Biofilm Formation and Chemostat Dynamics: Pure and Mixed Culture Considerations James D. Bryers Swiss Federal Institute for Water Resources and Water Pollution Control, €A WAG/ETH, Swiss Federal Institute of Technology, CH-8600 Diibendorf, Switzerland Accepted for Publication December 30, 1983 Time-dependent biofilm formation effects on continu- ous fermenter operation are modelled here in general for a mixed culture of N different microorganisms grow- ing on a single substrate. Dynamic computer solutions are detailed for two versions of the general model: a pure culture and a simple two-cell mixed culture. Pure culture model predictions compare favorably with two pure culture experiments in the literature where signifi- cant biofilm formation was noted. A mixed culture of one microbe (C,) having a higher growth rate than a sec- ond microbe (C,) is simulated for two hypothetical sce- narios of microbe C2 having different magnitudes of cell deposition rate. Biofilm effects on the estimation of ki- netic and stoichiometric parameters in both model ver- sions, plus the impact of biofilms on mixed culture dy- namics, are discussed. INTRODUCTION Biofilms-adherent microorganisms often entrapped within an extracellular polymeric matrix-can develop on any surface exposed to an active microbial culture. Biofilms within fermenters can create such problems as: 1) erratic effluent biomass concentrations, 2) obscure continuous culture washout, 3) atypical ecological niches within the reactor, and 4) physical fouling of reactor in- ternals (e.g., impellers, baffles, heat exchange surfaces, pH probes, and DO probes). Despite an increasing awareness of biofilm formation and its associated detri- mental effects, biofilm formation in a chemostat is often considered only a mere operating nuisance. In the inter- pretation of resultant chemostat data, the subtle effects of biofilms are all too often ignored; such neglect can pro- duce inaccurate estimates of kinetic/stoichiometric pa- rameters and can lead to erroneous conclusions about the ecological dynamics of mixed cultures. Historically, the effects of biofilm formation on fer- menter operation were not considered until 1 9 6 4 , ' ~ ~ even though the effects of microbial attachment on apparent microbial activity were noted in 1943.3 Topiwala and Ha- mer4 first quantified the effects of a constant biofilm Biotechnology and Bioengineering, Vol. XXVI, Pp. 948-958 (1984) 0 1984 John Wiley &Sons, Inc. amount on the steady-state substrate and suspended bio- mass concentrations in a chemostat. This classical note predicted the extension (or elimination) of culture wash- out as a function of the assumed constant biofilm amount. The Topiwala-Hamer model (THM) was de- rived for pure cultures with constant kinetidstoichiomet- ric parameters equal for both attached and suspended microorganisms; no mass transfer limitations were con- sidered. Wilkinson and Hamer5 experimentally verified the THM in continuous mixed culture studies where maxi- mum biofilm thickness was reported at ca. 700 pm. Biofilm research increased dramatically during the sev- enties with most theoretical efforts directed toward mod- elling substrate mass transfer and biological reaction within a biofilm of constant thickness. Grady6 provides an excellent review of such biofilm-substrate kinetic models. Characklis and colleague^^-^^ present the only comprehensive studies (both experimental and mathe- matical) of biofilm accumulation in chemostats; regretta- bly biofilm formation was carried out at constant dilution rate(s), far in excess of the culture washout. Finally, Balt- zis and Fredrickson" extend the THM to competition be- tween two different microbial populations for one limit- ing substrate where one population forms an attached monolayer (not a strict biofilm). Their study is entirely theoretical, presenting steady-state stability analysis of the system equations without experimental verification. One purpose of this article is to present a simple gen- eral unsteady state model for biofilm formation within a continuous mixed culture system. For verification, pre- dictions of a pure culture limiting case of the model are compared to existing literature data. Then the dynamics of a simple two-species mixed culture biofilm are consid- ered as a function of reactor operating parameters. The second, perhaps more important purpose of this article is to clarify how a chemostat behaves when biofilm forma- tion occurs and how to correctly interpret data resulting from such systems. CCC 0006-3592/84/080948-11$04.00 MODEL DEVELOPMENT General Model The mathematical description for biofilm accumula- tion is based upon the scenario proposed elsewhere by Characklis and c o - w o r k e r ~ . ~ ~ ~ The general mixed culture model is based upon the following assumptions: 1) The reactor is operated in the continuous flow mode and completely mixed with volume V(L3) and internal surface area A ( L 2 ) . 