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Mass transfer mechanisms in a heterotrophic biofilm
Water Res. Vol. 19, No. II, pp. 1369-1378. 1985 Printed in Great Britain. All fights reserved
0043-135,4:85 $3.00+0.00 Copyright ~ 1985 Pergamon Press Ltd
MASS TRANSFER MECHANISMS IN A HETEROTROPHIC BIOFILM H. SIEGRIST a n d W. GUJER Swiss Federal Institute for Water Resources and Water Pollution Control (EAWAG), 8600 Diibendorf, Switzerland
(Received July 1984) Al~'tract--The diffusion coefficients of three different chemical species in naturally grown, heterotrophic biofilms have been measured and a simple model of mass transfer in a biofilm matrix is developed. The mechanical structure of the biofilm matrix reduces the molecular diffusion to about 50-80~o of the value in pure water. Depending on the roughness of the biofilm surface and the flow conditions eddy diffusion increased the mass transfer into the biofilm near the surface. The influence of the diffusion potential and the donnan potential on ions have been evaluated by comparing the diffusion coefficients of a positively and a negatively charged ion and a neutral molecule in experiments with different background electrolyte concentrations. Mass transfer effects by electrostatic forces are negligible at the ionic strength of waste water and tap water.
Key words--biofilm, mass transfer, diffusion coefficient, diffusion potential, donnan potential, advection, external mass transfer, eddy diffusion
NOMENCLATURE A = cross-sectional area of the hole in the plastic piece supporting the membrane (Fig. 1) (ML -3) C~(t) = concentration in the small compartment of the experimental reactor at time t (Fig. 3) (ML -~) Cl(0) = Ct at the beginning of an experiment (ML -3) C~(tr) = C~ at the end of an experiment (ML -3) Cl(O) + Cl(te) (ML -3) C~,v,r~ concentration in the large compartment of the experimental reactor, practically independent of time (ML -3) D~=diffusion coefficient of the freely movable particle i (L-'T-i) D~' = diffusion coefficient of the ion i influenced by the diffusion potential [see equation (12) and Table I, col. I0] (L-'T -I) D o = diffusion coefficient in pure water (L2T -I) D m = diffusion coefficient of the membrane (L2T - ~) DB~ = apparent diffusion coefficient over the entire biofilm (L-T -I) D~io= average diffusion coefficient in the biofilm matrix close to the membrane (no eddy diffusion effects, see ddifr) (L2T -t) d~, at., = thickness of the effective laminar layer on both sides of the membrane system (Fig. 4) (L) dBio = average thickness of the biofilm (Fig. 2) (L) d, aay = part of the biofilm in which eddy diffusion predominates (L) drier=part of the biofilm in which molecular diffusion predominates (L) d m = thickness of the membrane (L) dw~t = water film thickness with the same mass transfer resistance as the corresponding biofilm [equation (6)1 (L) 1 = ~ Z Z,c~; ionic strength (ML -3) J = specific flux through the membrane system (ML--'T -I)
kt, = mass transfer coefficient for the component i of a certain layer n (LT -I) K~= mass transfer coefficient for a whole system of different effective layers for the component i (LT -I) KI = overall mass transfer coefficient for the membrane system with biofilm (LT -I) K2 = overall mass transfer coefficient for the membrahe system without biofilm (LT -~) ksio = Ds~o/de~; mass transfer coefficient for the biofilm (LT -l) V = volume of the small cell (Fig. 3) (L 3) z~= charge of the ion i gdry wt. P = 100"gwet w - - -~- -, average density of the biofilm ( ~ TS).
LNTRODUCTION T h e substrate u p t a k e rate o f m o s t biofilm systems is limited by mass transfer. Therefore, it is i m p o r t a n t to characterize the mass transfer m e c h a n i s m s a n d diffusion coefficients in the biological matrix. M o s t biofilm models use a fixed diffusion coefficient over the entire biofilm depth. Nevertheless, J a n s e n a n d Kristensen (1980) report diffusion coefficients o f m o r e t h a n 100K of the value in pure water. This suggests t h a t processes o t h e r t h a n molecular diffusion influence mass transfer. H a r r e m o ~ s (1978) a n d Riemer (1977) o b t a i n e d different ratios for the diffusion coefficients o f m e t h a n o l a n d nitrate in a denitrifying biofilm as c o m p a r e d to values in pure water. It appears, therefore, that ions are influenced by electrostatic forces t h a t m a y decrease or increase their molecular diffusion.
