Turbulent diffusion, microscale

The motion of substances on the synoptic scale is often assumed to be pure advection. The flux 

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In the mesoscale model, setting Tf = 0 forces the fluid velocity seen by the particles to be equal to the mass-average fluid velocity. This would be appropriate, for example, for one-way coupling wherein the particles do not disturb the fluid. In general, fluctuations in the fluid generated by the presence of other particles or microscale turbulence could be modeled by adding a phase-space diffusion term for Vf, similar to those used for macroscale turbulence (Minier Peirano, 2001). The time scale Tf would then correspond to the dissipation time scale of the microscale turbulence. 

The phase-space diffusion terms in Eq. (5.2) generate a very large number of terms in the GPBE (many of which are zero). For example, considering only the fluid-particle interaction term in the limiting case in which particle-velocity fluctuations are due to microscale fluid turbulence (i.e. Bp = 0, Bp, = 0) yields the diffusion terms in velocity phase space... 

The numerics in Table 16.2 make two points. One is that turbulence is difficult to achieve at the mesoscale and nearly impossible to achieve in micro- and nanoscale devices. The other point is that diffusion becomes so fast at the microscale that cross-channel (e.g., radial) mixing is essentially instantaneous for all but the very fastest reactions. Thus composition and temperature will be approximately uniform in the cross-channel direction. The solutions to the convective diffusion equations in... 

The border diffusion layer model was introduced as an amendment to the film model to present a more realistic description. It accounts for an undefined film thickness, turbulence effects, and the role of molecular diffusion. When the flow is turbulent, the flow around the bubble is split into four sections the main turbulent stream, the turbulent boundary layer, the viscous sublayer, and the diffusion sublayer. Eddy turbulence accounts for mass transfer in the main turbulent stream and the turbulent boundary layer. The viscous sublayer limits eddy turbulence effects so that the flow is laminar and mass transfer is controlled by both molecular diffusion and eddy turbulence. Microscale eddy turbulence is assumed to be dominant in the viscous sublayer. Mass transfer in the diffusion sublayer is controlled almost completely by molecular diffusion (Azbel, 1981). 

The Reynolds number in microreaction systems usually ranges from 0.2 to 10. In contrast to the turbulent flow patterns that occur on the macroscale, viscous effects govern the behavior of fluids on the microscale and the flow is always laminar, resulting in a parabolic flow profile. In microfluidic reaction systems, where the characteristic length is usually greater than 10 pm, a continuum description can be used to predict the flow characteristics. This allows commercially written Navier-Stokes solvers such as FEMLAB and FLUENT to model liquid flows in microreaction channels. However, modeling gas flows may require one to take account of boundary sUp conditions (if 10 < Kn < 10 , where Kn is the Knudsen number) and compressibility (if the Mach number Ma is greater than 0.3). Microfluidic reaction systems can be modeled on the basis of the Navier-Stokes equation, in conjunction with convection-diffusion equations for heat and mass transfer, and reaction-kinetic equations. 

Due to the small characteristic dimension, the flow in microchemical systems is laminar. As a result, mixing relies only on molecular diffusion instead of the more efficient turbulence that large-scale systems typically exhibit. At the same time, the diffusion time scale is much shorter due to the small size of a microscale device. However, structural elements that play the role of static micromixers may be necessary to spread fast flows, enhance fluid-solid contact, increase mixing of incoming gases, etc. One such example is the post-micromixer discussed in Ref. [5]. 

Reactant gases and reaction products from one electrode can also easily diffuse to the adjacent electrode and affect the oxygen partial pressure. While reasonable OCVs can be achieved with microscale interdigitated electrode patterns [71], very low OCVs are attributed to turbulent flow and gas intermixing between the closely spaced microelectrodes [72, 78], especially under wet gas conditions [20, 76]. 

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