EXPERIMENTAL STUDIES and MATHEMATICAL MODELING OF BACTERIAL TRANSPORT
through SATURATED POROUS MEDIA

Prasanna A. Deshpande

The study of transport of microorganisms through porous media is important for 1) bioremediation, 2) the fate of microorganisms in the subsurface, and 3) the use of microorganisms in engineered systems.  Some bioremediation systems in operation today make use of indigenous populations of bacteria to remediate contaminants in the environment.  The contaminated sites can be augmented by injection of viable non-native cultures of microorganisms which are suited to tackle the specific contaminants in the environment.  This technology is known as bioaugmentation.  An accurate model of microbial transport in the subsurface can help predict the range of the injected bacteria and their attachment to the soil at the contaminated sites.

Previous studies on the transport of inorganic colloids through sand columns have shown that the kinetics of attachment can be modeled as either first or second order (Hornberger et al, 1992).  We have extended this work to biological colloids using a common, rod shaped, gram negative soil bacteria pseudomonas fluorescens.  In particular, we have studies the effect of two suspension characteristics on the kinetics - 1) the salt concentration and 2) the valence of the electrolyte dissolved in the bacterial suspension.  The schematic diagram of the experimental set-up is shown below:

The bacteria were grown in a BioFlo 3000 bioreactor (not shown in the diagram above), harvested, suspended in a solution of desired salt concentration and passed through a saturated soil column.  The column was packed in a manner so the chances of air bubbles being trapped are minimal.  The sand was shaken and washed using distilled water to remove bound clays.  The effluent concentration of suspended bacteria was monitored using a spectrophotometer and the breakthrough and effluent data was collected.  Experimental parameters that were kept constant during the entire set of experiments are tabulated below:

Set of Experimental Parameters Held Constant

The following shows a schematic comparison between the breakthrough curves of a non-binding tracer (phenol red) and that of bacteria suspended in a 10-2M phosphate solution.

As can be seen, the breakthrough curve for the tracer (red) reaches a maximum relative concentration (C/Co) of 1.0 which the bacterial breakthrough curve (green) does not.  Further, the tracer profile is flat till the elution starts where as the bacterial breakthrough curve has a slope to it.  For bacterial system, this slope can be positive, negative or zero.

It was found that with increasing concentration of dibasic phosphate salts, the breakthrough curves changed remarkably indicating a change in the kinetics of attachment.  The kinetics changed from blocking (2^nd order-green) to 1^st order (yellow) and then finally to ripening (~2^nd order-blue) with increasing salt concentration.  They respectively represent decreasing, constant, and increasing rate of attachment with time.  These results are displayed below:

To investigate the effect of salt concentration, the change in the overall surface charge of the bacteria was measured.  As depicted below, measurements of zeta potential of the bacteria at corresponding salt concentrations show a decrease in the magnitude of their negative surface charge with increase in salt concentration.  This trend indicates that the electrostatic repulsion between the bacteria and the sand particles is decreasing, causing greater attachment at higher salt concentrations.  Similar zeta potential experiments are planned on the sand particles.

In the next figure, the same kinds of kinetics are observed in the case of monovalent sodium chloride salt, however the change is far less pronounced.

The advection - dispersion equation with kinetic Langmuirian model for attachment is shown here:

In the kinetic model for attachment, the dynamic sorbed concentration of the bacteria is shown as a function of the rate of attachment and detachment process.  The forward rate of attachment is further shown to be a function of a parameter related to the sorption capacity of the soil as well.  This model can simulate the blocking and 1^st order phenomena and is called the ‘blocking’ model.  The detachment process is currently not studied in this research and hence the detachment coefficient is set to zero.

A FORTRAN code was developed to simulate the process by a finite difference scheme (seen above) whose stability is governed by the Peclet No. and Courant No. criteria.  Some terms and concepts used in colloid filtration theory are exhibited below:

This theory was used to relate the attachment coefficient, k_c, to collision efficiency, alpha, and to collector efficiency, eta, as shown below:

The expression shown for collector efficiency is based on Happel’s sphere in cell model.  This expression can be substituted for collector efficiency in the attachment rate coefficient expression.  Values for collision efficiency were estimated by fitting the model to the experimental data.

To account for ripening, Tien’s (1989) model for rise in collector efficiency (displayed above) was incorporated.  The term ‘specific deposit’, sigma, used in the expression is a volumetric ratio of the sorbed bacteria to the soil particle.  The exponent of this term, n, was fitted to the data.  N_R is a size ratio and eta₀ is the clean bed collector efficiency, obtained from the expression for eta_Diff in the 'Application of Colloid Filtration Theory' above.

An example of the blocking model prediction with experimental data at a particular phosphate concentration is depicted above.  Both the blocking as well as the ripening model were fitted to the data by a two parameter fit (alpha; S_max and alpha; n respectively) which are tabulated later.

The next figure above shows an example of the fit of ripening model to the experimental data at a particular salt concentration.  The model fits the data well except the ‘tail’ of the curve because the detachment process was ignored in this study.

Table of Fitted Parameters and Comparison with Experimental Values

The table of the sets of two parameter fits is above.  The fit was done by using a least square algorithm.  The values for collision efficiency approach 1.0 at high concentrations as expected.  Values for maximum sorption capacity match well with those experimentally measured and values for the exponent used in ripening model stay fairly constant, though somewhat lower than reported in the literature (n = 0.75) for spherical abiotic colloids (Tien, 1989).

Conclusions, followed by a list of references and acknowledgments are listed below:

Conclusions

1. The bacteria Pseudomonas fluorescens shows three different kinds of attachment kinetics viz. blocking, ripening, and 1^st order behavior.
2. Increasing salt concentration and valence of the electrolyte makes the attachment kinetics change from 2^nd order with blocking to 1^st order and then to 2^nd order with ripening.
3. With increasing salt concentration the fitted values of collision efficiency approach the limit of 1.0.
4. The mathematical model can be used to describe the convection-dispersion equation with three different attachment kinetics or to estimate the colloid filtration parameters.

References

1. Hornberger, G.M., Saiers, J.E., Liang, L., Water Resources Research, 1994, 30, 2499-2506.
2. Tien, C., "Granular Filtration of Aerosols and Hydrosols", Butterworths, p 333, 1989.

Acknowledgments

1. NSF Combined Research/Curriculum Development Program Award No. EEC-9420526
2. Michigan Research Excellence Fund

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