2 ) Biomass concentration of the j t h suspended microbe is denoted Cj(Mx/L3) with j = 1 . , . N , where N is the total number of species in the mixed culture. 3) All suspended microbes form biofilms to some ex- tent. Biomass areal concentration of thejth attached mi- crobe is denoted Bi(Mx/L2) with j = l . . . N . 4) Accumulation of each attached microbial species is the sum of rates of three individual processes: cellular de- position RF(Mx/L2) , growth rate of attached microbe R?(M,/L2), and a fraction4 of the total biofilm removal rate RH (Mx/L2) . 5 ) Nonviable biofilm material (i.e., extracellular poly- mers or residue of cell lysis) is not modelled here. Conse- quently, the total biofilm areal density M ( M x / L 2 ) is the sum of the areal concentrations of all attached microbes. TrulearI2 does present mass balances for both intra- and extracellular carbon in biofilms growing in pure culture chemostats. Also, endogenous decay processes are ig- nored; implications of this assumption are discussed in a later section. 6 ) The fraction4 is assumed, without verification, to be equal to the weight fraction of microbej in the biofilm; i.e.,fj = B j / M . Due to assumption 5 , C$,I f j = 1.0. 7) Nutrient feed streams to the reactor are sterile. 8) Both suspended and attached mixed cultures grow on a single growth-limiting substrate S ( M s / L 3 ) . Sus- pended growth rates of individual microbial species are considered Monod-like expressions of S; i.e., pjC; = @;SCj/(K{ + S) (1) Attached microbial growth rates are identical Monod ex- pressions using biofilm concentrations and could incor- porate an effectiveness factor TJ to account for possible in- ternal mass transfer resistances to S within the biofilm; i.e., External mass transfer resistances are considered negligi- ble in most well-stirred fermenters. PitcherI3 describes one such effectiveness factor TJ for Monod-like expres- sions as a function of a modified Thiele modulus +p where and (adapted here to the specific biofilm situation), (4) N K[(L2/KsDe) J = l c ( p J B J J ‘ p = (1 + K)[2K - 2 In (1 + K)]1’2 where p is the biofilm volumetric density (Mx/L3) , L is the biofilm thickness (L) defined as ( M / p ) , a, is the attached microbial yield coefficient ( M x / M s ) , D, is the effective diffusivity of S in the biofilm ( L 2 / t ) , and K is equal to S / K , . 9) Biofilm removal is due to prevailing shear stresses in the reactor which are considered constant for this article. Consequently, the rate of biofilm removal is assumed a function only of the total biofilm mass at the surface. Trulear and Characklis9 suggested the following expres- sion for biofilm removal rate, RR = kR M 2 / M M (5) where kR is the maximum biofilm removal rate at steady- state biofilm concentration ( l / t ) and MM is the steady- state maximum biofilm concentration ( M x / L 2 ) . 10) Cellular deposition rates are assumed proportional to the surface area of the reactor unoccuppied by total biofilrn and the concentration of specific suspended mi- crobe. If M* (Mx/L2) is the maximum surface concentra- tion considered attainable by deposition only, then, using a modified form of an expression suggested by Baltzis and Fredrickson,” the cellular deposition rate is, (6) where kJ” is the deposition rate constant for j t h microbe Given the above assumptions, the following equations describe mixed culture biofilm formation in a chemostat: The attached microbial equations, j = 1 + N , are RJ” = kJ” (M* - M ) CJ (L3/Mxt) . dBJ/dt RJ” -k RY - 4 R R (7) The total biofilm equation is N dM/dt = c (Rf + RY) - RR (8) J = 1 The suspended microbial balances, j = 1 + N , are dC,/dt = -DCJ + pJCJ - RJ”A/V + f , R R A / V (9) The limiting substrate balance is N dS/dt = D(So - S) - C [ (p lC, /Y/ ) + (R,GA/Va,)J /= 1 (10) where YJ is the suspended microbial yield coefficient ( M x / M , ) and D is the reactor dilution rate (lit). Case I: Pure Culture Conditions Under pure culture conditions in the chemostat, j = 1 and the general model reduces to the three equations be- low. 949 BRYERS: BlOFlLM FORMATION AND CHEMOSTAT DYNAMICS The total biofilm equation is dM/dt = kD(M* - M)C + vfiSM/(K, + S ) - kRM2/MM (11) The suspended biomass balance is dC/dt = -DC - kD(M* - M ) C A / V + f iSC/(K, + S ) -t kRM2A/MMV (12) The substrate balance is dS/dt = D(So - S) - ;SC/Y(K, + S ) - vfiSMA/a(K, + S)V (13) where 7 = tanh 4p /+p as before but, for a single popul- ation, 4p = KJ~PL~/K,~D,/(I + K)J~K - 2 In(1 + K ) , All other definitions remain unchanged. Note