Reynolds number liquid phase

Eo = Eotvos number = gA dVc Re = Reynolds number = du /[L Ap = density difference between the phases p = density of continuous liquid phase d = drop diameter [L = continuous liquid viscosity surface tension u = relative velocity... 

The rate of mass transfer in the liquid phase in wetted-waU columns is highly dependent on surface conditions. When laminar-flow conditions prevail without the presence of wave formation, the laminar-penetration theory prevails. When, however, ripples form at the surface, and they may occur at a Reynolds number exceeding 4, a significant rate of surface regeneration develops, resulting in an increase in mass-transfer rate. 

It follows that since the addition of metal oxides has such a profound effect on the properties of liquid silicates such as the viscosity, that the Reynolds number of liquid silicates in metal-silicate liquid two-phase systems will influence the boundary layer thickness to a greater extent than in the liquid metals and alloys, mainly because of the higher viscosity of the silicate. 

When the two liquid phases are in relative motion, the mass transfer coefficients in eidrer phase must be related to die dynamical properties of the liquids. The boundary layer thicknesses are related to the Reynolds number, and the diffusive Uansfer to the Schmidt number. Another complication is that such a boundaty cannot in many circumstances be regarded as a simple planar interface, but eddies of material are U ansported to the interface from the bulk of each liquid which change the concenuation profile normal to the interface. In the simple isothermal model there is no need to take account of this fact, but in most indusuial chcumstances the two liquids are not in an isothermal system, but in one in which there is a temperature gradient. The simple stationary mass U ansfer model must therefore be replaced by an eddy mass U ansfer which takes account of this surface replenishment. 

Hg, Hi = height of gas, liquid phase transfer unit, inches Re = Reynolds number of gas phase... 

The relation between c and / and X (defined by equation 5.1) is shown in Figure 5.4, where it is seen that separate curves are given according to the nature of the flow of the two phases. This relation was developed from studies on the flow in small tubes of up to 25 mm diameter with water, oils, and hydrocarbons using air at a pressure of up to 400 kN/m . For mass flowrates per unit area of U and G for the liquid and gas, respectively, Reynolds numbers Rei L d/fii ) and Rec(G d/fia) may be used as criteria for defining the flow regime values less than 1000 to 2000, however, do not necessarily imply that the fluid is in truly laminar flow. Later experimental work showed that the total pressure has an influence and data presented by Gr1H ITH(i9) may be consulted where... 

The results presented in Fig. 5.41 clearly show that two-phase mean heat transfer coefficients are strongly influenced by the liquid superficial Reynolds number (Rcls). As shown in Fig. 5.41, the heat transfer coefficient increases proportionally as Rcls increases. 

Fig. 5.47 A plot of the ratio of the experimentally determined heat transfer coefficients divided by the predicted values from the Chen (1966) and Gungor and Winterton (1986) correlations as a function of the liquid phase Reynolds number. Reprinted from Bao et al. (2000) with permission...

The effect of various parameters on the difference between vapor and liquid pressure is illustrated in Figs. 8.3 and 8.4. The effect of the Fuler and Weber numbers as well as the thermal parameter is highly noticeable. An increase in Fu, We and d- leads to a decrease in AP, whereas the difference of both phase pressures is practically independent of Reynolds number. An increase in the Froude number is accompanied by an increase in AP for a small Fr. At Fr > 10 the effect of Fr on AP is negligible. 

Example 5.10 A liquid-phase, pilot-plant reactor uses a 12-ft tube with a 1.049-in i.d. The working fluid has a density of 860 kg/m, the residence time in the reactor is 10.2 s, and the Reynolds number is 8500. The pressure drop in the pilot plant has not been accurately measured, but is known to be less than 1 psi. The entering feed is preheated and premixed. The inlet temperature is 60°C and the outlet temperature is 64°C. Tempered water at 55°C is used for cooling. Management loves the product and wants you to design a plant that is a factor of 128 scaleup over the pilot plant. Propose scaleup alternatives and explore their thermal consequences. 

Another complication, caused by stirring the two phases at the same speed, occurs when the two solutions have different viscosities, which is common for immiscible liquids. The key fluid flow parameter is the Reynolds number. Re, which is the ratio of inertial to viscous forces in the solution, as indicated by... 

It was shown that a normalized version of the two-phase friction factor, CfTpl CfQ, is uniquely related to X. The normalizing friction factor, CfQ, is calculated from single-phase friction factor correlations using a Reynolds number calculated as if both phases flow as liquid,... 

For gas-liquid flows in Regime I, the Lockhart and Martinelli analysis described in Section I,B can be used to calculate the pressure drop, phase holdups, hydraulic diameters, and phase Reynolds numbers. Once these quantities are known, the liquid phase may be treated as a single-phase fluid flowing in an open channel, and the liquid-phase wall heat-transfer coefficient and Peclet number may be calculated in the same manner as in Section lI,B,l,a. The gas-phase Reynolds number is always larger than the liquid-phase Reynolds number, and it is probable that the gas phase is well mixed at any axial position therefore, Pei is assumed to be infinite. The dimensionless group M is easily evaluated from the operating conditions and physical properties. 

The gas-phase wall heat-transfer coefficient can be evaluated by using the gas-phase Reynolds number and Prandtl number in Eq. (33). The thermal conductivities of liquids are usually two orders of magnitude larger than the thermal conductivities of gases therefore, the liquid-phase wall heat-transfer coefficient should be much larger than the gas-phase wall heat-transfer coefficient, and Eq. (34) simplifies to... 

The final parameter to be evaluated is the liquid-phase Peclet number, and the graph given by Levenspiel (L10) can be used for this purpose. It must be remembered that the film Reynolds number should be used in estimating the Peclet number. 

Reynolds numbers calculated for the in vivo hydrodynamics are considerably lower than those of the corresponding in vitro numbers, both for bulk and particle-liquid Reynolds numbers. Remarkably, bulk Reynolds numbers in vivo appear to have about the same magnitude as particle-liquid Reynolds numbers characterizing the flow at the particle surface in vitro using the paddle apparatus. In other words, it appears that hydrodynamics per se play a relatively minor role in vivo compared to the in vitro dissolution. This can be attributed to physiological co-factors that greatly affect the overall dissolution in vivo but are not important in vitro (e.g., absorption and secretion processes, change of MMC phases,... 

Studies on the dissolution of solids in the liquid phase include that of Hixson and Baum(74) whose correlation of data in terms of Reynolds, Sherwood and Schmidt numbers, discussed in detail in Section 10.2 in connection with mass transfer during leaching, is one of the most frequently used methods for calculating the mass transfer coefficient for the solid dissolution. 

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