Mixing criterion

The compromises in mixing optimization that may be required on scale-up often result in the use of the common mixing criterion of equal power per unit volume or, in some cases, equal tip speed. Both of these recommendations are more relevant for utilization of the same impeller type as well as geometric similarity. Laboratory evaluation of the mixing requirements for a crystallization operation should be carried out in a minimum 0.004 m liter vessel (4 liters) for preliminary data and a further evaluation at 0.1 to 1 m as practical. 

To be used when the main object is mixing criterion... 

The mixing of saturated, or even unsaturated, flow streams in a crystallizer can produce a supersaturated mixture depending on their respective temperature, composition, flowrate and the solute solubility. Toussaint and Donders (1974) identified this particular problem, which so often leads to encrustation, and defined a mixing criterion for safe crystallizer operation which is satisfied when no supersaturation can occur whatever the ratio in which the flowstreams are mixed. 

Toussaint, A.G. and Bonders, A.J.M. (1974) The mixing criterion in crystallization by cooling. Chemical Engineering Science, 29, 237-245. 

To avoid the dependency of mixing quality on quadrat size and the number of particles, Aubin et al. [31] proposed an alternative method based on the analysis of spatial point patterns. This method differs from quadrat analysis mentioned above in that it is based on the distance Xi from each point to the nearest event (tracer particle) for a chosen lattice of m sample points in the domain and therefore it does not require the studied region to be divided into quadrats. The variance of the point-event distances around distance % [Equation (5.14)] provides a means to evaluate the mixedness of a system with respect to a well-mixed criterion. This predefined criterion is set hy the distance Xr, which corresponds to the scale of segregation whereby two events are considered spatially close enough to be mixed. Inthis case the variance is defined via... 

In addition to the use of a melting point determination as a criterion of purity, an equally valuable application is for the identification of oiganic compounds. If the melting point is known within one degree, the major proportion of possible substances is immediately eliminated from consideration. The study of the general chemical properties of the compound and a mixed melting point determination (Section 1,17) will largely establish the identity of the compound. 

The calculation mixes all single determinant wavefunctions that can be obtained from the ground state by exciting electrons from a subset of the occupied orbitals (of the ground state) to a subset of the unoccupied orbitals. The subsets are specified as a fixed number (highest occupied or lowest unoccupied) or by an energy criterion associated with the energy difference between the occupied orbital and the unoccupied orbital. 

The energy of interaction between a pair of solvent molecules, a pair of solute molecules, and a solvent-solute pair must be the same so that the criterion that = 0 is met. Such a mixing process is said to be athermal. The solvent and solute molecules must be the same size so that the criterion... 

Solutions can deviate from ideality because they fail to meet either one or both of these criteria. In reference to polymers in solutions of low molecular weight solvents, it is apparent that nonideality is present because of a failure to meet criterion (2), whether the mixing is athermal or not. 

The criterion of maintaining equal power per unit volume has been commonly used for dupHcating dispersion qualities on the two scales of mixing. However, this criterion would be conservative if only dispersion homogeneity is desired. The scale-up criterion based on laminar shear mechanism (9) consists of constant > typical for suspension polymerization. The turbulence model gives constant tip speed %ND for scale-up. 

Pickiug up the solids at the bottom of the tank depends upon the eddies and velocity fluctuations in the lower part of the tank and is a different criterion from the flow pattern required to keep particles suspended and moving in various velocity patterns throughout the remainder of the vessel This leads to the variables in the design equation and a relationship that is quite different when these same variables are studied in relation to complete uniformity throughout the mixing vessel. 

Criteria 2 to 6 are pragmatic criteria which are only applicable to qualitative explanations. These criteria only give qualitative information which is dealt with further below (Section 3.3.3.1). Criterion 7 gives better information with potential test probes (see Section 3.3.3.2). In all the criteria it must be remembered that only mixed potentials can be measured for extended objects to be protected [see the explanation to Eqs. (3-19) and (3-28)]. Criteria 5 and 6 are particularly to be observed for objects [22]. A comparison of the different criteria in field experiments has shown that, besides Criterion 1, good results are obtained with Criterion 3 [26]. 

However, it has to be considered that it is neither the content of free formaldehyde itself nor the molar ratio which eventually should be taken as the decisive and the only criterion for the classification of a resin concerning the subsequent formaldehyde emission from the finished board. In reality, the composition of the glue mix as well as the various process parameters during the board production also determine both performance and formaldehyde emission. Depending on the type of board and the manufacturing process, it is sometimes recommended to use a UF-resin with a low molar ratio F/U (e.g. F/U = 1.03), hence low content of free formaldehyde, while sometimes the use of a resin with a higher molar ratio (e.g. F/U = 1.10) and the addition of a formaldehyde catcher/depressant will give better results [17]. Which of these two, or other possible approaches, is the better one in practice can only be decided in each case by trial and error. 

The scale-up criterion that is probably most widely used for mixing-limited unit operations is based on constant power input per unit volume according to (Harnby etal., 1992). 

For each of the failure criteria, we will generate biaxial stresses by off-axis loading of a unidirectionally reinforced lamina. That is, the uniaxial off-axis stress at 0 to the fibers is transformed into biaxial stresses in the principal material coordinates as shown in Figure 2-35. From the stress-transformation equations in Figure 2-35, a uniaxial loading obviously cannot produce a state of mixed tension and compression in principal material coordinates. Thus, some other loading state must be applied to test any failure criterion against a condition of mixed tension and compression. 

Referring to Table 6.3, it can be seen that with geometric similarities in self controls there is no mixing variable. In practice, we would select the important criterion that needs to be controlled and then size the vessel accordingly. 

At the outset it is useful to consider some common examples of problems encountered in industrial mixing operations, since this will not only reveal the ubiquitous nature of the process, but will also provide an appreciation of some of the associated difficulties. Several attempts have been made to classify mixing problems and, for example, REAVELL(1) used as a criterion for mixing of powders, the flowability of the final product. HARNBY et at.(2) base their classification on the phases present that is liquid-liquid, liquid-solid and so on. This is probably the most useful description of mixing as it allows the adoption of a unified approach to the problems encountered in a range of industries. This approach is now followed here. 

Flow in a Tube. Laminar flow with a flat velocity profile and slip at the walls can occur when a viscous fluid is strongly heated at the walls or is highly non-Newtonian. It is sometimes called toothpaste flow. If you have ever used Stripe toothpaste, you will recognize that toothpaste flow is quite different than piston flow. Although Vflr) = u and z(7) = 1, there is little or no mixing in the radial direction, and what mixing there is occurs by diffusion. In this situation, the centerline is the critical location with respect to stability, and the stability criterion is... 

Due to the absence of a hydrodynamic effect, boundary film thickness is expected to be independent of speed of surface movement, as can be observed in the left part of the Stribeck curve. This is a significant criterion that distinguishes boundary lubrication from EHL and mixed lubrica-... 

Lohse et al. have summarized the results of recent work in this area [21]. The focus of the work is obtaining the interaction parameter x of the Hory-Huggins-Stavermann equation for the free energy of mixing per unit volume for a polymer blend. For two polymers to be miscible, the interaction parameter has to be very small, of the order of 0.01. The interaction density coefficient X = ( y/y)R7 , a more relevant term, is directly measured by SANS using random phase approximation study. It may be related to the square of the Hildebrand solubility parameter (d) difference which is an established criterion for polymer-polymer miscibility ... 

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