31    BIODEGRADATION KINETICS OF A SELF-INHIBITORY
SUBSTRATE BY STABLE STEADY-STATE BIOFILMS
Pablo B. Saez, Graduate Research Assistant
Bruce E. Rittmann, Professor
University of Illinois at Urbana-Champaign
Qui-bo Zhang, Research Assistant Professor
Research Center for Eco-Environmental Sciences
Beijing, People's Republic of China
INTRODUCTION
In the treatment of industrial wastewaters and hazardous wastes, many organic contaminants fall
into the category of self-inhibitory substrates, which are biodegradable electron donors that inhibit
the rate of microbial metabolism when present at high concentrations. The utilization kinetics for self-
inhibitory substrates usually are described with the Haldane modification of the Monod
expression:1"4
qmSXa
K + S + S2/Ki
in which (-rul) = the rate of substrate utilization [MSL"3T"'], S = the substrate concentration
[MSL3], Xa = concentration of organisms active in degrading the substrate [MXL-3], qm = maximum specific rate of substrate utilization in the absence of any inhibition effects [MSM,"'T"'],
K = half-maximum-rate concentration (in the absence of inhibition effects) |MSL"3], and K| = self-
inhibition constant [MSL3]. When S increases initially from zero, (-rul) increases similarly to the
Monod function. However, when S becomes greater than Shl dg = V KK;, (-rw) is a decreasing
function of S.  Dispersed-growth process cannot sustain stable steady states at S > Shj dg.3,5
Saez et al.6 and Gantzer7 recently showed that biofilm processes ought to be able to operate stably
and at steady state for concentrations greater than Shj dg. Extension of the range of concentrations for
stable operation is made possible by the "protection" afforded by diffusion-driven gradients in the
biofilm. As is illustrated schematically in Figure 1, stable utilization of a self-inhibitory substrate is
possible deep in the biofilm when diffusion through the outer (and inhibited) zone reduces the
concentration to noninhibitory values for the deeper zone, which can have strong positive growth.
[Recall that the net growth rate of cells in contact with S is
fgr = Y(-rul) - bXa (2)
in which rgr = cell net growth rate [MXL"3T_1], Y = true yield [MXMS"'], and b = specific
maintenance-decay coefficient [T"'j. When (-rul) is small, rgr becomes negative, which is the situation
for the zone of inhibition.]
Although Saez et al.6 and Gantzer7 showed that stable steady-state biofilms are possible for S >
Shj dg, they also showed that biofilms have an upper-limit concentration for stable operation. That
concentration is defined as Shi bf, and it can be computed only by solution of the differential equations
that constitute the steady-state model [e.g., equations 9-15 in Saezet al.6]. Shi bf occurs when the zone
of positive growth occupies only a small portion of the biofilm; any reduction in the size of the
positive-growth zone, by its being pushed relatively deeper into the film with a larger S, results in a net
negative growth rate integrated over the entire film.6,7
Whereas Shj bf defines the upper-limit concentration for maintaining a stable steady-state biofilm,
S!o defines the lower-limit concentration. S!o is the lowest concentration to support a stable steady-
state biofilm; for S < S|0, rgr is always negative8. Saez et al.6, Gantzer7, and Saez and Rittmann9
showed that S]o is computed for self-inhibitory substrates by
45th Purdue Industrial Waste Conference Proceedings, © 1991 Lewis Publishers, Inc., Chelsea, Michigan 48118.
Printed in U.S.A.
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