Dispersed phase viscosity

The use of the nomograph is as follows Find the intersecting point of the curves of continuous phase and dispersed phase viscosities on the binary field (left side of nomograph). A line is drawn from this point to the common scale volume fraction of dispersed phase and continuous phase liquids. The intersection of this line with the Viscosity of Emulsion scale gives the result. 

Hence it is the values of each viscosity, dispersed and continuous, and not just the viscosity ratio that is important in determining the average size. The average size increases with a decrease in either continuous or dispersed phase viscosity for fixed operating conditions. 

The average drop size increases with decrease in continuous or dispersed phase viscosity. 

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... 

The influence of dispersed-phase viscosity was found to be negligible by Hayworth and Treybal (H5), but found to be significant (K2) when a greater range of dispered-phase viscosity was investigated. From the graph of Hayworth and Treybal, the influence of interfacial tension appears, as in the case of bubbles, to be more at low flow rates than at high flow rates. 

Kalyanasundaram, Kumar, and Kuloor (K2) found the influence of dispersed phase viscosity on drop formation to be quite appreciable at high rates of flow. The increase in pd results in an increase in drop volume. To account for this, the earlier model was modified by adding an extra resisting force due to the tensile viscosity of the dispersed phase. The tensile viscosity is taken as thrice the shear viscosity of the dispersed phase, in analogy with the extension of an elastic strip where the tensile elastic modulus is represented by thrice the shear elastic modulus for an incompressible material. The actual force resulting from the above is given by 3nRpd v. 

The equation of Hayworth and Treybal (H5) is semi-empirical and is based on a force balance made by expressing the various contributing forces acting on the drop as fractions of the total drop volume. This procedure is probably not wholly justified, since the exact instant at which the forces act is not known, nor is their quantitative contribution to the total volume. The model also neglects the influence of dispersed-phase viscosity. 

However, the model of Rao et al. (R3) does not consider the influence of dispersed-phase viscosity. Further, the maximum size of the drop is limited to static drop size, which is true only for low flow rates. 

The improvement in this model (K2) takes the dispersed-phase viscosity into consideration and predicts better than the earlier models for situations when the dispersed phase is viscous. A typical set of values is shown in Fig. 25, from which it is seen that the model predicts better results in high flow range only. At lower flow rates, the predicted values are higher because the drop detaches at the nozzle tip itself and the application of Harkins and Brown s (H2) correction becomes important, which has been neglected in the model. 

Equation (147) neglects the influence of dispersed-phase viscosity by considering the dispersed phase to be inviscid, which is true for benzene. 

For this case, the first stage remains the same as before, except for the inclusion of the dispersed-phase viscosity, but the equation of motion for the second stage is changed to... 

Authors efforts in this part of the work have been concentrated on developing turbulence closures for the statistical description of two-phase turbulent flows. The primary emphasis is on development of models which are more rigorous, but can be more easily employed. The main subjects of the modeling are the Reynolds stresses (in both phases), the cross-correlation between the velocities of the two phases, and the turbulent fluxes of the void fraction. Transport of an incompressible fluid (the carrier gas) laden with monosize particles (the dispersed phase) is considered. The Stokes drag relation is used for phase interactions and there is no mass transfer between the two phases. The particle-particle interactions are neglected the dispersed phase viscosity and pressure do not appear in the particle momentum equation. 

More recent work (17) has covered viscous drops in turbulent flow, over a wide range of mixer types (SMV, SMX, SMXL, SMR, SMF), diameters (up to 80 mm), lengths, and dispersed-phase viscosities (up to 70 mPa) ... 

Fluid-dynamic operating conditions, such as axial or angular velocity (i.e., shear stress that determines drag force value) and transmembrane pressure (that determines disperse-phase flux, for a given disperse-phase viscosity and membrane... 

It should be noted that this type of blend (PU/PDMS) presents an improved chemical resistance [6] that makes them more base-resistant than acid-resistant. In addition, the relative viscosity % (or X) which is defined as the ratio of the dispersed phase viscosity (%) to the matrix viscosity ( m) plays an important role in the quality of the blend morphology formation. An empirical relationship [7] links the capillary number (Ca) to the viscosity ratio (Eq. 1). 

From this relation, the (maximum stable) droplet size follows, at a given shear rate and with a given interfacial tension. It is found that the exact value of Wecontinuous phase. This is because the droplet will deform more when the dispersed phase viscosity is lower, which will give a higher Laplace pressure and a lower external stress. An indication of the values of We., is given in Figure 15.7. 

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. 

The dimensionless tank viscosity group (Nvi = [Pc/pJ P- ND/o ) accounts for the effects of density difference between the phases and for the dispersed phase viscosity. 

Calabrese RV, Chang TPK, and Dang PT. Drop breakup in turbulent stirred-tank contactors. Part I Effect of dispersed-phase viscosity. AIChE J 1986 32 657-666. 

In nonagitated (static) extractors, drops are formed by flow through small holes in sieve plates or inlet distributor pipes. The maximum size of drops issuing from the holes is determined not by the hole size but primarily by the balance between buoyancy and interfacial tension forces acting on the stream or jet emerging from the hole. Neglecting any viscosity effects (i.e., assuming low dispersed-phase viscosity), the maximum drop size is proportional to the square root of interfacial tension a divided by density difference Ap ... 

Arai K., Konno M., Matunaca Y., Saito S., Effect of dispersed-phase viscosity on the maximum stable drop size for breakup in turbulent flow, J. Chem. Engng. Japan 10 (1977) 4, p. 325-330... 

Emulsion viscosity is higher than either dispersed phase viscosity or continuous phase viscosity. As the dispersed volume fraction is increased, the emulsion viscosity is increased. For a W/O emulsion, the viscosity could be increased from 10s mPa s to 100s mPa s. For example, in the Daqing ZX block, the viscosity of a produced emulsion from an ASP well was 195 cP. After dehydration, the oil viscosity was 48 cP, which is still higher than the oil viscosity of 37 cP from a waterflood well. 

Legisetty et al. [88] and Calabrese et al. [89] considered the effect of dispersed phase viscosity on drop breakage. In their models, attempts have been made to incorporate the effect of dispersed phase holdup on drop breakage by considering the turbulent velocity fluctuations to be damped by the dispersed phase drops as... 

The reader may be surprised not to And a Reynolds number defined speciflcally for the disperse phase. This is because the disperse-phase viscosity is well defined only for Knp 1 (i.e. the collision-dominated or hydrodynamic regime). In this limit, Vp oc oc Knp/Map so that the disperse-phase Reynolds number would be proportional to Map/Krip when Map < 1. However, in many gas-particle flows the disperse-phase Knudsen number will not be small, even for ap 0.1, because the granular temperature (and hence the collision frequency) will be strongly reduced by drag and inelastic collisions. In comparison, molecular gases at standard temperature and pressure have KUp 1 even though the volume fraction occupied by the molecules is on the order of 0.001. This fact can be... 

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