Interfacial equation

See also - electrode surface area, -> Gibbs-Lippmann equation, - interfacial tension, -> interface between two liquid solvents, -> interface between two immiscible electrolyte solutions -> Lippmann capillary electrometer, -> Lippmann equation -> surface, -> surface analytical methods, - surface stress. 

Young-Laplace Equation. Interfacial tension causes a pressure difference to exist across a curved surface, the pressure being greater on the concave side (i.e., on the inside of a droplet). In an interface between phase A in a droplet and phase B surrounding the droplet, the phases will have pressures and If the principal radii of curvature are Ri and R2, then... 

Exponential parameter shift factor in WLF equation Interfacial tension Shear strain Shear rate... 

See also -> electrode surface area, Gibbs-Lippmann equation, -> interfacial tension, interface between... 

Prefactor in the Arrhenius- or Van t Hoff equations Interfacial area density denoting the interface area per unit... 

This rule is approximately obeyed by a large number of systems, although there are many exceptions see Refs. 15-18. The rule can be understood in terms of a simple physical picture. There should be an adsorbed film of substance B on the surface of liquid A. If we regard this film to be thick enough to have the properties of bulk liquid B, then 7a(B) is effectively the interfacial tension of a duplex surface and should be equal to 7ab + VB(A)- Equation IV-6 then follows. See also Refs. 14 and 18. 

Referring to Fig. IV-4, the angles a and /3 for a lens of isobutyl alcohol on water are 42.5° and 3°, respectively. The surface tension of water saturated with the alcohol is 24.5 dyn/cm the interfacial tension between the two liquids is 2.0 dyn/cm, and the surface tension of n-heptyl alcohol is 23.0 dyn/cm. Calculate the value of the angle 7 in the figure. Which equation, IV-6 or IV-9, represents these data better Calculate the thickness of an infinite lens of isobutyl alcohol on water. 

Assume that an aqueous solute adsorbs at the mercury-water interface according to the Langmuir equation x/xm = bc/( + be), where Xm is the maximum possible amount and x/x = 0.5 at C = 0.3Af. Neglecting activity coefficient effects, estimate the value of the mercury-solution interfacial tension when C is Q.IM. The limiting molecular area of the solute is 20 A per molecule. The temperature is 25°C. 

Values of interfacial tension of nucleus from turbulent jet measurements, by various equations [44]. 

Equations X-12 and X-13 thus provide a thermodynamic evaluation of the change in interfacial free energy accompanying adsorption. As discussed further in Section X-5C, typical values of v for adsorbed films on solids range up to 100 ergs/cm. ... 

Ruch and Bartell [84], studying the aqueous decylamine-platinum system, combined direct estimates of the adsorption at the platinum-solution interface with contact angle data and the Young equation to determine a solid-vapor interfacial energy change of up to 40 ergs/cm due to decylamine adsorption. Healy (85) discusses an adsorption model for the contact angle in surfactant solutions and these aspects are discussed further in Ref. 86. 

The extensive use of the Young equation (Eq. X-18) reflects its general acceptance. Curiously, however, the equation has never been verified experimentally since surface tensions of solids are rather difficult to measure. While Fowkes and Sawyer [140] claimed verification for liquids on a fluorocarbon polymer, it is not clear that their assumptions are valid. Nucleation studies indicate that the interfacial tension between a solid and its liquid is appreciable (see Section K-3) and may not be ignored. Indirect experimental tests involve comparing the variation of the contact angle with solute concentration with separate adsorption studies [173]. 

The matter of rfi is of some importance to the estimation of solid interfacial tensions and has yet to be resolved. On one hand, it has been shown that the Giralfco and Good model carries the implication of rr being generally significant [10], and on the other hand, both Good [193] and Fowkes [145] propose equations that predict... 

Li and Neumann sought an equation of state of interfacial tensions of the form 7 l = /(Tlv. TSv). Based on a series of measurements of contact angles on polymeric surfaces, they revised an older empirical law (see Refs. 216, 217) to produce a numerically robust expression [129, 218]... 

Using appropriate data from Table II-9, calculate the water-mercury interfacial tension using the simple Girifalco and Good equation and then using Fowkes modification of it. 

An equation algebraically equivalent to Eq. XI-4 results if instead of site adsorption the surface region is regarded as an interfacial solution phase, much as in the treatment in Section III-7C. The condition is now that the (constant) volume of the interfacial solution is i = V + JV2V2, where V and Vi are the molar volumes of the solvent and solute, respectively. If the activities of the two components in the interfacial phase are replaced by the volume fractions, the result is... 

Thus, adding surfactants to minimize the oil-water and solid-water interfacial tensions causes removal to become spontaneous. On the other hand, a mere decrease in the surface tension of the water-air interface, as evidenced, say, by foam formation, is not a direct indication that the surfactant will function well as a detergent. The decrease in yow or ysw implies, through the Gibb s equation (see Section III-5) adsorption of detergent. 

Then, from equation (A3.3.31) and equation (A3.3.32), we obtain the spectmm of interfacial fluctuations ... 

A fiill solution of tlie nonlinear radiation follows from the Maxwell equations. The general case of radiation from a second-order nonlinear material of finite thickness was solved by Bloembergen and Pershan in 1962 [40]. That problem reduces to the present one if we let the interfacial thickness approach zero. Other equivalent solutions involved tlie application of the boundary conditions for a polarization sheet [14] or the... 

Within this contimiiim approach Calm and Flilliard [48] have studied the universal properties of interfaces. While their elegant scheme is applicable to arbitrary free-energy fiinctionals with a square gradient fomi we illustrate it here for the important special case of the Ginzburg-Landau fomi. For an ideally planar mterface the profile depends only on the distance z from the interfacial plane. In mean field approximation, the profile m(z) minimizes the free-energy fiinctional (B3.6.11). This yields the Euler-Lagrange equation... 

In liquid-phase sintering, densification and microstmcture development can be assessed on the basis of the liquid contact or wetting angle, ( ), fonned as a result of the interfacial energy balance at the solid-liquid-vapour intersection as defined by the Young equation ... 

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