Mass surface tension

Moore RH, Ingall ED, Sorooshian A, Nenes A (2008) Molar mass, surface tension, and droplet growth kinetics of marine organics from measurements of CCN activity. Geophys Res Lett 35 L07801. doi 10.1029/2008GL033350... 

A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

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]). 

D, 5 = average drop diameter, ft / = disk radius, ft F = spray mass velocity, lb/(min ft of wetted disk periphery) P/ = hquid density, Ib/fo N = disk speed, r/min p = hquia viscosity, lb/(ft min) a = surface tension, Ib/min"... 

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. 

At any instant, pressure is uniform throughout a bubble, while in the surrounding emulsion pressure increases with depth below the surfaee. Thus, there is a pressure gradient external to the bubble which causes gas to flow from the emulsion into the bottom of the bubble, and from the top of the bubble back into the emulsion. This flow is about three times the minimum fluidization velocity across the maximum horizontal cross section of the bubble. It provides a major mass transport mechanism between bubble and emulsion and henee contributes greatly to any reactions which take place in a fluid bed. The flow out through the top of the bubble is also sufficient to maintain a stable arch and prevent solids from dumping into the bubble from above. It is thus responsible for the fact that bubbles can exist in fluid beds, even though there is no surface tension as there is in gas-liquid systems. 

Hughmark and Pressburg (H14) studied holdup and pressure drop for cocurrent gas-liquid flow, and correlated holdup with a function of gas and liquid flow rates, surface tension, densities of gas and liquid, viscosities of gas and liquid, and total mass velocity. 

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. 

Figure 6.22 shows the effect of APG additives on the dynamic and the static surface tension for different mass concentrations, measured at 75 and 95 °C. The... 

As can be seen in Table 6.5, ONB in APG solution of concentration C = 100 ppm took place at significantly higher surface temperatures. It should be noted that the ONB in surfactant solutions may not be solely associated with static surface tension Sher and Hetsroni (2002). Other parameters such as heat flux, mass flux, kind of surfactant, surface materials, surface treatments, surface roughness, dynamic surface tension and contact angle need to be considered as well. 

At the interface the mass and thermal balance equations are valid. If one assumes that the liquid-vapor interface curvature is constant, accordingly (7)3-71)1111 = c/T men, Where Pq and Pl are the vapor and liquid pressure at the interface, a is the surface tension, and/ men is the meniscus radius. 

---