Reynolds micromixers

Thus, the reactor will be perfectly mixed if and only if = at every spatial location in the reactor. As noted earlier, unless we conduct a DNS, we will not compute the instantaneous mixture fraction in the CFD simulation. Instead, if we use a RANS model, we will compute the ensemble- or Reynolds-average mixture fraction, denoted by ( ). Thus, the first state variable needed to describe macromixing in this system is ( ). If the system is perfectly macromixed, ( ) = < at every point in the reactor. The second state variable will be used to describe the degree of local micromixing, and is the mixture-fraction variance (maximum value of the variance at any point in the reactor is ( )(1 — ( )), and varies from zero in the feed streams to a maximum of 1/4 when ( ) = 1/2. 

One of the principal difficulties faced when employing Lagrangian micromixing models is the determination of tm based on properties of the turbulent flow fields. Researchers have thus attempted to use the universal nature of high-Reynolds-number isotropic turbulence to link tm to the turbulence time scales. For example, in the E-model (Baldyga and Bourne 1989) the engulfment rate essentially controls the rate of micromixing and is defined by... 

The reaction system, the experiment procedure, and the analytical method used for the determination of micromixing in the TIJ mixer are the same as those described in the last section of this book but Mahajan et al. correlated their experimental data not with impinging velocity w() but with the jet Reynolds number Re. Also, the researchers employed the measure of increasing both the initial concentration CBo and the reaction temperature to raise the sensitivity of the procedure. The characteristic reaction time constant tK = 200 ms at 25 °C and CBo = 2.5 mM, while rR = 65 ms at 35 °C and CB0 = 4.7 mM, which can be used to bound the micromixing times, rM, no greater than them, respectively. 

The Eulerian (bottom-up) approach is to start with the convective-diffusion equation and through Reynolds averaging, obtain time-smoothed transport equations that describe micromixing effectively. Several schemes have been proposed to close the two terms in the time-smoothed equations, namely, scalar turbulent flux in reactive mixing, and the mean reaction rate (Bourne and Toor, 1977 Brodkey and Lewalle, 1985 Dutta and Tarbell, 1989 Fox, 1992 Li and Toor, 1986). However, numerical solution of the three-dimensional transport equations for reacting flows using CFD codes are prohibitive in terms of the numerical effort required, especially for the case of multiple reactions with... 

H.M. Xia, C. Shu, S.Y.M. Wan, Y.T. Chew, Influence of the Reynolds number on chaotic mixing in a spatially periodic micromixer and its characterization nsing dynamical system techniques, J. Micromech. Microeng., 16(1) 53-61 (2006). 

Che-Hsin L, Chien-Hsiung T, Lung-Ming F (2005) A rapid three-dimensional vortex micromixer utilizing self-rotation effect under low Reynolds number conditions. J Micromech Microeng 15 935. http //dx.doi.Org/10.1088/0960-1317/15/5/006 Bessoth F, deMello A, Manz A (1999) Microstructure for efficient continuous flow mixing. Anal Commun 36(6) 213-215... 

Hassell D, Zimmerman W (2006) Investigation of the convective motion through a staggered herringbone micromixer at low Reynolds number flow. Orem Eng Sci 61(9) 2977-2985... 

Bhagat A, Peterson E, Papautsky I (2007) A passive planar micromixer with obstructions for mixing at low Reynolds numbers. J Micromech Microeng 17 1017... 

Exp. Batch Size (mL) Agitator Speed (rpm) Reynolds Flow (W/kg) (W/kg) Macromixing Time (s) Micromixing Time (s)... 

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