Mixing phenomena

In a turbulent flow field, a random flow of eddies is commonly superimposed on the overall average fluid flow. In mixing equipment, the motor provides the power, which turns the impeller. This energy is transferred from the agitator into the largest scales of motion (eddies) of the fluid in the tank. This energy is then transferred (cascaded) from the largest 

For a turbulent flow field in an agitated vessel, the average energy dissipation rate per unit mass will be equal to the power input into the system, P, per unit mass, and is given by 

In the presence of a dispersed phase (e.g., the monomer drops in the suspension polymerization), the turbulent intensity decreases due to the decrease of the velocity fluctuations of the continuous phase [24]. Doulah [25] proposed the following relation to account for the reduction of the energy dissipation rate in the presence of a second dispersed phase  

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Axial-flow turbines are often used in blendiug pseudoplastic materials, and they are often used at relatively large D/T ratios, from 0.5 to 0.7, to adequately provide shear rate in the majority of the batch particularly in pseudoplastic material. These impellers develop a flow pattern which may or may not encompass an entire tank, and these areas of motion are sometimes referred to as caverns. Several papers describe the size of these caverns relative to various types of mixing phenomena. An effec tive procedure for the blending of pseudoplastic fluids is given in Oldshue (op. cit.). 

For tlie clTcct and quaiUificalion of the vertical mixing phenomena, however, see Thoiuami and Mueller... 

Other model representations of flow mixing cases in chemical reactors are described by Levenspiel (1972), Fogler (1992) and Szekely and Themelis (1971). Simulation tank examples demonstrating non-ideal mixing phenomena are CSTR, NOSTR, TUBMIX, MIXFLO, GASLIQ and SPBEDRTD. 

Application of integrated stable hydrogen isotope and hydrogeochemical models to the present free waters systems provides important information on their sources, mixing phenomena and underground dynamics that can be profitably used in problems of groundwater resources management, as well as in environmental protection. 

Dupre, B. Allegre, C. J. (1983). Pb-Sr isotope variation in Indian Ocean basalts and mixing phenomena. Nature, 303, 142-6. 

Diffusion flames can best be described as the combustion state controlled by mixing phenomena—that is, the diffusion of fuel into oxidizer, or vice versa—until some flammable mixture ratio is reached. According to the flow state of the individual diffusing species, the situation may be either laminar or turbulent. It will be shown later that gaseous diffusion flames exist, that liquid burning proceeds by a diffusion mechanism, and that the combustion of solids and some solid propellants falls in this category as well. 

Fig. 9.15 Principle of residence time measurement of the continuous heavy phase in a countercurrent extractor. After feeding a short test signal, for example, a colored tracer, the color intensity c or Cq, respectively, is measured downstream at two cross sections ot and ft) as a function of time. The test signal curve widens downstream, owing to the various mixing phenomena.

Tired of so much chemistry, some readers may now turn with pleasure to Part IV, in which transport and mixing phenomena are explained. Furthermore, Part IV provides the conceptual and mathematical framework for building models for the quantitative description of the dynamic behavior of organic chemicals in environmental systems. 

Monitoring such operations implies specific measures and modelling tools which correctly handle gas mixing phenomena. When such conditions are obtained the total saving is estimated at 20 % of the cushion gas cost. 

In order to analyze mixing phenomena occurring very close to the first fluid contact, i.e. directly behind the mixing element, a planar design completely covered by a transparent plate was chosen (see Figure 1.67) [112]. This permits characterization without any dead times, hence permitting observation of the entire mixing process. 

For simulation, a 3-D random walk algorithm was developed to study diffusion-controlled mixing phenomena [160]. Several assumptions were made, i.e. only EOF carries out fluid transport, only neutral and point-like analytes are present and the transport in each dimension is fully independent. An elastic collision mechanism was applied for molecule-wall collisions. The analyte was introduced as a stream of 200 molecules ms-1. 

The modeling can be improved by increasing the number of ideal reactors so that a complex network composed of fictitious interacting compartments is created. This approach can be applied to describe a large number of industrial reactors, in which partial mixing phenomena take place [3, 10]. 

Mixing substances in a vessel is a technique that goes back to a time when primitive men used to cook. Subsequently, even after experiences spanning several thousand years, mixing phenomena in a stirred vessel have not been sufficiently elucidated. 

Mixing phenomena in chemical equipment are accelerated by a forced flow, that is, convection and velocity fluctuation. In general, forced flow in equipment is produced by a movable part such as an impeller. Mixing phenomena are classified into two categories ... 

The correspondence of the conditions for the maximum and minimum values of H( t) with the practical mixing phenomena is considered. The condition under which H(t) takes the maximum value is realized when the perfect mixing flow is established in the equipment, that is, when the concentration of tracer in the equipment is perfectly homogeneous every time and the concentration of tracer at the outlet decreases exponentially. On the other hand, the condition under which H t) takes the minimum value is realized when a piston flow is established in the equipment, that is, when the tracer does not disperse in the... 

Since it is not easy to express the RTD function by using an accurate formula, the mixing phenomena have been frequently discussed based on mixing models that can sufficiently express RTD. One such model is the series of perfectly mixed vessels model (a string of perfectly mixed tanks of equal size model hereafter SPMV model). This model consists of a series of equivolume perfect mixing tanks as shown in Figure 2.4(a). 

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