that there is no need for both attached microbial and total biofilm equations since, at j = 1, the total biofilm is composed of only one species. Results from an experimental chemo- stat study using Pseudomonas putidu, with observed biofilm formation, will be compared in the next section to predictions obtained from eqs. (11)-(13) above. Case I / : Binary Culture Conditions model reduces to the six equations below: The biofilm microbe 1 equation is Here , j = 1, 2 for a binary culture and the general dB, /d t = ky(M* - M)C1 + vpiB1 - f ikRM2/MM (14) The biofilm microbe 2 equation is dB2/dt = k$'(M* - M)C2 + vp2B2 - f 2 k R M 2 / M ~ (15) The total biofilm equation is d M / d t [(M* - M ) ( k f C , + kfC2)l + ~ ( p i B 1 + ~ $ 3 2 ) - kRM2/MM (16) The suspended microbe 1 balance is dCl/dt = -DC1 - kr(M* - M)CiA/V + pic1 + fikRM2A/MMV (17) The suspended microbe 2 balance is dC2/dt = -DC2 - k f ( M * - M)C2A/V + p2C2 + f2kRM2A/MMV (18) The substrate balance is dS/dt = D(So - S) where 11 is a function of the modified Thiele modulus &, as before, except +p is redefined as, (1 + K)[2K - 2 In (1 + K)I1l2 Steady and unsteady state solutions of eqs. (14)-( 19), at different dilution rates for various culture conditions (e.g., k f >> k f at fil > F 2 ) , will be presented in the next section. RESULTS Pure Culture Case MolinI4 studied Pseudomonas putida (ATCC-111-72) in continuous culture at various dilution rates with as- paragine as the sole carbon and single limiting substrate. The fermenter was inocculated at a substrate concentra- tion of 3.0 g,/L, operated batchwise until suspended biomass = 600 mg,/L, then nutrient flow was started to affect a dilution rate of 0.6 h-'. The dilution rate was then varied from a minimum D = 0.1 h-' by regular in- crements to a maximum D = 2.2 h-' without observing culture washout. After each dilution rate shift, the reac- tor was operated for a certain time period prior to sam- pling: 16 h for D = 0.6 and 0.1-0.6 h-l; 7 h for D = 0.8-1.1 h-l; and 3 h for D = 1.3-2.2 hF1. M01in'~ reports considerable biofilm developed on all fermenter surfaces during the above experiments. Al- though biofilm formation was not continuously moni- tored during the experiment, the total biofilm amount at the completion of the culture was measured. Figures 1 and 2 summarize effluent biomass (as dry weight) and substrate concentrations reported by MolinI4 for con- stant inlet concentrations of 1.0 and 2.0 g,/L asparagine, respectively. Table I provides a summary of parameters required by the pure culture model (PCM), eqs. (11)-(13), to simu- late the experiments of Molin. All values are directly from the original article except for the following: at- tached and suspended stoichiometric coefficients, satura- tion constants, deposition rate constants, and the surface concentration M* due to deposition only. A relatively high value for the biofilm density of 50 mg,/cm3 was cal- culated from Molin's data of maximum biofilm mass, thickness, and reactor surface area. The reader should note, under these conditions of thickness and density, model estimates of #p indicate G 1.0 and that internal mass transfer effects are negligible. Implications of ne- glecting internal mass transfer on the results will be dis- cussed in a later section. Equations comprising the PCM are solved simultaneously using parameters in Table I with a dynamic simulator computer package named MIMIC.15 Predictions of both the steady-state THM and the dy- namic PCM for effluent substrate and suspended bio- mass concentrations are superimposed upon "steady- 950 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 26, AUGUST 1984 ecL 0 0 5 1 0 1 5 2 0 D I L U T I O N R A T E , 0 ( I / h ) Figure 1. Steady-state (m) effluent substrate and (0) suspended cell mass reported by Molin (ref. 14) for Pseudomonasputida grown in chemostat culture at So = 1.0 g,/L asparagine. Growth conditions are given in Table I. The symbol (-) indicates predictions of steady-state THM and (------) indicates steady-state predictions of dynamic PCM. - 1 6 0 TH M I - 800- 0 0 P 700- I . - 1 4 - Y v) - 0 8 - z Y V u1 l d' - 600- a = 500- 0 m 0 4 0 - W 0 z v) 3 u1 300 - 200 - c z W 2 LL LL 3 100- W l . . . . I . . . . , 0 - = 0 05 1 0 1 5 20 D I L U T I O N R A T E D ( l / h ) Figure 2. Steady-state (m) effluent substrate and (0) suspended cell mass reported by Molin (ref. 14) for Pseudomonasputidu grown in chemostat culture at So = 2.0 gJL asparagine. Growth conditions are given in Table I . The symbol (-) indicates predictions of steady-state THM and (------) indicates steady-state predictions of dynamic PCM. Table I. Pseudomonasputidu results of Molin (ref. 14). Dilution rates varied from 0.1 to 2.2 h-I. Parameter A" V" i" kRb kDC