Viscosity, continuous phase

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). 

When a dispersed phase is passed through a nozzle immersed in an immiscible continuous phase, the most important variables influencing the resultant drop size are the velocity of the dispersed phase, viscosity and density of continuous phase, and the density of the dispersed phase (G2, HI, H5, M3, Nl, P5, R3, S5). In general, an increase in continuous-phase viscosity, nozzle diameter, and interfacial tension increases the drop volume, whereas the increase in density difference results in its decrease. However, Null and Johnson (N4) do not find the influence of continuous-phase viscosity significant and exclude this variable from their analysis. Contradictory findings... 

This equation too is solved with the same boundary conditions as Eq. (148). A series of equations results when different combinations of fluids are used. There is no change for the first stage. All the terms of equation of motion remain the same except the force terms arising out of dispersed-phase and continuous-phase viscosities. The main information required for formulating the equations is the drag during the non-Newtonian flow around a sphere, which is available for a number of non-Newtonian models (A3, C6, FI, SI 3, SI 4, T2, W2). Drop formation in fluids of most of the non-Newtonian models still remains to be studied, so that whether the types of equations mentioned above can be applied to all the situations cannot now be determined. 

Calderbank and Korchinski (Cl) showed that the correlations described above are limited in applicability to systems in which the viscosity of the continuous phase is lower than 5 cp. Johnson and Braida (Jl) used an additional parameter in the ordinate of Fig. 7 to extend its range to continuous-phase viscosities of 20 cp. The parameter was (/ / Mwater) Data ou systeffis involving field viscosities up to 400 cp. (Wl) showed that the best correlation would be that of Boussinesq, using an experimental value of e. 

This work shows that high shear rates are required before viscous effects make a significant contribution to the shear stress at low rates of shear the effects are minimal. However, Princen claims that, experimentally, this does not apply. Shear stress was observed to increase at moderate rates of shear [64]. This difference was attributed to the use of the dubious model of all continuous phase liquid being present in the thin films between the cells, with Plateau borders of no, or negligible, liquid content [65]. The opposite is more realistic i.e. most of the liquid continuous phase is confined to the Plateau borders. Princen used this model to determine the viscous contribution to the overall foam or emulsion viscosity, for extensional strain up to the elastic limit. The results indicate that significant contributions to the effective viscosity were observed at moderate strain, and that the foam viscosity could be several orders of magnitude higher than the continuous phase viscosity. 

Other researchers have also observed an increase in HIPE viscosity with increasing phase volume ratio [77] however, the effects of droplet size, polydis-persity or continuous phase viscosity were not investigated. Further studies [78] revealed that the viscosity increased for smaller mean droplet radii this effect was found to be greater at higher internal phase ratios. The total interfacial area increases as droplet size decreases, so viscosity also increases as more energy is required to deform the larger network of thin films [79]. 

Behrend, O., Ax, K., Schubert, H. (2000). Influence of continuous phase viscosity on emulsification of ultrasound. Ultrasonics Sonochemistry, 7, 77-85. 

Dispersed phase uiscosityy(Continuous phase viscosity)... 

Non-dairy creams (cream alternatives) are O/W emulsions stabilized by milk proteins. A relatively thick adsorption layer provides stability, mostly by steric stabilization and partly by electrostatic stabilization [829]. Figure 13.3 shows an example of a soybean-oil and milk-protein emulsion stabilized by fat globules and protein membranes. Stabilizers, such as hydrocolloid polysaccharides, are added to increase the continuous phase viscosity and reduce the extent of creaming. They must be stable enough to have a useful shelf-life but de-stabilize in a specific way when they are... 

We now consider a 40% silicone oil premixed emulsion dispersed in an aqueous phase. In Fig. 9 the evolution of mean diameter is plotted as a function of the applied shear rate. The dispersed phase volume fraction is kept constant at 75%, while the emulsifier concentration in the continuous medium is varied from 15 wt % to 45 wt %. The error bars show the distribution width deduced from the measured uniformity. At a given shear rate, smaller droplets with lower uniformity are produced (see Fig. 9) when surfactant concentration increases. For example at 45% of Ifralan 205 the uniformity never exceeds 15% whatever the applied shear rate, whereas it is of the order of 25% for 15% of Ifralan 205. Some microscope pictures of the emulsions obtained are given in Fig. 10. To understand the evolution, we may argue that the continuous phase viscosity increases... 

