Roughness liquids

TABLE 10.IB Some Values of Surface and Interfacial Tensions Between Solids and Liquids (Rough Estimates)... 

Recall the Stokes law, related the force F) acting on a sphere of radius R to velocity of the sphere in a viscous liquid, v = FIAnr R (t is viscosity of the liquid). Roughly, by analogy with the sphere in viscous liquid, the diffusion coefficient is... 

Contact angle Interaction to a liquid probe, three-phase angle Surface tension Type of liquid, roughness, chemical heterogeneity Static and dynamic experiments... 

Point C is the upper critieal point of the mixture Cj is the lower point in the diagram. In the one-phase zone, the mixture is liquid, roughly, to the left of C and gas to the right of C. The turning point, A, corresponds to the maximum molar fiaetion of the first component in the two-phase zone. The tangent line to the binodal is vertieal at this point The area above CA corresponds to retrograde eondensation, where liquid precipitates as the pressure in the gas phase decreases. The area of normal eondensation lies below CiA... 

We have repeatedly observed that the slowly converging variables in liquid-liquid calculations following the isothermal flash procedure are the mole fractions of the two solvent components in the conjugate liquid phases. In addition, we have found that the mole fractions of these components, as well as those of the other components, follow roughly linear relationships with certain measures of deviation from equilibrium, such as the differences in component activities (or fugacities) in the extract and the raffinate. 

In the context of the structural perturbations at fluid-solid interfaces, it is interesting to investigate the viscosity of thin liquid films. Eaily work on thin-film viscosity by Deijaguin and co-workers used a blow off technique to cause a liquid film to thin. This work showed elevated viscosities for some materials [98] and thin film viscosities lower than the bulk for others [99, 100]. Some controversial issues were raised particularly regarding surface roughness and contact angles in the experiments [101-103]. Entirely different types of data on clays caused Low [104] to conclude that the viscosity of interlayer water in clays is greater than that of bulk water. 

The importance of the solid-liquid interface in a host of applications has led to extensive study over the past 50 years. Certainly, the study of the solid-liquid interface is no easier than that of the solid-gas interface, and all the complexities noted in Section VIM are present. The surface structural and spectroscopic techniques presented in Chapter VIII are not generally applicable to liquids (note, however. Ref. 1). There is, perforce, some retreat to phenomenology, empirical rules, and semiempirical models. The central importance of the Young equation is evident even in its modification to treat surface heterogeneity or roughness. ... 

It is helpful to consider qualitatively the numerical magnitude of the surface tensional stabilization of a particle at a liquid-liquid interface. For simplicity, we will assume 6 = 90°, or that 7sa = 7SB- Also, with respect to the interfacial areas, J sA = SB, since the particle will lie so as to be bisected by the plane of the liquid-liquid interface, and. AB = rcr - The free energy to displace the particle from its stable position will then be just trr 7AB- For a particle of l-mm radius, this would amount to about 1 erg, for Tab = 40 ergs/cm. This corresponds roughly to a restoring force of 10 dyn, since this work must be expended in moving the particle out of the interface, and this amounts to a displacement equal to the radius of the particle. 

The fimctiong(ri is central to the modem theory of liquids, since it can be measured experimentally using neutron or x-ray diffraction and can be related to the interparticle potential energy. Experimental data [1] for two liquids, water and argon (iso-electronic with water) are shown in figure A2.4.1 plotted as a fiinction ofR = R /a, where a is the effective diameter of the species, and is roughly the position of the first maximum in g (R). For water, a = 2.82 A,... 

Figure Bl.22.6. Raman spectra in the C-H stretching region from 2-butanol (left frame) and 2-butanethiol (right), each either as bulk liquid (top traces) or adsorbed on a rough silver electrode surface (bottom). An analysis of the relative intensities of the different vibrational modes led to tire proposed adsorption structures depicted in the corresponding panels [53], This example illustrates the usefiilness of Raman spectroscopy for the detennination of adsorption geometries, but also points to its main limitation, namely the need to use rough silver surfaces to achieve adequate signal-to-noise levels.

Enthalpy of Vaporization (or Sublimation) When the pressure of the vapor in equilibrium with a liquid reaches 1 atm, the liquid boils and is completely converted to vapor on absorption of the enthalpy of vaporization ISHv at the normal boiling point T. A rough empirical relationship between the normal boiling point and the enthalpy of vaporization (Trouton s rule) is ... 

Below Tg the material is hard and rigid with a coefficient of thermal expansion equal to roughly half that of the liquid. With respect to mechanical properties, the glass is closer in behavior to a crystalline solid than to a... 

In general, all of the chlorobenzenes are less toxic than benzene. Liquid chlorobenzenes produce mild to moderate irritation upon skin contact. Continued contact may cause roughness or a mild bum. SoHds cause only mild irritation. Absorption through the skin is slow. Consequently, with short-time exposure over a limited area, no significant quantities enter the body. 

In the special case that A and B are similar in molecular weight, polarity, and so on, the self-diffusion coefficients of pure A and B will be approximately equal to the mutual diffusivity, D g. Second, when A and B are the less mobile and more mobile components, respectively, their self-diffusion coefficients can be used as rough lower and upper bounds of the mutual diffusion coefficient. That is, < D g < Dg g. Third, it is a common means for evaluating diffusion for gases at high pressure. Self-diffusion in liquids has been studied by many [Easteal AIChE]. 30, 641 (1984), Ertl and Dullien, AIChE J. 19, 1215 (1973), and Vadovic and Colver, AIChE J. 18, 1264 (1972)]. 

Example 6 Losses with Fittings and Valves It is desired to calculate the liquid level in the vessel shown in Fig. 6-15 required to produce a discharge velocity of 2 m/s. The fluid is water at 20°C with p = 1,000 kg/m and i = 0.001 Pa - s, and the butterfly valve is at 6 = 10°. The pipe is 2-in Schedule 40, with an inner diameter of 0.0525 m. The pipe roughness is 0.046 mm. Assuming the flow is tiirhiilent and taking the velocity profile factor (X = 1, the engineering Bernoulli equation Eq. (6-16), written between surfaces 1 and 2, where the... 

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