Reacting channel flows

On inserting this ansatz into Eq. (123), the solution can be determined in the form of an eigenfunction expansion, as shown by Walker [163]. The parameter controlling the number of terms of this expansion having to be taken into account is Pe h/L, which is usually of the order of 0(0.01 - 1) in micro reactors. For this reason, often only the first term contributes. With the entrance condition cj, (f) = 1, the axial dependence can then be written as 

Commenge et al. extended the one-dimensional model of reacting flows to include Taylor-Aris dispersion, i.e. they considered an equation of the form 

---

Consider a model problem that is motivated by the chemically reacting plug flow in a channel that has both homogeneous and heterogeneous chemistry (Section 16.3). Assume... 

Chapters 6 and 7 discuss many of the underlying fluid mechanical aspects of stagnation flows and channel flows. The intent here is to put those fundamentals to use in terms of practical, chemically reacting flows. There are numerous applications that could be discussed. We choose a few to illustrate salient points about the modeling. 

As the reacting gas flows down the channel, it interacts with the channel walls, decomposes, and leaves a film on these walls. If the wall deposit is rapid and heavy, the reactants will deplete so that the gas composition will vary with x. Although this is a technologically important case, it requires a two-dimensional (partial differential equations) description. For the present problem, we will assume that depletion is slow enough for us to neglect, and gas composition will not be a function of x. 

Parallel to the determination of the profile measurement data within the burnout chamber boundary conditions at the different inlets are determined. Velocity measurements arc carried out on several profiles covering the total depth of the channel between the gasification/ combustion zone and the burnout zone as well as in the outlet area of the slot and the three nozzles for obtaining the combustion air volume flows added to the reacting main flow. 

Channel Flow with Soluble or Rapidly Reacting Walls... 

Channel Flow with Soluble or Rapidly Reacting Walls 67 with the function satisfying the recursion relation... 

For the fully developed velocity profile the mathematical problem again reduces to the solution of the steady form of the convective diffusion equation for the solute concentration. In contrast to the diffusion equation treated in the channel flow problem with soluble or rapidly reacting walls, it is necessary to include here the lateral convection term to account for the product removal through the membrane walls, putting... 

Levich (1962) showed that a similarity solution exists to the problem as posed. We present his solution in a somewhat different form with the aim of paralleling our earlier treatments of convective diffusion layers and, in particular, the developing diffusion layer in a channel flow with a rapidly reacting wall. In direct analogy with Eq. (4.3.4) we introduce the new dependent variable... 

The differential equation may be seen to be exactly the same as Eq. (4.3.7) governing the developing diffusion layer in channel flow, with the boundary conditions the same as those appropriate to the case of a rapidly reacting wall, for which the solution is given by Eq. (4.3.19). 

A single-channel manifold also can be used for systems in which a chemical reaction generates the species responsible for the analytical signal. In this case the carrier stream both transports the sample to the detector and reacts with the sample. Because the sample must mix with the carrier stream, flow rates are lower than when no chemical reaction is involved. One example is the determination of chloride in water, which is based on the following sequence of reactions. ... 

---