Times of mixing

A proposal based on Onsager s theory was made by Landau and Lifshitz [27] for the fluctuations that should be added to the Navier-Stokes hydrodynamic equations. Fluctuating stress tensor and heat flux temis were postulated in analogy with the Onsager theory. Flowever, since this is a case where the variables are of mixed time reversal character, tlie derivation was not fiilly rigorous. This situation was remedied by tlie derivation by Fox and Ulilenbeck [13, H, 18] based on general stationary Gaussian-Markov processes [12]. The precise fomi of the Landau proposal is confimied by this approach [14]. 

Determination of mixing times using Computationai Fiuid Dynamics (CFD)... 

Gas constant (J/mol K) coarse particle radius Specific weight of feed Degree of mixing Time scale (s)... 

Several experimental techniques may be used, such as acid/base titration, electrical conductivity measurement, temperature measurement, or measurement of optical properties such as refractive index, light absorption, and so on. In each case, it is necessary to specify the manner of tracer addition, the position and number of recording stations, the sample volume of the detection system, and the criteria used in locating the end-point. Each of these factors will influence the measured value of mixing time, and therefore care must be exercised in comparing results from different investigations. 

A similar experiment was conducted using N-299 carbon black. In this case the premastication was limited to 3 min of mixing time. The average batch temperature measured after this mixing operation was 309°F. Each experiment was performed in duplicate the average of two mixes is shown in Figure 16.6. The viscosity of the final control compound was similar to that of the premasticated mbber. 

Gao, Z., Min, J., Smith J. M., and Thorpe, R. B., Large Eddy Simulation of Mixing Time in a Stirred Tank with Duals Rushton Turbines . 12th European Conference on Mixing, Bologna, Italy, pp. 431-438 (2006). 

Fig. 16.3 The calculated trNOE intensity as a function of mixing time without (left part) and with (right part) spin diffusion through intermole-cular cross-relaxation. For the calculations the distance between the protons was assumed to be 2 A, and the rotational correlation time used was 0.1 ns for the free ligand and 10 ns for the pro-...

Figure 1.19. Example 1.3. Degree of mixing as a function of mixing time...

Procedure. A gram of the mineral was preconditioned for 90 minutes with 5cc of a 0.2 kmol/m sodium chloride solution at 75 C on a wrist action shaker. Then a 5cc solution of known surfactant concentration is added and allowed to shake for four hours. Four hours mixing was found to be sufficient to reach equilibrium from adsorption test conducted as a function of mixing time. The... 

The completely mixed limit is in fact rather easy to achieve with ordinary mixing techniques. The approximation can be thought of in terms of mixing time tmix versus residence time r of the fluid in the reactor. If... 

In the laboratory-frame NOE experiments the coherent transfer can be eliminated by a random variation of mixing time within a range that represents a small fraction of the total mixing time. In these conditions, the sin(wirm) terms average to zero, and the incoherent exchange averages to a nonzero value. 

Figure 8 A comparison of the effects of mixing time on batch and continuous flocculation of kaolin at 3% solids by weight by 4mgL of a non-ionic polymer (after Suharyonofl ...

Table 3.8 The effect of mixing time on the level of air entrainment in laboratory mixes...

Fig. 7.44 Effect of mixing time after addition of air-entraining admixture (mix 3.1) in combination with superplasticizer (mix 3.2) on the total air content in (a) fresh concrete and (b) hardened concrete (Mark and Gjoerv [131]).

Time. An example of the breakup of agglomerates of solid oxidizer as a function of mixing time is given in Figure 4. 

Figure 4. Effect of mixing time on breakup of agglomerates...

Figure 5.6 Mean square of differences between consecutive Raman spectra as a function of mixing time of a binary system. Reprinted from Vergote etal. (2004)62 with permission from Elsevier.

Ritman, E.L., Borah, B., Dufresne, T.E., Phipps, R.J., Sacha, J.P., Jorgensen, S.M., and Turner, R.T. 2002. 3-D Synchrotron pCT allows unique insight of changes in bone quality. The American Society for Bone and Mineral Research Annual Meeting, San Antonio TX, September 20-24. Ross, K.A., Pyrak-Nolte, L.J., and Campanella, O.H. 2004. The use of ultrasound and shear oscillatory tests to characterize the effect of mixing time on the rheological properties of dough. Food Res. Int. 37, 567-577. 

Figure 3.28 Fraction of undispersed carbon black, larger than 9 /im, as a function of mixing time inside a Banbury mixer. The open circles denote experimental results and the solid line a theoretical prediction. The broken line denotes the fraction of aggregates of size below 500 nm.

M 14] [P 14] It was shown above that mixing of droplets is fairly fast at an aspect ratio of about 0.4, in the order of 4—5 s [29], It was assumed that a further reduction of mixing time is not possible, as the flow reversibility poses limits here, which is the relaxation of a new flow pattern, with increased or fresh interface, to the original state. 

Typical Results Numerical analysis of mixing time... 

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