Two-fluid systems

When the problem is to disrupt Ughtly bonded clusters or agglomerates, a new aspect of fine grinding enters. This may be iUustrated by the breakdown of pigments to incorporate them in liquid vehicles in the making of paints, and the disruption of biological cells to release soluble produces. Purees, food pastes, pulps, and the like are processed by this type of mill. Dispersion is also associated with the formation of emulsions which are basically two-fluid systems. Syrups, sauces, milk, ointments, creams, lotions, and asphalt and water-paint emulsions are in this categoiy. 

The CD model was first proposed by Curl (1963) to describe coalescence and breakage of a dispersed two-fluid system. In each mixing event, two fluid particles with distinct compositions first coalesce and then disperse with identical compositions.75 Written in terms of the two compositions (f>A and [Pg.292]

Wettability refers to the preferential spreading of one fluid over solid surfaces in a two-fluid system and is dependent upon the interfacial tension. The wetting... 

Based on unit interfacial surface in two-fluid systems or based on unit surface of solid in gas-solid systems. 

These relative permeability curves have several characteristics which appear to apply quite generally to most two-fluid systems. As shown in Figure 98, the oil relative permeability is zero below a finite oil saturation known as the equilibrium oil saturation and then increases with increasing oil saturation until it reaches a value of one... 

The two fluid system uses a jet of air surrounding the grout jet. Typically, this increases the radius of influence by several inches. 

To express the force equilibrium condition in a mathematical form, we can now consider a force balance on an arbitrary surface element of a fluid interface, which we denote as A. A sketch of this surface element is shown in Fig. 2-14, as seen when viewed along an axis that is normal to the interface at some arbitrary point within A. We do not imply that the interface is flat (though it could be) - indeed, we shall see that curvature of an interface almost always plays a critical role in the dynamics of two-fluid systems. We denote the unit normal to the interface at any point in A as n (to be definite, we may suppose that n is positive when pointing upward from the page in Fig. 2-14) and let t be the unit vector that is normal to the boundary curve C and tangent to the interface at each point (see... 

We see that the shear- (i.e., tangential-) stress components are discontinuous across the interface whenever gradv y is nonzero. Now, the interfacial tension for a two-fluid system, made up of two pure bulk fluids, is a function of the local thermodynamic state - namely, the temperature and pressure. However, it is much more sensitive to the temperature than to the pressure, and it is generally assumed to be a function of temperature only. If the two-fluid system is a multicomponent system, it is often the case that there may be a preferential concentration of one or more of the components at the interface (for example, we may consider a system of pure A and pure B, which are immiscible, with a third solute component C that is soluble in A and/or B but that is preferentially attracted to the interface), and then the interfacial tension will also be a function of the (surface-excess) concentration of these solute components. Both the temperature and the concentrations of adsorbed species can be functions of position on the interface, thus leading to spatial gradients of y. 

We wish to consider the linear stability of the two-fluid system inside the cylinder to an infinitesimal perturbation of shape. To analyze this problem, you should use cylindrical coordinates (r, 9, z) with the positive z axis being vertically upward. The disturbance to the interface shape can be expressed in the form... 

A determination of the critical exponent 8 has been made for the liquid-liquid system, n-decane-fifi dichloroethyl ether (chlorex). Utilizing schlieren photographs of the system in an ultracentrifuge at a temperature slightly below the critical solution point, the density gradient was obtained as a function of radius. These gradients, used in conjunction with sedimentation theory, provided a means for calculating values for the exponent 8. The values thus obtained are consistent with accepted values for the exponents / and y in two-fluid systems. They are, however, smaller than those found for pure fluids. 

This case is thus in agreement with the findings of Thompson et al. (T2), that for a given two-fluid system heat transfer is practically independent of orifice diameter. This conclusion, though it may apply for the 0.04- to 0.064-in. nozzles tested by Thompson et al, is subject to reservation for larger diameters. The extensive study of Minard and Johnson (M5) reveals a relatively small but appreciable effect of nozzle diameter over the range from 0.04 to 0.86 in. 

For a system of two incompressible Newtonian fluids separated by an immiscible interface, and neglecting inertial forces, the two-fluid system of Eq. 2 can be simplified to... 

Shanna,M.M. and P.V.Danckwerts. "Chemical methods of measuring interfacial areas and mass transfer coefficients in two-fluid systems". Brit.Chem.Engng. 15 No 4 (1970) 206. 

Thus, experimental data of superficial phases velocities along the SS/SW transitional boundary can be used to extract the dynamic coefficient for a variety of two-fluid systems, tube diameters, and operational conditions. 

With the correlation obtained for C, the dynamic model for formulated in Equation 23 is completed and can be applied as a predictive tool for analyzing the stability characteristics of a variety of two-fluid systems. 

The role of laminar/turbulent flow regime transitions in determining the SS/SW transition has been demonstrated via the variation of tube diameter in air-water systems. Clearly, the same basic phenomena are expected due to variations of the physical properties of the phases when dealing with various two-fluid systems. 

Thus, the sheltering coefficient is determined by the liquid layer Froude number. However, for a given two-fluid system, the Froude number along the stratified-wavy transition boundary demonstrates a relatively small variation. Therefore,... 

The dynamic component of the closure law proposed includes a dynamic coefficient, C. This coefficient has been found to depend on the liquid layer Froude and Reynolds numbers. With the proposed dynamic model for the interfacial shear stress the transient two-fluid equations are capable of predicting the conditions for the evolution of waves in a variety of two-fluid systems (without any further tuning). 

The data-base which has been found suitable for extracting the information on the dynamic interaction and correlating the dynamic interfacial shear stress component consists of the fluids flow rates along a stratified-smooth/wavy transitional boundary. More experimental data is needed to further substantiate the correlation for the dynamic coefficient. In particular, there is a need for additional data on this transition in systems of high liquid Reynolds numbers (e.g., high pressure steam/ water systems and large diameter tubes) and in two-fluid systems of either comparable phase velocities or faster lower turbulent layers (e.g., viscous-oil/water systems, downward inclined gas liquid systems). 

There are only minor differences between the electrolyte composition of plasma and the rest of the extracellular fluid. The main difference between these two fluid systems resides in the higher protein concentration in plasma. Consequently, electrolyte shifts between the two body systems follow the laws of Don-nan. Thus, the concentration of cations in the various interstitial compartments will indirectly be regulated by the amount of protein in those fluid systems, but in general, the plasma concentration of anions is higher than that of cations. 

The main advantage of a two fluid system is that the processing-out of fission products from the fuel salt is simplified by the absence of fhorium. The prime method is known as vacuum distillation (ORNL 3791, 1966) and was developed in 1964. After removal of all UF4, the carrier salt would be evaporated off af low pressure and high temperature (1000°C) and recycled, leaving most fission products behind in the still bottoms. 

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