1369
[370
H. SmoaJs-r and W. GUJER
~
/ E
~ ))"r'~"~ !
~
Membrane (5art0r=us membrane filter with printed btack network) stuck over a central h01e in a plastic support which is mounted with a d0ubte sidedtape on the
disc of a rotat,og
:~~
biotogia( contactor. "----Waterlevel
""
~
Fig. 1. Sketch o f the rotating biological contactor used to grow the biofilm directly on membranes
t~
,@Filament
,//
f
f
/ / /.~ Water / /
';
f;,
/ ; / - F e r r i c oxid, //" particles
o, l dBio
the biofilm
Fig. 2. Schematic view of the biofilm. Ferric oxide particles are necessary to mark the surface of the biofilm.
-
Br0mide eteetr0de
Reference electrode Biofiim Membrane Ptastic support with central hote Smal compartment (V :75mr) Large compartment (V:120Oral)
Fig. 3. Two-compartment reactor to observe mass transfer.
with activated sludge and fed with either a synthetic waste water (20 mg l-i peptone and 13 mg 1- I meat extract, Exp. BI-B7) or diluted primary effluent ( ~ 1 0 0 m g C O D I -t, Exp. A1 + A 2 ) . The dilution rate was 2 h -t, the rotational speed 120 rpm and the temperature 20°C. After 3-6 days the membranes with the plastic support were taken out of the reactor and the biofiim thickness was measured with the microscope. The biofilm water interface was marked with small particles o f ferric oxide (Fig. 2). The bottom of the biofilm was visible to a thickness o f 500/~m by ~the printed black network on the membrane. The difference in thickness was read on the microscope micrometer. To estimate the real biofilm thickness, the micrometer reading was multiplied with the quotient of the refractive index o f water and air (n,,=/n=i r = 1.34).
Mass tramfer experiments
EXPEltliVlEN'rAL SYSTEM ~ £V.4gLUATION OF THE M E A S U l t ~
Biofilm growth Heterotrophic biofilms were grown directly on membranes which were mounted over a cemrai hole in a piece o f plastic. A rotating biological contactor =erred as a laboratory reactor (Fig. I). The reactor has been inoculated
Mass transfer was observed in a two-ceil system for the three, chemical species bromide ion, sodium ion and ,glucose (Fig. 3). At t = O, a large pulse inp~,t o f the diffusing species was injected into the larger compartment o f the diffurdon cell. Concemration within the large compartment stayed euentially constant throughout the experiment (experimental conditions, see Table I). I n ~ e small ceil, t h ¢ ~
of bromide ion concentration with time was observed with a bromide electrode. The ¢onzerttration of sodium ion and glucose were measured in samples taken at the beginning
Table 1. E~porinumtal condition= and me~ured valueJ Col.
1
2
3
NaBr
Gluc
KNO3
Ct(0)
=0
C~=
Exp.
