Liquid-filled cylindrical capillary

Figure 2. Flow of a single gas bubble through a liquid-filled cylindrical capillary. The liquid contains a soluble surfactant whose distribution along the bubble interface is sketched.

At temperatures below the critical point of the diffusing gas, the increase of pressure first leads to multilayer adsorption until finally all pores are filled with liquid. This phenomenon is called capillary condensation and this process starts when the gas pressure P surpasses the pressure Pt given by the Kelvin equation which is for a cylindrical capillary ... 

For experimental observation of the drainage and stability of liquid films the capillary cell illustrated in Fig. 16 is widely used (Scheludko and Exerowa 1959). First, the cylindrical glass cell is filled with the working liquid (say, water solution) next, a portion of the liquid is sucked out from the cell through the orifice in the glass wall. Thus, in the central part of the cell a liquid film is formed, which is encircled by a Plateau border. By adjustment of the capillary pressure the film radius, / , is controlled. The arrow (see Fig. 16) denotes the direction of illumination and... 

The open-pore theory was elaborated and given quantitative tfeatment by Cohn, who calculated thermodynamically the pressure required to fill open and cylindrical capillaries of radius r as a consequence of the deposition of successive layers of the liquid adsorbate (not by capillary condensation) as... 

The phenomena of capillary penetration of liquids into pore spaces filled with a fluid are related to the rise of liquids in capillary tubes where the flow is driven by interfacial pressure differences, as described by the Laplace equation of capillarity (equation (7.1)). The magnitude of the pressure difference across each liquid-fluid interface (meniscus) depends on the local curvature which is determined by the local wetting properties and pore geometry. In a cylindrical capillary, where the capillary wall is completely wettable by the liquid, the liquid-vapour interface can be assumed to be a hemisphere and = R2 = r r << a, cf. equation (7.48) below), where r is the capillary radius. Then, equation (7.1) becomes particularly simple and reduces to the following ... 

As a nonwetting liquid, mercury does not penetrate pores by capillary action. Filling of a pore requires an external force, inversely proportional to the pore size. The relationship below was first described by Washburn [93] considering the pores as cylindrical, nonintersecting capillary tubes. 

It is widely accepted that two mechanisms contribute to the observed hysteresis. The first mechanism is thermodynamic in origin [391,392], It is illustrated in Fig. 9.14 for a cylindrical pore of radius rc. The adsorption cycle starts at a low pressure. A thin layer of vapor condenses onto the walls of the pore (1). With increasing pressure the thickness of the layer increases. This leads to a reduced radius of curvature for the liquid cylinder a. Once a critical radius ac is reached (2), capillary condensation sets in and the whole pore fills with liquid (3). When decreasing the pressure again, at some point the liquid evaporates. This point corresponds to a radius am which is larger than ac. Accordingly, the pressure is lower. For a detailed discussion see Ref. [393],... 

Another pore filling model based upon capillary equilibrium in cylindrical pores has recently been proposed in which the condition of thermodynamic equilibrium is modified to include the effects of surface layering and adsorbate-adsorbent interactions [135-137]. Assuming that the vapor-liquid interface is represented by a cylindrical meniscus during adsorption and by a hemispherical meniscus during desorption, and invoking the Defay-Prigogene expression for a curvature-dependent surface tension [21], the equilibrium condition for capillary coexistence in a cylindrical pore is obtained as... 

Problem 12-10. Capillary Instability of a Gas Cylinder in a Liquid. Consider an infinitely long cylindrical interface of radius R that is filled with a gas and surrounded by an exterior liquid (r > R). The surface tension is denoted as y and the density of the liquid is p. We consider an initial infinitesimal perturbation of the shape... 

At adsorption temperatures below the critical temperature of the component to be adsorbed, the adsorbent pores may fill up with liquid adsorpt. This phenomenon is known as capillary condensation and enhances the adsorption capacity of the adsorbent. Assuming cylindrical pores, capillary condensation can be quantitatively described with the aid of the Kelvin equation, the degree of pore filling being inversely proportional to the pore radius. 

The interface gas/electrolyte in a cylindrical pore consists of a meniscus and a thin film of electrolyte above the meniscus (see Fig. 98 a). The formation of the meniscus in a narrow capillary partially filled with a liquid is a well-known phenomenon. Evidence for the presence of a thin film of electrolyte above the meniscus was established by Will [24] and by Knaster and Temkin [25] for partially immersed electrodes. Good agreement was found between the experimental data on the H2 oxidation... 

A critical water-wall interaction was determined by complementary studies of the condensation/evaporation transition in open pores and of the liquid-vapor coexistence in closed pores [30, 32, 205, 208], Such studies were performed for water confined in cylindrical pores of the radius Rp= 12 A. The liquid density in open pore was obtained by direct equilibration in the Gibbs ensemble of confined water and a bulk liquid water at ambient pressure, starting from completely filled pores [208]. The liquid density obtained is a monotonic function of the water-waU potential Uq, and the values obtained at T = 300 K are shown in Fig. 65 (solid squares). In parallel, the density of liquid water at equilibrium with saturated vapor in pore was calculated (Fig. 65, open circles). It also depends on Uo, however, weaker than the density in an open pore. Liquid densities in closed and open pores become equal at Uq — l.Okcal/mol (see crossing point in Fig. 65). If —Uq < l.Okcal/mol, only water vapor is stable in the pore. Accordingly, liquid is stable in the pore, if -Uq >1.0 kcal/mol. Thus, the value of Uq —1.0 kcal/mol separates regimes of capillary evaporation and capillary condensation [32, 208]. This value approximately coincides with the critical water-wall interaction, which provides an absence of wetting or drying transitions up to the liquid-vapor critical point (see Section 2.4). 

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