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Research Papers

Metabolic Mass Transfer in Monotonic Growth of Microorganisms

[+] Author and Article Information
Peter Vadasz1

College of Engineering, Forestry and Natural Sciences, Northern Arizona University, P.O. Box 15600, Flagstaff, AZ 86011-5600; and Faculty of Engineering, University of KwaZulu-Natal, Durban 4041, South Africapeter.vadasz@nau.edu

Alisa S. Vadasz

College of Engineering, Forestry and Natural Sciences, Northern Arizona University, P.O. Box 15600, Flagstaff, AZ 86011-5600; and Faculty of Engineering, University of KwaZulu-Natal, Durban 4041, South Africa

1

Corresponding author.

J. Heat Transfer 133(1), 011008 (Sep 30, 2010) (9 pages) doi:10.1115/1.4002416 History: Received November 11, 2009; Revised August 10, 2010; Published September 30, 2010; Online September 30, 2010

Microorganism growth and reproduction have been traditionally modeled independently of the direct effect of the metabolic process. The latter caused inconsistencies between the modeling results and experimental data. A major inconsistency was linked to the experimentally observed lag phase in the growth process. Attempts to associate the lag phase to delay processes have been recently proven incorrect. The only other alternative is the existence of unstable stationary states resulting from the explicit inclusion of the metabolic mass transfer process via the resource consumption and utilization. The proposed theory that accounts for the latter is presented, analyzed, and compared with experimental data both qualitatively as well as quantitatively.

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Figures

Grahic Jump Location
Figure 2

Phase diagram for the solution of monotonic growth corresponding to rmδ>1 in terms of the specific growth rate ẋ/x versus the cell concentration x for rm=5×10−7 (cell/ml)−1, δ=107 cells/ml, and μmax=3×10−4 s−1 (reproduced from Vadasz and Vadasz (12))

Grahic Jump Location
Figure 1

A typical microbial growth curve (reproduced from Vadasz and Vadasz (22))

Grahic Jump Location
Figure 3

The effect of the maximum specific growth rate, μmax, on LIP and lag. Analytical results in the time domain for rm=10−5 (cell/ml)−1 and δ=1.5×108 cells/ml, subject to initial conditions of xo=1.1458×105 cells/ml, ẋo=7.5×10−3 cells/(ml s), and different values of μmax ranging from μmax=0.3×10−3 s−1 and up to μmax=2×10−3 s−1. (Reproduced from Vadasz and Vadasz (12).)

Grahic Jump Location
Figure 4

(a) The relationship between the maximum specific growth rate μmax and LIP for three different values of rm. (b) The relationship between the maximum specific growth rate μmax and lag for three different values of rm. (Reproduced from Vadasz and Vadasz (12).)

Grahic Jump Location
Figure 5

(a) The relationship between the maximum specific growth rate μmax and LIP for four different values of the initial growth rate ẋo. (b) The relationship between the maximum specific growth rate μmax and lag for four different values of the initial growth rate ẋo. (Reproduced from Vadasz and Vadasz (12).)

Grahic Jump Location
Figure 6

The effect of the initial growth rate ẋo on LIP and lag. Analytical results for rm=10−5 (cell/ml)−1, μmax=3×10−4 s−1, and δ=1.5×108 cell/ml, subject to the initial condition of xo=1.1458×105 cell/ml, and for different values of ẋo ranging from ẋo=7.5×10−4 cell/(ml s) up to ẋo=50 cells/(ml s). (Reproduced from Vadasz and Vadasz (12).)

Grahic Jump Location
Figure 7

The effect of the initial cell concentration xo on LIP and lag on a phase diagram in terms of the specific growth rate ẋ/x versus the cell concentration x. Analytical results for rm=5×10−4 (cell/ml)−1, μmax=3×10−4 s−1, and δ=1.5×108 cells/ml, subject to the initial growth rate condition of ẋo=1 cell/(ml s), and for different values of xo ranging from xo=1×107 cells/ml up to xo=6×107 cells/ml. (Reproduced from Vadasz and Vadasz (12).)

Grahic Jump Location
Figure 8

Comparison of the neoclassical values of the lag duration with the classical lag duration values obtained by a variation in μmax over six orders of magnitude from μmax=2×10−4 s−1 up to μmax=1×102 s−1. The value of b for evaluating the neoclassical lag was b=1.17, i.e., about 1% above y3s=ln(x3s), or 17% above the unstable stationary points x3s. The markers represent the evaluated results. (Reproduced from Vadasz and Vadasz (12).)

Grahic Jump Location
Figure 9

Comparison of the neoclassical model analytical solution for monotonic growth based on Vadasz and Vadasz (15-16) with the experimental data based on O’Donovan and Brooker (25) (here redrawn from published data). The initial cell concentration is xo=1.1458×105 (cfu/ml), and the estimated parameter values are as presented by Vadasz and Vadasz (12). (Reproduced from Vadasz and Vadasz (12).)

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