C2 10-3 M
= 10-2 M
C= = l0 -3 M
[ [6] 10-3 M
BI B2 B3 114 B5 B6
10.0 10.0 10.0 1.0 1.0 20.0
2.0 2.0 2.0 4.0 4.0 4.0
200 200 0 2.0 !.0 5.0
B7
4.0
4.0
0
BI-B7 A1 A2 AI +A2
1.0 1.0
4.0 4.0
0 2.0
4
5
6
C~
t
7
8
9
Measured mass transfer ~ient
11
Corrected ratio
ratio
§
front column S
(~/0)
f~
205 205 5.0 2.5 1.5 15.5
0.0~ 0.024 1.00 0.20 0.33 0.68
2.0 1.4 2.0 2.5 2.2 2.3
0.5 0.6 s 0.5 t 0.5 0.6 0.7
1:0.580:0.343 1:0.603:0.420 1:0.938:0.473 | :0.363 1:0.832:0.414 1:0.864:0.508
5 5 4 1 1 6
1:0~38:0.33 t:0.60:0.40 1:0.94:0.45 1: - - :0.36 1:0.83:0.41 1:0.86:0.48
0.73 0.75 0.97 -0.91 0.92
2
1.00
1,9
0.8
1: I. 120:0.412
3
I : I. 12:0.40
1.06
2.6 2.6
0.6 0.5 0.5 0.5
l: 1.003:0.363 1:0.837:0.357
1 I
1: 1.00:0.36 1:0.84:0.35
1.00 0.91
!.00 0.20
(~) D~a,.'D~,~,'Dc.,~. =~
¶
I
0.5 2.5
D~=,:D~=,:D~
10
Dr~,am,~
tp = Density of the biofilm (.~rs). ok, ~f = ~ = Reduction factor. §Diffusion of the ions decreau~ by the activity coeffm/ent aad the ionic =trength (SieIrist, 1985).
,~ D ~ ' D ~ ~ N = ~ = ~'D*Nalb + D " " Mass transfer coefficient ratios are used be~mt¢ difftulion ¢odkiemu ~ with increasingbiofdm thickn¢~. BI-B7--biofilm grown with peptone and meat extract; AI + A2~bio~lm grown with primary effluent. ¢~
M a s s transfer m e c h a n i s m s in a biofilm
1371
Table 2. Effect of the diffusion potential (Fig. 17) Col.
12
13
D ~r~o
DNaB¢o
D ~k.=../D~
D ~.=,,
D~.~
D ~,b./DN.,
D~o Values in pure water
Dn°sq~/ Ds°~.o
D ~ o ~ / Dr~.~,,
Values from col. 12+ 13
DN°Ik~ Values from cot, 10 + II (Table 1)
DN~
Exp.
Dn,aR~ Values from col, l0 + I I (Table 1)
Values in pure water
Values from col, 15 + 16
1.06 1.04 0.81 -0.86 0.84 0.74
0.79 0.80 0.97 -0.92 0.93 1,06
0.78 0.85
1.00 0.92
B[ B2 B3 B4 B5 B6 B7 BI-B7 AI A2 AI + A 2
1.36 1.33 1.03 -I. 10 1,08 0.95
0.78
1.00 1.10
0.78
14
15
and at the end o f each experiment. S o d i u m was a n a l y s e d by a t o m i c a b s o r p t i o n a n d the glucose by a dissolved o r g a n i c c a r b o n analyser. Mass transfer t h r o u g h the m e m b r a n e w a s observed b o t h with and w i t h o u t biofilm. The m a s s transfer coefficient was c a l c u l a t e d based on the c h a n g e o f the c o n c e n t r a t i o n with time, the v o l u m e o f the small cell (V),
16
1.22
1.22
17
0.96 0.98 I. 18 -1.12 1.14 1.29 1.22 1.12
the area o f the hole in the s u p p o r t of the m e m b r a n e (A) a n d the c o n c e n t r a t i o n difference between the large a n d the s m a l l cell [according to e q u a t i o n (1)1.
vdC= dt = A "j = A "K(C 2 - C,).
(1)
Table 3. Effect of the donnan potential (Figs 18 and 19) Col.
Exp. BI
B2 B3 !t4 B5 B6 B7 BI-B7 AI A2
18
19
DN^nR~o DGn=csi.
DGI~
Values from col, 10 + 11 (Table 1)
D~.gro Values in pure water
--
20
DNtIk~ao/DN°BrO DGIa¢L,o/DGIu=o Values from from col. 18 + 19 i
-2.16 ---2.65
0.42 s
0.92 --
1.13
2.78 --
0.421
Col.
21
Exp.
