Effect of axial dispersion on microbial growth

Abstract

The extent of microbial growth in a continuous flow reactor is influenced by various degrees of fluid mixing which may range from one extreme of plug-flow to the other extreme of completely mixed flow. To assess the effect of mixing on the extent of microbial growth various flow models such as the tanks-in-series model and the axial dispersion model are often employed. Such flow models have been successfully applied to biological waste treatment processes by Murphy (1971) and Lee et al. (1971).The purpose of this note is to present and discuss the analytical solutions of differential equations describing the extent of microbial growth based on the axial dispersion model under the assumption that the specific growth rate does not depend on the substrate concentration. The assumption permits the differential equations to be solved analytically and provides useful limiting case for more complicated substrate limited systems. These results should be useful in connection with fermentation processes and biological waste water treatment.dimensionless form with Danckwerts' boundary conditions:where Pe is the Peclet number. Pe is a measure of the degree of mixing, ranging from Pe = 0 (completed mixed flow) to Pe = c4 (plug flow).The solution can be obtained by a standard method such as Laplace transformation for the following three cases:where Specifically two problems are considered. The first is concerned with steady state solution with nonsterile feed.The second is concerned with the transient and steady state solution with sterile feed. (ii) Pe = 4K Pe STEADY STATE GROWTH WITH NONSTERILE FEED [ X ( 0 ) > 01 1 + 2 ( 1x ) X ( z ) = Pe 1 + -4The differential equation based on the axial dispersion model for this case can be represented in the following

Backmixing in gas‐liquid reactors

“…Most studies reported thus far have indicated that the axial dispersion coefficieiit in an unpacked bubble column is independent of liquid velocity. Chen ( 1972), however, reported that this observation is due to the fact that in all studies, the interstitial liquid velocity has been less than 10% of the rising velocity of the bubbles ub. At U L > 0.1Ub, Chen (1972) presented the dependency of the dispersion coefficient 011 the liquid velocity as…”

Effect of longitudinal mixing on microbial growth in a multi‐stage column bioreactor

“…With sterile feed operation (C,,=O), eqn (4) for the bottom stage reduces to and the respective equations for other stages are the same as eqns ( 5 ) and (6). The solution in this case is given by cx,i= 0 (28)…”