Mixing of fluids

Mixing of fluids is a discipline of fluid mechanics. Fluid motion is used to accelerate the otherwise slow processes of diffusion and conduction to bring about uniformity of concentration and temperature, blend materials, facihtate chemical reactions, bring about intimate contact of multiple phases, and so on. As the subject is too broad to cover fully, only a brier introduction and some references for further information are given here. 

A tubular plug flow (Figure 5-28) reactor assumes that mixing of fluid does not take place, the velocity profile is flat, and both temperature and composition are uniform at any cross-section in the reactor. 

Tables 7-21 and 7-22 summarize the rules-of-thumb involving mixing, agitation, and reactors, respectively [48]. The following considerations are essential during mixing of fluids in a reactor [49] ...

Mixing of fluids is necessary in many chemical processes. It may include mixing of liquid vith liquid, gas with liquid, or solids with liquid. Agitation of these fluid masses does not necessarily imply any significant amount of actual intimate and homogeneous distribution of the fluids or particles, and for this reason mixing requires a definition of degree and/or purpose to properly define the desired state of the system. 

Convection. Heat transfer by convection arises from the mixing of elements of fluid. If this mixing occurs as a result of density differences as, for example, when a pool of liquid is heated from below, the process is known as natural convection. If the mixing results from eddy movement in the fluid, for example when a fluid flows through a pipe heated on the outside, it is called forced convection. It is important to note that convection requires mixing of fluid elements, and is not governed by temperature difference alone as is the case in conduction and radiation. 

If fluids initially in equilibrium with quartz ascend rapidly, some metastable minerals (amorphous silica, cristobalite, wairakite) may precipitate because of supersaturation with respect to Si02 (e.g., Wolery, 1978 Bird and Norton, 1981). Important processes for the supersaturation and deviation from the equilibrium between fluids and rocks are adiabatic boiling, mixing of fluids and conductive cooling of fluids (Giggenbach, 1984). 

Therefore, in order to know the change in dissolved silica concentration and temperature during the precipitation of quartz and cristobalite and mixing of fluids, the following equation could be used ... 

Dimoplon, W. (1978) Hyd. Proc. 57 (May) 221. What process engineers need to know about compressors. Fischer, R. (1965) Chem. Eng., NYT2 (Sept. 13th) 179. Agitated evaporators, Part 2, equipment and economics. Fossett, H. and Prosser, L. E. (1949) Proc. Inst. Mech. Eng. 160, 224. The application of free jets to the mixing of fluids in tanks. 

Because there is no back-mixing of fluid elements along the direction of flow in a tubular reactor, there is a continuous gradient in reactant concentration in this direction. One does not... 

Mixing of fluid elements having different ages. Microscopic mixing produced by eddy diffusion effects is an example of this case. 

Fig. 22.5. Concentrations of components (sulfate, sulfide, carbonate, methane, and acetate) and species (O2 and H2) that make up redox couples, plotted against temperature, during a model of the mixing of fluid from a hot subsea hydrothermal vent with cold seawater. Model assumes redox couples remain in chemical disequilibrium, except between 02(aq) and H2(aq). As the mixture cools past about 38 °C, the last of the dihydrogen from the vent fluid is consumed by reaction with dioxygen in the seawater. At this point the anoxic mixture becomes oxic as dioxygen begins to accumulate.

Fig. 22.6. Redox potentials (mV) of various half-cell reactions during mixing of fluid from a subsea hydrothermal vent with seawater, as a function of the temperature of the mixture. Since the model is calculated assuming 02(aq) and H2(aq) remain in equilibrium, the potential for electron acceptance by dioxygen is the same as that for donation by dihydrogen. Dotted line shows currently recognized upper temperature limit (121 °C) for microbial life in hydrothermal systems. A redox reaction is favored thermodynamically when the redox potential for the electron-donating half-cell reaction falls below that of the accepting half-reaction.

There is no axial mixing of fluid inside the vessel (i.e., in the direction of flow). 

There is complete radial mixing of fluid inside the vessel (i.e., in the plane perpendicular to the direction of flow) thus, the properties of the fluid, including its velocity, are uniform in this plane. 

There is no axial mixing of fluid inside the vessel. 

Although there is a distribution of residence times, the complete mixing of fluid at the microscopic and macroscopic levels leads to an averaging of properties across all fluid elements. Thus, the exit stream has a concentration (average) equivalent to that obtained as if the fluid existed as a single, large fluid element with a residence time of t = V/q (equation 2.3-1). 

The nature of mixing of fluid elements during flow through the vessel as characterized, so far, by the degree of segregation (Section 13.5) thus, in a CSTR (i.e., a... 

A fourth aspect also has to do with the nature of mixing of fluid elements of different... 

PF can be used to illustrate extremes described by early mixing and late (or no) mixing. In BMF, mixing of fluid elements of all ages takes place early -at the point of entry. In PF, mixing takes place late -in fact, not at all (in the axial direction). We may then use a combination of two vessels in series, one with BMF and one with... 

The segregated-flow reactor model (SFM) represents the micromixing condition of complete segregation (no mixing) of fluid elements. As noted in Section 19.2, this is one extreme model of micromixing, the maximum-mixedness model being the other. 

The IEM model is a simple example of an age-based model. Other more complicated models that use the residence time distribution have also been developed by chemical-reaction engineers. For example, two models based on the mixing of fluid particles with different ages are shown in Fig. 5.15. Nevertheless, because it is impossible to map the age of a fluid particle onto a physical location in a general flow, age-based models cannot be used to predict the spatial distribution of the concentration fields inside a chemical reactor. Model validation is thus performed by comparing the predicted outlet concentrations with experimental data. 

The results of earlier work by Chu, Kalil, and Wetteroth(117) suggested that transfer coefficients were similar in fixed and fluidised beds. Apparent differences at low Reynolds numbers were probably due to the fact that there could be appreciable back-mixing of fluid in the fluidised bed. 

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