KSC Mw" M" SOa Y and 01" Parameters used in either the dynamic pure culture model (PCM) or the steady-state Topiwala-Hamer model (THM) to simulate (cm2) (cm3) (h-l) U - 1 ) (L/mg, h) (mg,/L) (mg,/cm2) (mgJcm2) ( mg, 1 L) (mgJmg,) Value 800 970 0.59 0.2 3.0 X lo-' 10.0 0.50 5.0 X 1000 and 2000 0.32 aValue is taken directly from ref. 14. bValue is estimated from ref. 14 data. Value is assumed. BRYERS: BlOFlLM FORMATION AND CHEMOSTAT DYNAMICS 95 1 state” data from Molin experiments 1 and 2 in Figures 1 and 2, respectively. While both models simulate overall trends in each experiment, only the PCM is able to pre- dict the subtle variations seen in suspended biomass con- centrations. Predictions of both models do not coincide at high D values, although theoretically, equations compris- ing the PCM will reduce to the THM under assumptions of S, C , and M at steady state. Note, however, that the PCM is a dynamic model and its predictions are depen- dent upon initial conditions which are determined by the previous simulation. Biofilm formation and suspended biomass concentra- tions predicted via PCM for experiment 2 are illustrated in Figure 3 as a function of the time elapsed since a D value shiftup. Predicted biofilm concentrations do not at- tain steady state after D shifts until D 2 0.5 h-l. Since effluent suspended biomass concentrations are depen- dent upon both suspended growth and biofilm removal processes, no true steady state in C as possible until M reaches a constant value. Consequently, at D < 0.5 h-l, predicted effluent suspended biomass concentrations are not at steady state and, thus, are dependent upon the time elapsed prior to sampling. Apparent yield (Y,) is defined traditionally for steady- state chemostats as an expression which does not account for the substrate utilized for biofilm growth. In both experiments above, Y, values increased from Y, 2 0.2 mgJmg, at D = 0.1 h-l to Y, 0.40-0.45 mg,/mg, at D = 1.0 h-l. In- creasing yield values with increasing D are often attrib- - cy E u . x m E - 06 5 0 5 z g 0 4 0 0 z 03 A - :: 0 2 - m A 01 a I- 0 t uted to either increasihg maintenance energy require- ments at the lower dilution rates or to physiological changes in the microorganisms. Tempest and Neijssel16 proffer “apparatus effects” as a more plausible alterna- tive to the convenient “maintenance” explanation. Illus- trations above indicate that the PCM, based upon con- stant, equal stoichiometry for both suspended and attached growth processes, also predicts Y, values to in- crease with increasing D . In these cases, Y, increases due to the increasing (yet unaccounted for) contribution of biofilm removal processes to the suspended biomass con- centration. Since biofilm removal processes are highly dependent upon shear stresses prevailing in the reactor, trends in variable Y, with D are likely to differ between reactors operated at either different impeller speeds or fitted with a different numbers of impellers. The major error in chemostat data interpretation, when biofilm for- mation has not reached a steady state, is the use of eq. (21) which does not compensate for the substrate utilized for biofilm growth. Bryers17 and Zelver18 derive the fol- lowing integral definition of yield: [M( t ) - M(0)] + F 1‘ C dt F 1: (So - S) dt (22) 0 Y = directly from the steady-state version of the PCM, where F is the inlet nutrient volumetric flow rate (L3/ t ) . Using eq. (22), and C and S data predicted by the PCM after any dilution rate shift, Y = 0.32 mgJmg,, exactly the value used in the computer simulation. Under conditions u 20 20 20 20 20 20 20 10 10 10 TIME ELAPSED BETWEEN DILUTION RATE SHIFTS (H) BOO “E 700 9 600 - a 500 I 2 m 400 ~ n 300 5 a u . x 0 cn cn w Y, 200 2 100 2 t z _1 U U o w Figure 3. Predictions of PCM for transient periods after dilution rate shifts for suspended cell mass and biofilm areal concentrations. The (0) data for suspended cell mass is from Molin (ref. 14), experiment 2, with So = 2.0 gJL. Values in parentheses denote dilution rates. 952 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 26, AUGUST 1984 of steady state with respect to S, C , and M, eq. (21) is still insufficient to estimate true stoichiometry. Assuming at- tached and suspended yield terms to be equal, at steady state, eq. (13) reduces to the following, Y = ( p C + vpMA/V) /D(So - S) (23) which does account for the biofilm's use of substrate. Figure 4 serves to illustrate, for experiment 2 condi- tions, the increasing use of substrate for biofilm growth predicted by the PCM. Biofilm substrate utilization rate is shown 1) negligible early in the experiment, 2) contributing to 50% of the total substrate removal rate at D = 1.2 h-l, and 3) reaching a maximum of 74% of the