Contact angle effect

Effects based on physicochemical behaviours Effects based on the structure Shape of the droplet/contact angle Effect of impurities... 

Here, 7j is the liquid surface tension, Sp>0 is a scaling constant, which includes both contact angle effects and the substantially larger scaling for capillary pressure in hydrophobic media. For the dependence of capillary pressure on liquid volume fraction, we use a simplified van Genuchten function see [14],... 

G. Rosengarten, D.J.E. Harvie, J. Cooper-White, Contact angle effects on microdroplet deformation using CFD, Appl. Math. Model., 2006, 30, 1033-1042. 

W. W. M. Siu and S. H.-K. Lee. "Effective conductivity computation of a packed bed using constriction resistances and contact angle effects," Int. J. Heat Mass Transfer, 43, 3917-3924, 2000. 

The seven known parameters that affect the bubble point pressure include the surface tension (liquid type), contact angle, effective pore diameter (which takes into account screen style, mesh, and metal type), liquid temperature, degree of subcooling (pressure), and pressurant gas type and temperature. The model will be validated through data collected over the past half-decade, as well as with data from the current work, which spans the space of these seven parameters. Ultimately, to be of topmost relevance for all future cryogenic propulsion missions, the model will be formulated in such a way that typical mission parameters like screen mesh, liquid properties, and pressurant gas properties can be input into the equation to obtain bubble point pressure easily and quickly at any desired condition. 

Siegel, in 1961, was the first to conduct experiments in micro-gravitational conditions. He considered both inertial and dynamic contact angle effects. Many other works were conducted in that condition since this seminal paper. A review is given in Ref. 86. 

Derive the equation for the capillary rise between parallel plates, including the correction term for meniscus weight. Assume zero contact angle, a cylindrical meniscus, and neglect end effects. 

Calculate the vapor pressure of water when present in a capillary of 0.1 m radius (assume zero contact angle). Express your result as percent change from the normal value at 25°C. Suppose now that the effective radius of the capillary is reduced because of the presence of an adsorbed film of water 100 A thick. Show what the percent reduction in vapor pressure should now be. 

The effect of surface roughness on contact angle was modeled by several authors about 50 years ago (42, 45, 63, 64]. The basic idea was to account for roughness through r, the ratio of the actual to projected area. Thus = rA. lj apparent and similarly for such that the Young equation (Eq.-X-18) becomes... 

Lin et al. [70, 71] have modeled the effect of surface roughness on the dependence of contact angles on drop size. Using two geometric models, concentric rings of cones and concentric conical crevices, they find that the effects of roughness may obscure the influence of line tension on the drop size variation of contact angle. Conversely, the presence of line tension may account for some of the drop size dependence of measured hysteresis. 

The effect of temperature on contact angle is seldom very great, as a practical observation. Some values of d0/dTare included in Table X-2 a common figure is about -0.1 degrees/K (but note the case of CS2 on ice also rather large temperature changes may occur in L1-L2-S systems (see Ref. 160). 

Bikerman [182] criticized the derivation of Eq. X-18 out of concern for die ignored vertical component of On soft surfaces a circular ridge is raised at the periphery of a drop (see Ref. 67) on harder solids there is no visible effect, but the stress is there. It has been suggested that the contact angle is determined by the balance of surface stresses rather than one of surface free energies, the two not necessarily being the same for a... 

The adsorption isotherm corresponding to Eq. X-51 is of the shape shown in Fig. X-1, that is, it cannot explain contact angle phenomena. The ability of a liquid him to coexist with bulk liquid in a contact angle situation suggests that the him structure has been modihed by the solid and is different from that of the liquid, and in an enmirical way, this modihed structure corresponds to an effective vapor pressure F , F representing the vapor pressure that bulk liquid would have were its structure that of the... 

The terms wetting and nonwetting as employed in various practical situations tend to be defined in terms of the effect desired. Usually, however, wetting means that the contact angle between a liquid and a solid is zero or so close to zero that the liquid spreads over the solid easily, and nonwetting means that the angle is greater than 90° so that the liquid tends to ball up and run off the surface easily. 

Fig. Xm-3. Effect of contact angle in determining water repellency of fabrics.

Clearly, it is important that there be a large contact angle at the solid particle-solution-air interface. Some minerals, such as graphite and sulfur, are naturally hydrophobic, but even with these it has been advantageous to add materials to the system that will adsorb to give a hydrophobic film on the solid surface. (Effects can be complicated—sulfur notability oscillates with the number of preadsoibed monolayers of hydrocarbons such as n-heptane [76].) The use of surface modifiers or collectors is, of course, essential in the case of naturally hydrophilic minerals such as silica. 

It was pointed out in Section XIII-4A that if the contact angle between a solid particle and two liquid phases is finite, a stable position for the particle is at the liquid-liquid interface. Coalescence is inhibited because it takes work to displace the particle from the interface. In addition, one can account for the type of emulsion that is formed, 0/W or W/O, simply in terms of the contact angle value. As illustrated in Fig. XIV-7, the bulk of the particle will lie in that liquid that most nearly wets it, and by what seems to be a correct application of the early oriented wedge" principle (see Ref. 48), this liquid should then constitute the outer phase. Furthermore, the action of surfactants should be predictable in terms of their effect on the contact angle. This was, indeed, found to be the case in a study by Schulman and Leja [49] on the stabilization of emulsions by barium sulfate. 

The first term on the right is the common inverse cube law, the second is taken to be the empirically more important form for moderate film thickness (and also conforms to the polarization model, Section XVII-7C), and the last term allows for structural perturbation in the adsorbed film relative to bulk liquid adsorbate. In effect, the vapor pressure of a thin multilayer film is taken to be P and to relax toward P as the film thickens. The equation has been useful in relating adsorption isotherms to contact angle behavior (see Section X-7). Roy and Halsey [73] have used a similar equation earlier, Halsey [74] allowed for surface heterogeneity by assuming a distribution of Uq values in Eq. XVII-79. Dubinin s equation (Eq. XVII-75) has been mentioned another variant has been used by Bonnetain and co-workers [7S]. 

The polarization model suggests strongly that orientational effects should be present in multilayers. As seen in Section X-6, such perturbations are essential to the explanation of contact angle phenomena. 

Effect of the value of the contact angle 6 of mercury on the calculated value of pore radius at different values of applied pressure P... 

One other cause of hysteresis remains to be mentioned. As was pointed out earlier (p. 177) the contact angle may be different as the mercury is advancing over or receding from a solid surface, and it depends also on the chemical and physical state of the surface the mercury may even react with the surface layer of the solid to form an amalgam. A change in 9 of only a few degrees has a significant effect on the calculated value of pore radius (cf. Table 3.15). 

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