Coefficient to consider the influence of the diffusion potential [from equation (12)] for* Br Na
1.18 -22
23
Corrected ratios from col. 10 + 21
DB,~o:Dn=~:DG~=~.:DN=e,m,
1.007 1.007
0.994 0.994
1:0.57:0.33 1:0.59:0.40
0.73 0.74
B3 B4 B5 B6 B7
1.28
0.82 0.96 0.93 0.87 0.82
1:0.60:0.35 I: - :0.35 1:0.72:0.38 1:0.64:0.41 I:0.72:0.31 I:0.65:0.36 1:0.64:0.28 1:0.77:0.34 1:0.70:0.31 I:0.66:0.35
. . 0.84 0.78 .
1.07 1.17 1.28
BI-B7 AI 1.28 0.82 A2 1.04 0.96 A I + A2 BI-B7 and Al + A 2
25
Dl,~
BI B2
1.04
24
. 0.87
. .
. .
26
DN,,.,
D~.~
27
DN,,~./DN~
Dn.~b o Values from cot. 22 + 23
D~,~JDN, tk.o Values from col. 13 + 24
Values from col. 22 + 23
DN=a,tJDN, ~ Values from col. 16 + 26
1.38 1.35
1.07 1.04
0.79 0.80
0.96 0.97
0.86 0.82
1.05 1.00
0.89
1,08
. . 1.19 1.28 . . 1.15
. .
. .
. . 0.93 I.O0 . . 0.90
--
+0.07_.+0.04 Literature values
1:0.64:0.33
*Ci in equation (12) is assumed to be (C a+ C~)/2. This corresponds with the assumption that within the biofilm the effecUve concentration C~ is equal to the average concentration in the two reactor compartments.
tDn.~,, = 2 D ~ " DN.~o values from col. 22.
DBrLo+ DN.~
1372
H. SIEGRISTand W. GUJER =
~"
=~
Exp.
=,.
~
= ...a
Averaae ! ~".':"":".': ~I ' D ~• o ' , DM a.... t n u s i~o n coefflc ent I/..-.'..: :
dl = 0
for
I
I
I
I
I I
i
~E u
a) with biofdm
D~a .
I0 , IO.
0 60 064
l~ 0 ~*0 033 -
~:
q~,o3 : 2. Io" M 4-
b) without
08r •
CNa8¢ : 5" 10"3 M C~ : I0 -2 M
~o
dBio > 100 ym
*astewater
Exp (table l, ¢o(.10) Theory ([>>CNaBr)
8-
Thickness i ~:.-":!' ".": i.:, of the kl~l :d~iio' dM tayer I 1:'. ?."
B2
Biofllm grown on synthettc I0 I I
• SOdKlm ion - Brom*de ion
.'~.
biofilm
-=
Fig. 4. Schematic view of the membrane system.
For Cz>>C~we obtain Kg
0 ~J
V Q(t)-Q(O)
(2) A-t C , - C l=,=.~ The mass transfer coefficientsfor sodium ion and glucose were obtained from equation (2). Mass transfer coefficients for bromide ion were computed with a leasts squares iteration program, which employed approx. 10 bromide measurements for each experiment. An overall mass transfer coefficient can be evaluated from the average diffusion coefficient and the thickness of each layer of the exlmdmental system (Fig. 4) by equation (3). I
d,
I
From the difference of the reciprocal mass transfer coefficients of the membrane system with (K l) and without biofilm (K2), one gets the inverse mass transfer coefficient of the biofilm, kaio: 1
l
I
daio
(4)
K l K2 ke,o /)nio The thickness of the apparent laminar subtayer at the side of the biofilm (d0 decreases with increasing mulllmess of tl~ biofilm surface. If the laminar sublayer disap~ars completdy (d~, > 100/am), the turbulent water layer reaches the surface of the biofilm, resulting in the following change of equation (4), ]
1
d~i o
d2
Bmfitm thickness
[pro]
Fig. 5. Results of an experiment with a h ~ back~ound electrolyte concentration (I>>C~). Since ionic strength is much higher than the observed salt coacentration (NaBr), electrostatic effects are negligible and the ratios of the diffusion coefficients of the different components are equal to the ratios in pure water. Experiments were made at different KNO 3- a n d NaBr-concentrations and different KNO3/NaBrratios because mass transfer of ions is influenced by the concentration of the background electrolyte (potassium nitrate, KNO3) and the observed salt (sodium bromide, NaBr). Figures 5-8 show the difference of the reciprocal values of the mass transfer coefficient with and without biofilm ( 1 / K I - I/K2) vs the m e a s u r e d biofilm thickness. Figures 5 and 6 are the results of Exp. B3 10
(5)
KI K2 D,,io DO From experimental evaluations [observing the overall mass transfer coefficient(K2) with increasing stirring rate] and order of magnitude estimations the laminar sublayer thickness at the side of the large cell was estimated at less than 30/~m. Consequently, the influence of this phenomenon upon the biofilm resistance is at most 15*, therefore equation (4) was used for data evaluation.
