Turbulent mixing definition

In the absence of experimental tracer data, it is also possible to estimate Fickian transport coefficients from channel geometry and discharge. Equations for estimating these coefficients reflect the fact that lateral, or transverse, mixing is caused by turbulence (by definition there is no lateral advection in a river), whereas longitudinal mixing, while partly influenced by turbulence, is often caused primarily by variations in longitudinal water velocity in different parts of the charmel. 

Smaller particles primarily see only the fluctuating velocity component. When the particle size is much less than 100 /zm, the turbulent properties of the fluid become important. This is the definition of the boundary size for microscale mixing. 

We have already likened the macroscopic transport of heat and momentum in turbulent flow to their molecular counterparts in laminar flow, so the definition in Eq. (5-60) is a natural consequence of this analogy. To analyze molecular-transport problems (see, for example. Ref. 7, p. 369) one normally introduces the concept of mean free path, or the average distance a particle travels between collisions. Prandtl introduced a similar concept for describing turbulent-flow phenomena. The Prandtl mixing length is the distance traveled, on the average, by the turbulent lumps of fluid in a direction normal to the mean flow. 

Distributions like those in Figure 10.4, for example, indicate that Yp or T differs from Yp(Z) or T(Z), respectively. If mixing were complete in the sense that all probability-density functions were delta functions and fluctuations vanished, then differences like T — T Z) would be zero. That this situation is not achieved in turbulent diffusion flames has been described qualitatively by the term unmixedness [7]. Although different quantitative definitions of unmixedness have been employed by different authors, in one way or another they all are measures of quantities such as Yp — Yp(Z) or T — T(Z). The unmixedness is readily calculable from P(Z), given any specific definition (see Bilger s contribution to [27]). 

Because of slip and turbulence, the average residence times of particles are substantially greater than the mean time of the air, definitely so in the case of countercurrent or mixed flow. Surface moisture is removed rapidly, in less than 5 sec as a rule,... 

Brodkey [56] stated that only with the advent of the modem turbulence theory a deep understanding of micro-mixing processes and turbulent scalar transfer processes on a microscopic level was possible and that this theory enabled the definition of measurable mixing criteria. Knowledge of the turbulence parameter made it possible to estimate the degree of mixing. The parameters could be estimated from the geometry of the flow system and from simple empirical expressions. The... 

Between the definite regimes of laminar and turbulent flow there is a transitional Re range. The exact values of this number range are a function of many parameters, such as channel shape, surface roughness, and aspect ratio. The transition Re is generally expected to be in the range of 1,500 and 2,500 for most situations [39]. For microfluidic systems. Re are typically smaller than 100 and the flow is considered essentially laminar. This characteristic has a direct consequence on mixing within microfluidic devices. 

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