Mass transfer viscosity

Temperature affects all the physical properties relevant in mass transfer viscosity, density, surface tension, and diffusivity. The empirical factor most often used to account for temperature changes in all these parameters is the theta factor, 0,... 

Besides environmental and separation advantages, the use of supercritical fluids associated with PTC provides the extra benefit of an increased mass transfer. Viscosities and solute diffusivities of supercritical fluids are gas-like. 

As velocity continues to rise, the thicknesses of the laminar sublayer and buffer layers decrease, almost in inverse proportion to the velocity. The shear stress becomes almost proportional to the momentum flux (pk ) and is only a modest function of fluid viscosity. Heat and mass transfer (qv) to the wall, which formerly were limited by diffusion throughout the pipe, now are limited mostly by the thin layers at the wall. Both the heat- and mass-transfer rates are increased by the onset of turbulence and continue to rise almost in proportion to the velocity. 

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). 

The effects of a solvent on growth rates have been attributed to two sets of factors (28) one has to do with the effects of solvent on mass transfer of the solute through adjustments in viscosity, density, and diffusivity the second is concerned with the stmcture of the interface between crystal and solvent. The analysis (28) concludes that a solute-solvent system that has a high solubiUty is likely to produce a rough interface and, concomitandy, large crystal growth rates. 

As the polymer molecules form and dissociate from the catalyst, they remain ia solution. The viscosity of the solution increases with increasing polymer concentration. The practical upper limit of solution viscosity is dictated by considerations of heat transfer, mass transfer, and fluid flow. At a mbber soflds concentration of 8—10%, a further increase in the solution viscosity becomes impractical, and the polymerisation is stopped hy killing the catalyst. This is usually done by vigorously stirring the solution with water. If this is not done quickly, the unkilled catalyst continues to react, leading to uncontrolled side reactions, resulting in an increase in Mooney viscosity called Mooney Jumping. 

With regard to the liqiiid-phase mass-transfer coefficient, Whitney and Vivian found that the effect of temperature upon coiild be explained entirely by variations in the liquid-phase viscosity and diffusion coefficient with temperature. Similarly, the oxygen-desorption data of Sherwood and Holloway [Trans. Am. Jnst. Chem. Eng., 36, 39 (1940)] show that the influence of temperature upon Hl can be explained by the effects of temperature upon the liquid-phase viscosity and diffusion coefficients. 

It is important to recognize that the effects of temperature on the liquid-phase diffusion coefficients and viscosities can be veiy large and therefore must be carefully accounted for when using /cl or data. For liquids the mass-transfer coefficient /cl is correlated in terms of design variables by relations of the form... 

Mass-transfer theory indicates that for trays of a given design the factors most hkely to inflnence E in absorption and stripping towers are the physical properties of the flnids and the dimensionless ratio Systems in which the mass transfer is gas-film-controlled may be expected to have plate efficiencies as high as 50 to 100 percent, whereas plate efficiencies as low as 1 percent have been reported for the absorption of gases of low sohibility (large m) into solvents of relatively high viscosity. 

By contrast, the hqnid-phase Schmidt unmbers range from about 10" to lO and depeua strongly on the temperature. The effect of temperature on the liquid-phase mass-transfer coefficient is related primarily to changes in the hquid viscosity with temperature, and this derives primarily from the strong dependency of the hqnid-phase Schmidt number upon viscosity. 

D( = diffusion coefficient of solute in liquid g = gravity-acceleration constant h = length of wetted wall kf = mass-transfer coefficient, liquid phase r = mass rate of flow of hqnid. f = viscosity of liquid = density of hqnid... 

The mass-transfer coefficients depend on complex functions of diffii-sivity, viscosity, density, interfacial tension, and turbulence. Similarly, the mass-transfer area of the droplets depends on complex functions of viscosity, interfacial tension, density difference, extractor geometry, agitation intensity, agitator design, flow rates, and interfacial rag deposits. Only limited success has been achieved in correlating extractor performance with these basic principles. The lumped parameter deals directly with the ultimate design criterion, which is the height of an extraction tower. 