dBm
8.
Biofilm grown on synthetic wastewater l I l, ] OBr : Ot~
Exp.(hd~e I. co1.10) l"ht~y (I:C~)
1.0 :
tO :
t
: 06|=: 0.9/* : 0.45 1.0 : 0.43
C-,Naef= 5.10 -3 M IE
CC~= 10"2M
u 6- CKN03= 0 *0
RESULTS AND DISCUSSION
Mechanical resistance of the biofilm matrix Prior to this work, diffusion coefficients have been evaluated using only particulate biomass filtered onto a membrane (Willlamson and McCarty, 1976; Matson and Characklis, 1976; Pipes, 1974; Onuma. and Omura, 1982). Williamson and McCarty (1976) obtained diffusion coeff~ients of about 80% of tha values in pure water. H o w e v e r , filtered,biomass does not have the same structure as a grown biofilm. The mass transfer effect of the rough surface of the grown biofilms may be lost.
Cy
--
o
6oo Biofilm thickness
dei e
[pml
Fig. 6. Results o f an experiment without background electrolyte. The only eharIed ~ ~ the ~
the bromide ion. Due to the law of ~ , the mass transfer coefacients are equal for both ions. With decreasing background electrolytethe diffusion~ t s of the ions approach the values of the salt diffusion coe~cient.
Mass transfer mechanisms in a biofilm
B7
Exp. B 1 -
Exp. At * A2
B~ofitm grown on synthetic wastewater 10
=
I
=
~..c
ion
. . . . Mass
+O 7,
B r omm
//"
transfer model
/<
./
/
I
i
/
/.~/
/• /~"
/'2
=
.
i
I/"
/
I •" 0.70:0.31 " /
theory 1 : 0 . 6 ~ ' . 0 . 3 3
-
I
m
.
~ ~ ~ ' ~- 2 ~
=
I
/
..<.
4-
Exp.
/~
" //
/
/
" ~ / ' ~
i
OBr : ON• : DGtuc
~ . / //"/
i" Sodium ion
6- "
I0
A
•
I " Glucose
~'
8=of•Ira grown with primary effluent
=
DBt:DNa : DGIuc . " I Ezp(taDle3,mt22} I : 0 8 5 : 0 3 6 o ] Theory (no electro0.64:033 o~ static effects) :
1373
4
.=-'"
""
t
,,..~Vr" 0
'
0
///~
(~,o--8o- 6oo,m)
i
i
i
i
1(20 2O0 300 Biofilm thickness dBio
i
4O0
5OO
o
6OO
[iJml
,do
360
26o
Biofitm thidmess
5bo
dBio
600
[Ijm]
Fig. 8. Summary of the results of the experiments AI and A2. To compare the values of all experiments we have taken into account the effects of diffusion potential [see equation (I 2)], ionic strength and activity coefficient. The corrected results agree with fictitious values that would be measured if all components were freely movable. The ratios of the diffusion coefficients of the different components are equal to the ratios of the freely movable components in pure water. Fig. 7. Summary of the experiments BI-B7.
two experiments (Fig. 5: CKNO~>>CN.B. Fig. 6:
CKNo,= 0). In Figs 7 and 8 all the results of the experiments B I-B7, respectively, A1 and A2 are combined by considering the effects of diffusion potential, ionic strength and activity coefficient (see later). In Figs 9 and l0 the results from all 3 species and all experi-
ments are combined. The differences of the reciprocal values of the mass transfer coefficient in Figs 7 and 8 are multiplied by the corresponding diffusion coefficient of each component in pure water:
(, l)
d w , t = D ~ o KI,
Exp.