total substrate removal rate at D = 2.2 h-l. Al- though suspended biomass is unlikely to increase due to reproduction at D > 2.0 h-' (residence times < 0.5 h), substrate utilization by suspended bacteria, originating due to biofilm removal, can not be considered negligible. Simple Binary Culture Model The illustration of biofilm effects on a mixed culture will be considered here only for a simple binary microbial culture, with both microorganisms competing, attached and suspended, for a single limiting substrate. Growth kinetics for each bacteria are depicted in Figure 5 (PI > G 2 , K; = K s ) and are selected since under ideal circum- stances neither microbe 1 nor microbe 2 will coexist in a chemostat. Other mixed cultures scenarios are possible based on either different growth kinetics or on the spe- cific microbial interactions (e.g., competition versus commensalism versus predation) selected, but such vari- ations are not considered here. Two hypothetical cases based upon the above kinetics are treated with the binary culture model (BCM). In both cases, the deposition rate constant of the slower growing cell 2 is greater than for cell 1: in case A, kf = lOkf) and in case B, kf = 1000kf). Other model parameters used in the BCM simulations are given in Table 11. Once again, biofilm density is set equal to 50 mg,/cm3 which has the effect of "cultivating," computerwise, thin but reactive I 0 50 100 SUBSTRATE CONC (mg,/1) Figure 5. lations. Growth kinetics used in binary culture model (BCM) simu- Table II. Model parameters used in binary culture simulations. Batch initial conditions: S(0) = 3000.0 mg,/L, Cl,2 (0) and B,,2 (0) = 0.0 mg,/cm2. 1000.0 1000.0 0.3 10.0 0.50 0.0001 500.0 0.60 0.50 0.30 0.35 3.0 X (case A) 3.0 X lop2 (case B) 3.0 x 10-5 5.0 mg,/L, biofilms. At this specific density, heterogeneous biofilms would have to exceed ca. 100 pm before internal mass transfer resistances become significant. In the following hypothetical situations, biofilm thicknesses never exceed 100 pm, thus tacitly ignoring internal mass transfer ef- fects. . FRACTION OF SUBSTRATE W I- < a 0 N: 2 I- <- - 0.5 $ 2 5 0 0 - I- u) I ,' P(batch) I / I W 2 = -- rn '7 I- < a / m 0 ,*' 4 3 v) o o ' - - * c ' l 0.5 ' ' ' 1.0 I ' a * 1.5 * ' ' " 2.0 " DILUTION RATE D ( l l h ) Relative destinations of substrate utilized as predicted by PCM for Molin experiment 2. Figure 4. BRYERS: BlOFlLM FORMATION AND CHEMOSTAT DYNAMICS 953 Both hypothetical cases, A and B, are initiated as batch reactor simulations with the batch initial condi- tions given in Table 11. After eight hours simulated batch operation, continuous flow is initiated by setting D = 0.1 h-l. The dilution rate is then incrementally increased from 0.1 to 6.0 h-’ in case A (3.0 h-’ for case B), model- ling a chemostat experiment similar to the previous PCM analysis. The elapsed time between D shifts are as fol- lows: 30 h for D = 0.1 h-’, 20 h for D = 0.2-0.9 h-l, and 10 h for D = 1.0-3.0 h-’. Equations comprising the BCM are again solved numerically using the dynamic simulator computer package MIMIC. l5 BCM Simulations-Case A Case A simulates microbe 1 growing faster than mi- crobe 2, both in suspension and in a biofilm but microbe 2 having a l O X greater deposition rate. Deposition is modelled here as microbe transport to plus attachment at the reactor surface: therefore, a higher deposition rate for one species may arise from that species’ greater ability to produce either extracellular polymers or “holdfast” structures. Steady-state effluent substrate, suspended cell concen- trations (Cl and C2), biofilm composition (M andf,), and apparent yield values predicted from the BCM for case A conditions are given in Figures 6 and 7. Microbe 1 is predicted to persist in the reactor until D = 6.0 h-I (residence time is 0.167 h or 10 min), characteristic of chemostat biofilm formation as illus- trated previously for pure cultures. Not unexpectedly, microbe 1 dominates the suspended culture, although the BCM also predicts microbe 2 to remain in the reactor un- til D = 6.0 h-l but at very low concentrations (C, 5 3.0 mgJL). Predicted microbe 1 biofilm concentrations indi- cate the higher microbe 1 growth rate more than compen- sates for the 10 X greater deposition rate of microbe 2. At D = 1.2 h-l, microbe 1 comprises more than 90% of the Figure 6. (a) Predictions of BCM for case A conditions (see Table 11) for steady-state effluent concentra- tions of both microbes 1 and 2 plus limiting substrate. (b) Apparent yield values Y, calculated using errone- ous eq. (21). FRACTIONAL COMPOSITION OF BlOFlLM EQUAL TO MICROBE 1 DILUTION RATE , D ( I / h ) Figure 7. ( f l ) under case A conditions as a function of time elapsed after a dilution rate shiftup. The