Numerical Simulation of Multiphase Reactors with Continuous Liquid Phase

Figure 4.21 E-curves in the downcomer section for different current intensities and electrode positions (Essadki et al., 2011).

Figure 4.22 A typical response curve at the upper end of the riser for mixing time estimation (Essadki et al., 2011).

Actually, the full transport equation for tracer concentrations in an axisymmetric cylindrical coordinate system is given by the following 3D equation:

$\begin{array}{l}\frac{\partial (\rho c)}{\partial t}+\frac{1}{r}\frac{\partial }{\partial r}(\rho {\alpha }_{\text{l}}{u}_{r}rc)+\frac{1}{r}\frac{\partial }{\partial \theta }(\rho {\alpha }_{\text{l}}{u}_{\theta }c)+\frac{\partial }{\partial z}(\rho {\alpha }_{\text{l}}{u}_{z}c)=\frac{1}{r}\frac{\partial }{\partial r}\left(r{\alpha }_{\text{l}}{D}_{\text{eff}}\frac{\partial c}{\partial r}\right)+\\ \frac{1}{r}\frac{\partial }{\partial \theta }\left(\frac{D_{\text{eff}}}{r}{\alpha }_{\text{l}}\frac{\partial c}{\partial \theta }\right)+\frac{\partial }{\partial z}\left(D_{\text{eff}}{\alpha }_{\text{l}}\frac{\partial c}{\partial z}\right)\end{array}$

(4.211)

where D_eff is the effective diffusion ...