Exp. B1- B7 Biofi{m
~Jrown
600
on
A
=
synthetic wastewater = =
(6)
A2
A1 *
600
i
Ill
500"
'
Biofilm grown with primary effluent i
t
l
" -
1
= //
•
400-
g2,
.'.
Mass transfer
500"
///1~//I /
.= = ~ / /
m,i
.
Mass transfer m o d e .l ~- a/ . , / ' / I , ----E="400-
/. //
,,
- 300-
300-
.o~
///
,~
•
200-
,~/
~,~/ /. /
eg
.
I00- 3 ~ " / d 8 ~ ° :
0-80
pm
100/
•
e II
" ],fiden in,rval .
.
of
the linear r~ression of aU v~es
/
/
o
0
.
100 8iofiim
.
200
.
thickness
.
300 dBi o
0 r
.
400
500
[ml
600
o
360 8iofilm thickness
dBio
6o0 [jlm]
Fig. lO. Summary of the results of the experiments A I and A2. To combine the values of all three components, one has to multiply the values of Fig. 7 with the diffusion coefficients in pure water of each component, dw= is a fictitious water film thickness that would yield the same mass transfer coefficient as the observed biofilm. With increasing biofilm thickness, the average diffusion coefficient in the biofilm matrix increases too due to eddy diffusion in the upper part of the biofilm.
Fig. 9. Summary of the results of the experiments B I - B 7 .
t374
H. SIEGRISTand W. GUJER
1.5 I
B,ofdm 9r0waOn
.4°°t
~, , Y
d primary effluent I
0
100
I
I
I
I
t
200
300
400
500
600
~,
|
Biofilm thickness dora [/jrn]
o i]/ /
0
Fig. 11. Mean apparent diffusion coefficient over the entire biofilm in function of the biofilm thickness. (A) As pr~lict~l by transforming equation (4) D ~ = d s ~ / ( t / K l - t/K2); (B) as predicted by transforming equation (5) D~o= dmo/(I/Kl - IlK2 + dtlDo).
/
,Ldaiff-~ ,
100
,
i
,
200 300
,
,.
400 500
Biofdm thickness d0io [~rn]
Fig. 13. Mass transfer modell: thickness of the part of biofllm that is dominated by eddydiffusion (dm~), respectively, molecular diffusion a~) in function of the thickness of the biofilm (dmo= d~y + da~r).
The calculated effective water film thickness has the same mass transfer coefficient as the corresponding biofilm (Do/dw,t = D~/dmo). Figures 9 and 10 relate interpretation of this phenomenon is, that the lamithe calculated value (d,=) to the measured biofilm nar sublayer becomes ineffective as the surface roughthickness (d~o). ness of the biofilm protrudes into the turbulent flow If the average diffusion coefficient (Da~o) in the region. Apparently the small external mass transfer biofilm were constant, one would obtain a linear co¢ffacient for thin biofilms caused by the laminar relation between D~t and dmo. ExperimentalI results in water layer (d0 becomes negative with increasing • , Figs 9 and 10 indicate, however, the average diffusmn biofilm thickness. coefficient in the biofilm matrix (Da~) increases with increasing biofilm thickness. The observed value of Mass transfer model Dmo varies from a tow 40% to a high 140% of the Instead of assuming a negative external mass t t W corresponding value in pure water. This apparent fer coefficient, one may assume a fraction of the increase of the diffusion coefficient can be explained biofilm matrix close to the biofiim surface, where by eddy diffusion in the biofilm matrix close to the mass transfer is dominated by eddy diffusion. The biofilm surface (see Fig. 11). The irregularities and concentration gradient through this biofilm layer is filaments of the biofilm surface penetrate through the practically zero because the eddy diffusivity is much laminar waterfilm layer. Therefore the turbulent zone higher than molecular diffusivity (Fig. 12). reaches the surface of the biofilm and produces eddy The thicknes of the biofilm layer that is influenced diffusion in the biofilm matrix near to the surface. by eddy diffusion (a~r) depends on the surface This effect becomes visible by the moving of the morphology roughness of the biofilm and fluid flow filaments in the current. Picologlou et aL (1980) and conditions above the biofflrn surface. While the~ two Characklis (1981) showed in their experiments that parameters are very important, the following at~roxthe friction factor of a circular tube increases strongly imations are only valid for the system described in if the wall growth reaches a certain thickness. Their this paper. If we assume a constant diff~u!ion coefficient in the part of the biofilm layer whe,re molecular diffusion predominates (d,~f) we can write, 1 I based .on the above data, for the biofilm grown on synthetic substrates, the following (Fig. 13): ~srge to tl~ sinai ¢141
a,aay = 0.6 (d~o - 100/~m) L~iofilm
Mass transfer I
[= I: .~
LIRIImr
~
_~ ~
l l~l~
deddy ddiff T d~ 'a~2" Fig. 12. Simple model of mass transfer through the membrane and biofitm system.