BCM predictions for total biofilm concentration ( M ) and fraction of microbe 1 in biofilm 954 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 26, AUGUST 1984 biofilm. Apparent yield values [Fig. 6(a)] vary during D shifts, due to changes in culture composition and the washout or dilution effect at D = 0.4 h-l which is muted by increasing biofilm formation. At D > P I , apparent yield values equal the true stoichiometry for microbe 1 due to its predominance in the biofilm, the origin of all suspended biomass. BCM Simulations-Case B Case B simulates identical conditions to case A, except the deposition rate of microbe 2 is set 1000 X higher than that of microbe 1. Steady-state effluent substrate concen- trations, suspended microbe concentrations (C, and C,), biofilm composition ( M andfl), and apparent yield val- ues predicted by the BCM as a function of D are given in Figures 8 and 9. Figure 8(a) shows that both microorgan- isms again persist in the reactor until a D of 3.0 h-' (mean residence time is 0.33 h or 20 min) due to biofilm formation but, unlike case A, here microbe 2, the slowest growing microorganism, predominates when D > 0.3 h-l. Although C1 is predicted to persist throughout the simulated experiment, C1 concentrations after D = 0.3 h-' never exceed 30 mg,/L. Given the advantage of a much higher deposition rate, microbe 2 dominates the biofilm, not allowing microbe 1 to establish and take ad- vantage of its higher growth rate. Transient changes in microbe 1 versus microbe 2 con- centrations predicted after a shiftup from D = 0.2 -+ 0.3 h-l (Fig. 10) further illustrate the dominance of microbe B C M : CASE B , MICROBE CONCN., 200 C1 EFFLUENT or Cp 50r 2.0 2.5 3.0 1.0 1.5 0.5 0 1 I 1 I I - APPARENT , \ YIELD, Y 0.2 - (mg. lmg3 * b. 1 I I I I 0 0.5 1 .o 1.5 2.0 2 5 3.0 DILUTION RATE , D ( l l h ) Figure 8. (a) Predictions of BCM for case B conditions (see Table 11) for steady-state effluent concentra- tions of both microbes 1 and 2 plus limiting substrate; (b) apparent yield values (Yo) calculated using erro- neous eq. (21). DILUTION RATE D ( l / h ) The BCM predictions for total biofilm concentration ( M ) and fraction of microbe 1 in biofilm Figure 9. ( f l ) under case B conditions as a function of time elapsed after a dilution rate shiftup. BRYERS: BlOFlLM FORMATION AND CHEMOSTAT DYNAMICS 955 1 - o ) indicalu direction of increasing time SUSPENDED YICWOBE CWCM Time tncrrrnrnt between computer ‘dots’ (-) eguals t h CI ’00 (mgJU 50 I I 1 SUSPENDED MICROBE CONCN , Cz (mg /I) M 10 30 10 50 60 m 80 90 02- BlOFllY 821 CELL CWCY m 82 ( “ J , l d 0 1 - values in parenthesis = fz 0 5 0 10 0 15 0 2 0 0 TIME ELAPSED AFTER DILUTION RATE SHIFT (H) Figure 10. (a) Transient response of suspended microbes 1 and 2 con- centrations and (b) biofilm B, cell concentrations during a dilution rate shift from D = 0.2 to 0.3 h-1. The arrow in (a) indicates the direction of increasing elapsed time. 2 over microbe 1 due to the higher microbe 2 biofilm con- centration. Apparent yield values never equal the true stoichiometry of either species except for conditions D = 0.5-0.8 h-l, reflecting the combined influence of both biofilm microorganisms on substrate utilization. Changes in the various process rates at different stages of biofilm development are shown in Figure 11 and illus- trate the dynamics of biofilm formation on chemostat operation. Model Limitations Two processes that are associated with biofilms-mass transfer and endogenous decay-were either implicitly or explicitly ignored in the simulations above. The impact of neglecting these fundamental processes on the above results is not trivial and warrants some discussion. Under the simulation conditions above, internal mass transfer effects, although incorporated in the models, were tacitly ignored. External mass transfer resistances were explicitly ignored for the well mixed fermenters un- der consideration. However, in certain situations (e.g., plug flow reactors operated at laminar flow, slow moving or quiescent aquatic systems), external mass transfer could be significant. Under biofilm parameters (e.g., L, p, $, D,, K,) different from those used here, the modified Thiele modulus $p could be such that the effectiveness factor 7 << 1.0. What impact would either a finite mass transfer resis- tance (external or internal) or a significant endogeneous decay rate have on the results above? Several mechanisms could, alone or in combination, control the overall biofilm substrate removal rate; they are: 1) substrate mass transport to the biofilm, 2) substrate mass transport within the biofilm, and 3) simultaneous biological reac- tion. Substrate mass transport within the biofilm has been traditionally modelled with molecular