Mass transfer surface tension

There are many factors that determine whether a collision results in a coalescence. The processes by which two drops coalesce are those of film thinning and final rupture of the intervening film. These processes are determined by factors such as surfactants, mass transfer, surface tension gradients, physical properties, Van der Waals forces, and double-layer forces. In a turbulent flow field the situation is more involved.The droplets must first collide and remain in contact for a sufficient time for the coalescence to take place. A realistic coalescence efficiency will account for these factors. 

The role of coalescence within a contactor is not always obvious. Sometimes the effect of coalescence can be inferred when the holdup is a factor in determining the Sauter mean diameter (67). If mass transfer occurs from the dispersed (d) to the continuous (e) phase, the approach of two drops can lead to the formation of a local surface tension gradient which promotes the drainage of the intervening film of the continuous phase (75) and thereby enhances coalescence. It has been observed that d-X.o-c mass transfer can lead to the formation of much larger drops than for the reverse mass-transfer direction, c to... 

Static mixing of immiscible Hquids can provide exceUent enhancement of the interphase area for increasing mass-transfer rate. The drop size distribution is relatively narrow compared to agitated tanks. Three forces are known to influence the formation of drops in a static mixer shear stress, surface tension, and viscous stress in the dispersed phase. Dimensional analysis shows that the drop size of the dispersed phase is controUed by the Weber number. The average drop size, in a Kenics mixer is a function of Weber number We = df /a, and the ratio of dispersed to continuous-phase viscosities (Eig. 32). 

Minimum Wetting Rate The minimum liquid rate required for complete wetting of a vertical surface is about 0.03 to 0.3 kg/m s for water at room temperature. The minimum rate depends on the geom-etiy and nature of the vertical surface, liquid surface tension, and mass transfer between surrounding gas and the liquid. See Ponter, et al. Int. J. Heat Mass Tran.fer 10, 349-359 [1967] Trans. Inst. Chem. Eng. [London], 45, 345—352 [1967]), Stainthorp and Allen Trans. Inst. Chem. Eng. [London], 43, 85-91 [1967]) and Watanabe, et al. ]. Chem. Eng. [Japan], 8[1], 75 [1975]). 

Coalescence The coalescence of droplets can occur whenever two or more droplets collide and remain in contact long enough for the continuous-phase film to become so thin that a hole develops and allows the liquid to become one body. A clean system with a high interfacial tension will generally coalesce quite rapidly. Particulates and polymeric films tend to accumulate at droplet surfaces and reduce the rate of coalescence. This can lead to the ouildup of a rag layer at the liquid-hquid interface in an extractor. Rapid drop breakup and rapid coalescence can significantly enhance the rate of mass transfer between phases. 

For many laboratoiy studies, a suitable reactor is a cell with independent agitation of each phase and an undisturbed interface of known area, like the item shown in Fig. 23-29d, Whether a rate process is controlled by a mass-transfer rate or a chemical reaction rate sometimes can be identified by simple parameters. When agitation is sufficient to produce a homogeneous dispersion and the rate varies with further increases of agitation, mass-transfer rates are likely to be significant. The effect of change in temperature is a major criterion-, a rise of 10°C (18°F) normally raises the rate of a chemical reaction by a factor of 2 to 3, but the mass-transfer rate by much less. There may be instances, however, where the combined effect on chemical equilibrium, diffusivity, viscosity, and surface tension also may give a comparable enhancement. 

In their analysis, however, they neglected the surface tension and the diffusivity. As has already been pointed out, the volumetric mass-transfer coefficient is a function of the interfacial area, which will be strongly affected by the surface tension. The mass-transfer coefficient per unit area will be a function of the diffusivity. The omission of these two important factors, surface tension and diffusivity, even though they were held constant in Pavlu-shenko s work, can result in changes in the values of the exponents in Eq. (48). For example, the omission of the surface tension would eliminate the Weber number, and the omission of the diffusivity eliminates the Schmidt number. Since these numbers include variables that already appear in Eq. (48), the groups in this equation that also contain these same variables could end up with different values for the exponents. 