(7)
and ddi~, = 100/zm+ 0.4(dmo- 100/~m).
(8)
The molecular diffusion co¢ttlcient in the lower portions of the biofilm matrix is assumed al~i'ox 60°,/. of the value in pure water. With increasing bJofilrn thickness, the average apparent diffusion c ~ t ~ t would increa~ because of increasing importance of eddy diffusion in the upper part of the biofilm. For a biofilm grown on primary effluent we get similar
Mass transfer mechanisms in a biofilm
1375
Fig. 14. Scanning electron micrograph of the biofilm grown on synthetic waste water,
Fig. 15. Scanning electron micrograph of the biofilm grown with primary effluent.
results
significant relation between the mechanical resistance of the biofilm and biofilm density. Despite this, experimental results suggest the diffusion coefficient may slightly depend on biofilm density and is about 50-80% of the value in pure water for a biofilm density of about 2% TS. Biofilm density decreases slightly with increasing biofilm thickness. For Fig. 16 we used the average density of two or three measurements with different biofilm thickness, in each experiment. Biofilm density can be influenced by the following factors:
dd~er 0.4 (dBio -- 100/~m). =
(9)
The molecular diffusion coefficient in the biofilm matrix is about 50% of the value in pure water. The difference in the relative influence of eddy diffusion may be explained by looking at the structure of the two biofilms. A biofilm grown on synthetic wastewater has a more compact layer near the membrane and a light structure with filaments at the top of the biofilm. The light layer and the filaments can be removed by a water jet. The layer below can only be taken away with the finger. A biofilm grown with primary effluent has a more compact structure over the entire biofilm, there are only a few filaments at the top of the film. Because of these differences in the structure of the observed biofilms, eddy diffusion is more active in the former biofilm than in the latter (see Figs 14 and 15). Advection in the upper part of the biofilm has the following consequences for biofilms thicker than 100/a M: there exists no external mass transfer resistance, the concentration gradient of the substrate is smaller than for mass transfer by molecular diffusion only. All these effects increase the substrate uptake of the biofilm in the case of substrate limitation. Jansen and Kristensen (1980) estimate in a rotating drum system exceptionally high mass transfer coefficients which, in light of the above work, may likely be due to the contribution of eddy diffusion.
the the the the
fraction of exopolysaccharides in the biofilm, inorganic fraction, fraction of protozoa, worms and insects, types of microorganism that predominate.
Therefore it may be quite difficult to obtain a well defined relationship between diffusion resistance and biofilm density.
Mechanical resistance in relation to the molecular size of the chemical species As seen in Fig. 17, the relative magnitude of the diffusion coefficients of glucose, sodium and bromide
for experimenta/ resu/ts see tabl~ I, col 6 + ?
~ 1.0
I
l
o Biofilm grown with primary effluent
x
_~ o.'.
O'B,° Averoge diffusion c o e f h -
The mechanical resistance of the biofilm matrix-in relation to the biofilrn density The following considerations are valid only for the lower part of the biofilm in which only molecular diffusion is responsible for mass transfer. Unfortunately, the density differences between the different experiments are too small to obtain a
x Biofilm grown on synthetic waste water
in the blof drn mQtfix trent
t~
i I
o~ Density
I 2
~
[% rs]
close
fO the
rnernbrone {no eddy dlff )
Fig. 16. Reduction of the molecular diffusion coefficient in the biofilm in relation to the biofitm density.