diffusion only, but recent result^'^ indicate convective transport within a biofilm can occur; however, such a novel trans- port mechanism will not be considered in this discussion. Rather, the effects of finite mass transfer will be qualita- tively discussed for pure and mixed culture cases. For pure culture situations, finite internal or external mass transfer resistances would effectively reduce the overall substrate removal rate of the biofilm at a certain substrate concentration. This would, in turn, reduce the biofilm development rate and the portion of the sus- pended biomass in the chemostat that originates as biofilm. Generally speaking, external mass transfer resis- tances would reduce the deviation from ideal chemostat theory created by the biofilm’s presence but would also I F(S*-S) = 296 mgslh 1 42 D = O 2 I l h D z 0.6 l l h D = 1.5 l l h Fignre 11. Process dynamics predicted by BCM at three different stages of biofilm formation under case B simulation. Unless otherwise annotated, all numerical values represent biomass production rates and have units of mgJh. Note that at D = 1.5 h-1, the biofilm is constant at M = 0.5 mgx/cm2 and biofilm growth rate terms for microbes 1 and 2 equal their respective biofilm removal rates. 956 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 26, AUGUST 1984 reduce the maximum overall substrate removal rate. Spe- cifically, for first-order intrinsic biological reactions (i.e., S << Ks) , external mass transfer does not change the ap- parent order of the overall substrate removal rate since both transport and reaction are first-order processes; only the apparent rate constant is changed. For zero-or- der kinetics (i.e., K , << S), the observed rate is not influ- enced by external mass transfer. Numerous works exist describing the effects of internal mass transfer on biofilm substrate removal rates.6 For the pure culture case, where microorganisms are uni- formly distributed throughout the biofilm, internal mass transfer effectively reduces the amount of substrate that can be removed by the biofilm, decreasing the biofilm production rate, and thus the amount of biofilm en- trained into the liquid. As with external mass transfer, the general impact of internal mass transfer is to reduce the deviation caused by biofilms from ideal chemostat performance. Note that external mass transfer resis- tances are subject to change by engineering factors (e.g., fluid velocity) while internal mass transfer is a function of the physical and biological properties of the biofilm. Little is known about the effects of mass transfer on mixed culture biofilms. For example, where carbon re- moval and nitrification are combined in a wastewater treatment fixed-film reactor, heterotrophic bacteria ox- idizing organic carbon grow at markedly higher rates than the autotrophic bacteria (Nitrosomonas and Nitro- bacter spp.) oxidizing NH4f to NO; and then to NOT. Finite mass transfer resistances, predominantly internal, could foster a situation, as illustrated in Figure 12, where local bacterial turnover rates differ dramatically between species.20g21 If the total biofilm density remains constant during growth, then the different microbial turnover rates would create spatial profiles of each group in the biofilm. In such cases, the net biofilm development rate is an integral value of the species local net biomass pro- duction rates. Biomass removal from the biofilm would be dominated by the faster growing organism that is most likely inhabiting the upper layers of the biofilm. The model derived in this article does not pretend such fraction of Total Biofiim Density, f . 1 1 organics 1 I +-,DEPTH -4 Figure 12. Hypothetical mixed culture biofilm development under the influence of internal mass transfer resistances where the growth rates of the individual microbe groups differ markedly. Illustrated is a hypo- thetical situation of heterotrophs (HET) oxidizing organics and auto- trophs (Nitrosomonas = NSM and Nitrobacter spp. = NBC) oxidizing NH: and NO;, respectively. sophistication, and for the purposes of this article such a complex model is unnecessary. CONCLUDING REMARKS Dynamic models developed here extend previous steady-state, constant biofilm models by simulating not only the extension of washout brought about by biofilm formation, but also variable yield trends more accurately. These models are simple material balances and can be easily modified to simulate various mixed culture interac- tions (e.g., competition, mutualism, commensalism, and predation), different suspended growth dependences (e.g., substrate or product inhibition), and various biofilm pro- cesses (internal mass transfer resistance and endogenous decay). Implications of the above