Steam-liquid flow. Two-phase flow maps and heat transfer prediction methods which exist for vaporization in macro-channels and are inapplicable in micro-channels. Due to the predominance of surface tension over the gravity forces, the orientation of micro-channel has a negligible influence on the flow pattern. The models of convection boiling should correlate the frequencies, length and velocities of the bubbles and the coalescence processes, which control the flow pattern transitions, with the heat flux and the mass flux. The vapor bubble size distribution must be taken into account. 

VOF or level-set models are used for stratified flows where the phases are separated and one objective is to calculate the location of the interface. In these models, the momentum equations are solved for the separated phases and only at the interface are additional models used. Additional variables, such as the volume fraction of each phase, are used to identify the phases. The simplest model uses a weight average of the viscosity and density in the computational cells that are shared between the phases. Very fine resolution is, however, required for systems when surface tension is important, since an accurate estimation of the curvature of the interface is required to calculate the normal force arising from the surface tension. Usually, VOF models simulate the surface position accurately, but the space resolution is not sufficient to simulate mass transfer in liquids. 

SupercriUcal Fluid DeposiUon (SFD) Metal films may be grown from precursors that are soluble in CO2. The SFD process yields copper films with fewer defects than those possible by using chemical vapor deposition, because increased precursor solubility removes mass-transfer hmitations and low surface tension favors penetration of high-aspect-ratio features [Blackburn et al.. Science, 294, 141-145 (2001)]. 

The efficiency of extraction is mainly dependent on temperature as it influences physical properties of the sample and its interaction with the liquid phase. The extraction is influenced by the surface tension of the solvent and its penetration into the sample (i.e. its viscosity) and by the diffusion rate and solubility of the analytes all parameters that are normally improved by a temperature increase. High temperature increases the rate of extraction. Lou et al. [122] studied the kinetics of mass transfer in PFE of polymeric samples considering that the extraction process in PFE consists of three steps ... 

Here we also consider sorption kinetics as the mass-transfer barrier to surfactant migration to and from the interface, and we follow the Levich framework. However, our analysis does not confine all surface-tension gradients to the constant thickness film. Rather, we treat the bubble shape and the surfactant distribution along the interface in a consistent fashion. 

If the supply of surfactant to and from the interface is very fast compared to surface convection, then adsorption equilibrium is attained along the entire bubble. In this case the bubble achieves a constant surface tension, and the formal results of Bretherton apply, only now for a bubble with an equilibrium surface excess concentration of surfactant. The net mass-transfer rate of surfactant to the interface is controlled by the slower of the adsorption-desorption kinetics and the diffusion of surfactant from the bulk solution. The characteris-... 

The latter three factors are only relevant for the mass transfer if the Reynolds number (Re = p vr db / q) of the liquid flow around the particle is larger than 1. The size of the gas bubbles depends on liquid properties such as temperature, surface tension and viscosity but also on the dissipated power. If we have to deal with small gas bubbles in a bubble column than we can consider the gas bubbles as rigid. The mass transfer coefficient k q is then given by the equation ... 

Equation (65), the working equation for mass transfer, contains two independent variables and R. A second equation can be obtained from momentum transfer considerations. In the absence of surface tension forces, the momentum equations for a Newtonian fluid reduce to... 

The rate of mass transfer is a funetion, among other variables, of the drop size distribution or interfaeial area between the phases. The drop size is governed by the surface tension, and densities of the two phases and the type of agitation and design of the eontaetor. Up to a point, the smaller the drop, the greater the rate of mass transfer. 

The second complicating factor is interfacial turbulence (1, 12), very similar to the surface turbulence discussed above. It is readily seen when a solution of 4% acetone dissolved in toluene is quietly placed in contact with water talc particles sprinkled on to the plane oil surface fall to the interface, where they undergo rapid, jerky movements. This effect is related to changes in interfacial tension during mass transfer, and depends quantitatively on the distribution coefficient of the solute (here acetone) between the oil and the water, on the concentration of the solute, and on the variation of the interfacial tension with this concentration. Such spontaneous interfacial turbulence can increase the mass-transfer rate by 10 times 38). 

The effect of protein and other monolayers on mass-transfer rates depends quantitatively 50) on the surface compressional modulus, Cr this is defined as the reciprocal of the compressibility of the contaminating surface film, i.e., Cr = —A dU/dA. For films at the oil-water interface Cr is often close to II, the surface pressure, which is equal to the lowering of the interfacial tension by the film. 

---