Isothermal Laminar Flow with Negligible Diffusion

Consider isothermal laminar flow of a Newtonian fluid in a circular tube of radius R, length L, and average fluid velocity u. When the viscosity is constant, the axial velocity profile is 

This result is reminiscent of Equation (1.36). We have replaced the average velocity with the velocity corresponding to a particular streamline. Equation (8.2) is written as a partial differential equation to emphasize the fact that the concentration a = air, z) is a function of both r and z. However, Equation (8.2) can be integrated as though it were an ordinary differential equation. The inlet boundary 

---

ISOTHERMAL LAMINAR FLOW WITH NEGLIGIBLE DIFFUSION... 

Equation (8.9) can be applied to any reaction, even a complex reaction where ctbatch(t) must be determined by the simultaneous solution of many ODEs. The restrictions on Equation (8.9) are isothermal laminar flow in a circular tube with a parabolic velocity profile and negligible diffusion. 

We start with the case of d(z) injection profile into an isothermal column under laminar gas flow regime. The factors which cause broadening of the initial profile are longitudinal diffusion and radial diffusion across streamlines. These continuously change the concentration distribution and gradients. In the absence of any adsorption sojourn time of molecules on the wall (i.e. negligible adsorption-desorption energy), and only in this case, the two above diffusion processes yield ... 

---