analysis of biofilm formation in a chemostat are the following: 1) Biofilm formation will bias not only values as esti- mated from wash-out experiments but also can, if not considered, contribute to erroneous estimates of stoi- chiometry. Efforts to either minimize biofilm formation or, during an experiment, measure biofilm formation for use in appropriate material balances are urged. At least, an estimate of the maximum biofilm amount present at the end of an experiment would prove invaluable, as shown here, for interpreting chemostat data. 2) Estimates of stoichiometry in either pure or mixed cultures, using eq. (21), Y, = C/(So - S) , are wrong if biofilms occur. This equation ignores that part of the substrate used in biofilm growth, thus underestimating the true stoichiometry. 3) Effluent suspended biomass in a chemostat experi- encing biofilm formation arises due to suspended growth and biofilm removal precesses. As the dilution rate ap- proaches and exceeds f i , that portion of the suspended biomass due to suspended growth decreases. Although well past fi for washout, suspended biomass from the biofilm can actually utilize substrate at a significant rate. Note the tacit problem implied above with regard to data comparison between experiments or different sys- tems. Biofilm removal rates are highly dependent upon prevailing shear stresses. Consequently, two identical cultures, grown at identical nutrient conditions but with slightly different hydrodynamics (i.e., impeller speed, number, and location, number of baffles, etc.), could produce different effluent concentrations. 4) Decreasing apparent yield values with decreasing growth rate (or D) may not be due to so-called mainte- nance requirements but can, as shown here, be attributed to biofilm formation. 5) Successive washout of different members of a mixed population will be biased under conditions with biofilm formation. Depending on a cells ability to remain at a surface and attach, a higher growth rate is not sufficient to insure dominance of one species over another. 6) Model predictions suggest biofilms can be metaboli- cally more active (based upon total substrate uptake) BRYERS: BlOFlLM FORMATION AND CHEMOSTAT DYNAMICS 957 than suspended. Yet, until recently,22 microbial activity in most natural aquatic environments has been assessed by sampling free floating microorganisms, rather than ei- ther sessile or biofilm entrapped cells. Neglecting adher- ent biomass may underestimate the capacity of a water system to assimilate a particular pollutant load. References 1. D. H. Larsen and R. L. Dimmick, J. Bacteriol., 88, 1380 (1964). 2. R. I. Munson and B. A. Bridges, J. Gen. Microbiol., 37, 411 3. C. E. Zobell, J. Bacteriol., 46, 39 (1943). 4. H. H. Topiwala and G. Hamer, Biotechnol. Bioeng., 13, 919 5. T. Wilkinson and G. Hamer, Biotechnol. Bioeng., 16,251 (1974). 6. C. P. L. Grady, “Modeling of Biological Fixed Films-A State of the Art Review,” Proceedings of the First International Conference on Fixed Film Biological Processes, Kings Island, OH, 1982. (1964). (1971). 7. W. G. Characklis, Biotechnol. Bioeng., 23, 1923 (1981). 8. 1. D. Bryers and W. G. Characklis, Biotechnol. Bioeng., 24, 2451 9. M. G. Trulear and W. G. Characklis, J. Water Potlut. Control ( 1 982). Fed., 54, 1288 (1982). 10. W. G. Characklis and K. E. Cooksey, Adv. Appl. Microbiol., 29, 93 (1983). 11. B. C. Baltzis and A. G. Fredrickson, Biotechnol. Bioeng., 25,2419 (1983). 12. M. G. Trulear, “Cellular Reproduction and Extracellular Polymer Formation in the Development of Biofilms,” Ph.D. dissertation, Montana State University, Bozeman, MT, 1983. 13. W. H. Pitcher, Catal. Rev.-Sci. Eng., 12, 37 (1975). 14. G. Molin, Eur. J. Appl. Microbiol. Biotechnol., 13, 102 (1981). 15. “MIMIC-A digital simulation language,” Control Data Corp., Sunnyvale, CA, Ref. Manual No. 44610400, 1968. 16. D. W. Tempest and 0. Neijssel, Proceedings of the Third Interna- tional Symposium on Microbiology and Growth on C, Compounds, 17. J. D. Bryers, “Dynamicsof Early Biofilm Formation in aTurbulent Flow System,” Ph.D. dissertation, W. M. Rice University, Hous- ton, TX, 1980. 18. N. Zelver, “Biofilm Development and Associated Energy Losses in Water Conduits,” M.S. thesis, W. M. Rice University, Houston, TX, 1979. August, 12-16, 1980. 19. H. Siegrist and W. Gujer, unpublished. 20. 3. C. Kissel, P. L. McCarty, and R. L. Street, J . Environ. Eng., 110 (2), 393 (1984). 21. W. Gujer, 0. Wanner, and J. D. Bryers, Swiss Federal Institute of Water Research and Water Pollution Control (EAWAG), personal communication. 23. G. G. Geesey, R. Mutch, J. W. Costerton, and R. Green, Limnol. Oceanogr., 23, 1214 (1978). 958 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 26, AUGUST 1984