Meniscus radius

The situation shown in Figure lb is a coordinated evaporation from wide entrances A and B. Under continuous evaporation both menisci move inside the capillary having the same curvature. When one of the meniscus passes the narrowest section (rA > rB), the capillary equilibrium infringes, and mass transfer from A to B occurs spontaneously until the meniscus radii equalize. Such spontaneous mass transfer, known as jumps of Haines, occur when... 

FIGURE 40.15 Capillary-function curves determined using image analysis, (a) Spruce (Picea abies) the cells have thicker walls and smaller radial extension in latewood part, hence the highest value of the capillary-pressure curve. One also has to be aware that full saturation is obtained with a lower amount of water in latewood (the porosity of this part is very small) (b) beech (Fagus sylvatica) because beech is a pore diffuse-porous hardwood species, no significant difference is observed between these parts. The low capillary pressure obtained for saturation values above 0.2 corresponds to the meniscus radii located in the vessel elements. The dramatic increase for low saturation values is due to the small lumen diameters of the parenchyma and fiber cells. 

Radius of curvature of the meniscus Radius of micro-channel Temperature Inlet velocity... 

At the interface the mass and thermal balance equations are valid. If one assumes that the liquid-vapor interface curvature is constant, accordingly (7)3-71)1111 = c/T men, Where Pq and Pl are the vapor and liquid pressure at the interface, a is the surface tension, and/ men is the meniscus radius. 

The size of the largest pores that can be determined by this technique is limited by the rapid change in meniscus radius with pressure as the relative pressure P/P0 approaches unity. This limit corresponds to pore radii in the neighborhood of 150 to 200 A, corresponding to a relative pressure of 0.93 in the former case. The smallest pore radii that can be observed by this technique are those near 10 A. Although measurements may be reported corresponding to... 

Radius of curvature of the liquid meniscus Radius of the liquid bridge Radius of curvature of the tip Stiffness... 

A formula that accounts for the change in the meniscus radius in the middle of the biconcave drop during film formation is given in [64]... 

The capillary condensation method is widely used for the investigation of mesopores. The size of the largest pores, that can be measured, is limited by the rapid change of the meniscus radius with pressure as the relative pressure P/Pt nears unity (because of massive condensation of the adsorbent around the boiling point). This holds for radii of about 100 nm. The smallest pore sizes that can be determined by this method are about 1.5 nm. 

Equation (3.27) can be applied to both adsorption and desorption branches of the isotherm. For the model of a bundle of capillary tubes, it is more appropriate to use the desorption branch of the isotherm for the determination of the pore size distribution. The basic idea is that the effective meniscus radius is the difference between the capillary radius and the thickness of the multilayer adsorption at p/p°, which can be obtained from de Boer s t-plot. In practice, at each desorption pressure, P, the capillary radius can be calculated from Eq. (3.27). The actual pore radius is then the sum of the calculated capillary radius and the estimated thickness of the multilayer. The exposed pore volume and surface area can be obtained from the volume desorbed at that specific desorption pressure. This step can be repeated at different desorption pressures. Except for the first desorption step, the desorbed volume should be corrected for the multilayer thinning on the sum of the area of the previously exposed pores. The pore size distribution can then be determined from the slope of the cumulative volume versus r curve. 

It is important to realize that this discussion implies the existence of a continuous phase. The expression may no longer be valid when the meniscus radius becomes comparable with molecular dimensions ft the Laplace equation was derived assuming r b... 

Fig. 5.44 Pore filling during the grain growth. A large pore is stable until grain growth increases the liquid meniscus radius sufficiently for capillary refilling of the pore. Reproduced with permission from [101]. Copyright 1984, Springta...

For perfectly conducting liquids, Taylor [7] showed that a conical meniscus with a half angle of 49.3° is produced by considering the static equilibrium balance between the capillary and Maxwell stresses in Eqs. 3, 6, and 17. In the perfect conducting limit, the drop is held at constant potential, and hence, the gas phase electric field at the meniscus interface is predominantly in the normal direction. It can then be shown that the normal gas phase electric field scales as in which R is the meniscus radius which then stipulates from Eq. 7 that the Maxwell pressure Pm n,g scales as HR, therefore exactly balancing the azimuthal capillary pressure pc ylR for all values of R. This exact balance, and absence of a length scale selection, is responsible for the formation of a static Taylor cone (Fig. 1) in the dominant cone-jet mode in DC electrosprays [8]. 

When a meniscus radius exists at a liquid-vapor interface, there is a pressure difference across the interface, which can be determined by the Laplace-Young equation, i.e.,... 

Figure 10.35 Calculation model for pore refilling based on spherical grains surrounding the pore. Pore refilling depends on the liquid meniscus radius exceeding the pore radius. (From Ref. 57.)...

FIG. 15 System energy change with (a) the apparent contact angle 6 and (b) non-dimensional meniscus radius, when axisymmetric meniscus forms under a horizontal plate. The system is stable between states A and B. 

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