x+(P) In this inequality the capillary hysteresis on the level of one capillary is displayed. It is conditioned by the difference of the mechanisms of capillary condensation and desorption. Capillary condensation occurs by means of spontaneous filling at the moment of the loss of adsorption film stability on the internal surface of capillary. This process is not reversible. Desorption occurs at the moment of equilibrium meniscus formation on the open end of capillary. 

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