Viscosity markedly changes the picture and, usually, increasing viscosity lowers the mass-transfer coefficient. For the common application of waste treating and for some of the pubhshed data on biological slurries, data for kiO (shown in Fig. 18-28) is obtained in the literature. For a completely new gas or liquid of a liquid shiny system. Fig. 18-26 must be obtained by an actual experiment. 

FIG. 18-28 Usually, the gas-liquid mass-transfer coefficient, K, is reduced with increased viscosity. This shows the effect of increased concentration of microbial cells in a fermentation process. 

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. 

Engineering factors include (a) contaminant characteristics such as physical and chemical properties - concentration, particulate shape, size distribution, chemical reactivity, corrosivity, abrasiveness, and toxicity (b) gas stream characteristics such as volume flow rate, dust loading, temperature, pressure, humidity, composition, viscosity, density, reactivity, combustibility, corrosivity, and toxicity and (c) design and performance characteristics of the control system such as pressure drop, reliability, dependability, compliance with utility and maintenance requirements, and temperature limitations, as well as size, weight, and fractional efficiency curves for particulates and mass transfer or contaminant destruction capability for gases or vapors. 

However, it should be mentioned that the dissolution process of a solid, crystalline complex in an (often relatively viscous) ionic liquid can sometimes be slow. This is due to restricted mass transfer and can be speeded up either by increasing the exchange surface (ultrasonic bath) or by reducing the ionic liquid s viscosity. The latter is easily achieved by addition of small amounts of a volatile organic solvent that dissolves both the catalyst complex and the ionic liquid. As soon as the solution is homogeneous, the volatile solvent is then removed in vacuo. 

The combination of ionic liquids with supercritical carbon dioxide is an attractive approach, as these solvents present complementary properties (volatility, polarity scale.). Compressed CO2 dissolves quite well in ionic liquid, but ionic liquids do not dissolve in CO2. It decreases the viscosity of ionic liquids, thus facilitating mass transfer during catalysis. The separation of the products in solvent-free form can be effective and the CO2 can be recycled by recompressing it back into the reactor. Continuous flow catalytic systems based on the combination of these two solvents have been reported [19]. This concept is developed in more detail in Section 5.4. 

Convective heat transmission occurs within a fluid, and between a fluid and a surface, by virtue of relative movement of the fluid particles (that is, by mass transfer). Heat exchange between fluid particles in mixing and between fluid particles and a surface is by conduction. The overall rate of heat transfer in convection is, however, also dependent on the capacity of the fluid for energy storage and on its resistance to flow in mixing. The fluid properties which characterize convective heat transfer are thus thermal conductivity, specific heat capacity and dynamic viscosity. 

The simplest and most thoroughly studied solutions are those based on phosphoric acid at low temperatures (<35°C) which alone can fulfil all three requirements of acid solvent, film former (as metal phosphate) and diffusion agent by virtue of its viscosity. Thus copper and its main alloys of brasses and bronzes can be very effectively electropolished in 60-70% orthophos-phoric acid with the temperature maintained below 35°C under other conditions copper passivates or dissolves freely under mass transfer controlled conditions, but by varying the conditions appropriately polishing can be continued under mild agitation. An annotated polarisation curve is given in Fig. 11.7 readers are referred to recent studies for more detailed 2ispects " . 

The mass transfer coefficient is expected to relate gas power per unit volume and gas terminal velocity. Measurement of gas bubble velocity is troublesome in the experimental stage of aeration. Extensive research has been conducted for an explanation of the above correlation. Gas-liquid mass transfer in low viscosity fluids in agitated vessels has been reviewed and summarised as stated in (3.5.1.7)—(3.6.2) 3... 

Calderbank and Moo-Young (C5) have studied gas-liquid mass transfer in systems characterized by high viscosities and high diffusion coefficients, and have on the basis of data obtained in this and other studies developed correlations for the mass-transfer coefficients. 

With the density and viscosity of the gas neglected in comparison to those of the liquid, the corresponding mass-transfer coefficient is... 

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