Laminar-flow reactor material balance

A laminar-flow reactor (LFR) is rarely used for kinetic studies, since it involves a flow pattern that is relatively difficult to attain experimentally. However, the model based on laminar flow, a type of tubular flow, may be useful in certain situations, both in the laboratory and on a large scale, in which flow approaches this extreme (at low Re). Such a situation would involve low fluid flow rate, small tube size, and high fluid viscosity, either separately or in combination, as, for example, in the extrusion of high-molecular-weight polymers. Nevertheless, we consider the general features of an LFR at this stage for comparison with features of the other models introduced above. We defer more detailed discussion, including applications of the material balance, to Chapter 16. 

In a laminar flow reactor the concentration varies both radially and axially and depends on the specific rate. Along a stream line, the material balance is... 

The material balance on a laminar-flow reactor with negligible mass diffusion (discussed later in this chapter) is ... 

Write down in dimensionless form the material balance equation for a laminar flow tubular reactor accomplishing a first-order reaction and having both axial and radial diffusion. State the necessary conditions for solution. 

The design of plug flow reactors (tubular and tower devices) does not assume mixing in the direction of flow (axial turbulence), therefore the chemical processes within a blend of reactants occurs in laminar flow conditions. A combination of the displacement and plug flow reactors, with consideration of their material and thermal balances, makes it possible to calculate the optimal design of a device for any chemical process. 

Consider a first-order chemical reaction being carried out under isothermal steady-state conditions in a tubular-flow reactor. On the assumptions of laminar flow and negligible axial diffusion, the material balance equation is... 

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