An article by Karam (1) gives typical data to illustrate the difference between shear rate and shear stress. Table II is extracted from cross plots of their data, showing the shear rate required with different continuous phase viscosities and one dispersed phase viscosity to break up a second fluid of the same size droplet. This shows that the shear stress in grams per centimeter squared is the basic parameter and the viscosity and shear rate are inversely proportional to give the required shear stress. 

The rubber (dispersed) phase viscosity is determined by the rubber level and by the solution viscosity of the rubber. Furthermore, the grafting and cross-linking will also influence the viscosity. The SAN (continuous) phase viscosity is controlled by the molecular weight of the copolymer. 

Figure 14.2 Influence of viscosity ratio and continuous phase viscosity (/i) on drop breakup [15]. Reprinted with permission from H. J. Karam and J. C. Bellinger, Ind. Eng. Chem. Fundam., 7, 575 (1968). Copyright 1968 American Chemical Society...

The characteristic relaxation time t = 1 /(Hp was found to be insensitive to the droplet size a, weakly dependent on the continuous-phase viscosity, and perhaps weakly dependent on r and M also. Although the complete scaling law for r cannot be deduced from this limited set of data, it is evidently influenced by lubrication flow of liquid in the thin films between the deformed droplets, and perhaps also by the circulatory flow in the viscous droplets. 

The predictive method for drop size is given in the Kenics Bulletin (May 1988, p. 28, Fig. 5-1) and in Figure 10.34. The ratio of Sauter mean drop size to the mixer ID (d/D) is a function of the Weber Number (V Dp/cr) and the ratio of dispersed phase to continuous phase viscosity (p-j/p.,). Now let s do two examples for static mixers. 

The viscosity of an emulsion is directly proportional to the continuous-phase viscosity (rjc), and therefore, all the viscosity equations proposed in the literature are written in terms of the relative viscosity (17 )- If an emulsifying agent is present in the continuous phase, as is the case with emulsions, 17 Is then the viscosity of the emulsifier solution rather than the viscosity of the pure fluid phase (i.e., oil or water alone). When an emulsion is prepared, some of the emulsifying agent becomes adsorbed at the oil-water interface this adsorption tends to lower the original concentration of emulsifier in the continuous phase and cause an associated decrease in 7], However, the amount of emulsifier adsorbed is usually very low compared with the total amount present, and therefore any decrease in concentration of the emulsifier can easily be neglected (23). 

The viscosity of emulsions is a strong function of temperature it decreases with the increase in temperature (J8). The decrease in emulsion viscosity that occurs with raising the temperature is mainly due to a decrease in the continuous-phase viscosity. The increase in temperature may also affect the average particle size and particle size distribution. When the apparent viscosity of an emulsion (at a given shear rate) is plotted as a... 

The viscosity of an oil-in-water emulsion generally varies in proportion to the continuous-phase viscosity. If concentrated brines or brines containing additives are to be used, then the continuous-phase viscosity may be substantially greater than that of water, and a correction should be applied. Speciflc adjustment factors for this effect may be estimated as the ratio of viscosities of the brines in the known and unknown emulsions. 

Bulk Phase Usually refers to a dispersion as a whole. For example, in an emulsion the term bulk phase viscosity refers to the emulsion viscosity, as opposed to the continuous-phase viscosity. Thus the bulk phase is not a separate, single phase at all and may contain dispersed solid and liquid phases. 

Agitated dispersions at low impeller speeds or high continuous phase viscosities are in a state of laminar or transition flow. At low impeller Reynolds number, (NRe)T < 15, the flow is laminar around the impeller... 

Recently Stamatoudis (S32) investigated the effects of continuous phase viscosity on the dynamics of liquid-liquid dispersions in agitated vessels. 

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