1376
H. SIEGRISTand W. GUJER
r~
e~
~ 2.0
%
Dq = D,'Dj(I - :uzj)
for experimental results see tmNe 1.3, co17+22 T=
for biofilms
20 *C I
grown on synthetic waste water ( B I - B ? )
.I:Zl
"' 1.0 E
~
•~, 0 0
Dj
x Average values
o
f
1.0
~
o Average values for biofilms grown with primary effluent (AI + A2)
2.0
Diffusion in pure water Do [lO-Scrn 2 S"-1"1
Fig. 17. The average diffusion coctficient of glucose, sodium and bromide ion in relation to the values in pure water after considering the effects of diffusion potential [see equation (12)], ionic strength and alteration of the activity coefficient (Siegrist. 1985).
- -
:,/2j" D i
valid for ions with different charges. If there is a background electrolyte at a constant concentration in the system, the diffusion potential decreases with increasing concentration of the background electrolyte. Diffusion coefficients of the oppositely charged ions (i and j) in the system can be related to the quotient of the concentration of the observed ion and the ionic strength by the following equation (Siegrist, 1984).
D;/O,
= l + : ~ ( D J - O,). c_~ 2" D ..... ~, t
the pores of the biofilm may have the same physical size as the diameter of the chemical species, thus mechanical resistance for the larger particles would be higher than for the smaller ones, bioturbation (movement of protozoa and higher organisms) could increase the diffusion coefficient in the biofilm for all three observed species by the same amount. As seen from scanning electron micrographs (Figs 13 and 14) the size of the pores is much bigger than the size of the glucose molecule. An alteration of the diffusion coefficient due to bioturbation cannot be detected.
Z D;~'Ci
Z D,:~'Ci 2"1
The average diffusion coefficient does not change noticeably with ionic strength if the diffusion of the ion pair is of the same order of magnitude as that of the background electrolyte. In the above experiments, sodium bromide and potassium nitrate were used, which have about the same salt diffusion coefficients. Therefore, a linear relation between the gradient of D*/Di and the ratio of cJl (Fig. 18) is expected. As shown in Fig. 18, theoretical prediction and experimental results correspond quite well. For biofilm systems with an impermeable support at the back of the film, the following equation (Siegrist, 1985) can be written: D?/D, = 1 +
z~(Dj- D,)
(13)
flux of inert ions (background electrolyte) is zero.
Diffusion potential Molecular diffusion of neutral components is essentially not altered by effects other than the mechanical resistance of the biofilm matrix. However, the movement of ions is influenced by electrostatic forces. Consider a system with only two oppositely charged ions with different independent mobilities. Because of these different mobilities, one should obtain different fluxes for the ions along an equal concentration gradient. However, this is impossible since, due to the law of electronentrality, a diffusion potential would be formed, lowering the molecular diffusion of the quicker ion and increasing the diffusivity of the slower ion. One thus obtains for opposite ions the same diffusion coefficient called salt-diffusion Fq (Lakshminarayanaiah, 1969), where Du=D~*=D~=
(12)
background electrolyte at a constant concentration D..... *c= Z :~'C,
ion in the biofilm matrix are about the same as in pure water. This relationship could be affected by the following mechanisms:
(,l ! )
2.D,.Dj D, xDj
(10)
valid for ions with equal charge (no background electrolyte)
For wastewaters, the concentration of the observed ion is frequently less than 20% of the ionic strength, therefore the influence of the diffusion potential may generally be neglected. Only for a system with low background electrolyte concentrations, with large differences between the diffusion coefficients and bivalent ions, should the effect of the diffusion potential be taken into account.
Donnan potential If a solid matrix contains regularly dispersed, fixed, negatively or positively charged groups in em:ess, a donnan potential will be formed at the surface of the matrix (Hdferich, 1959). The donnan potential impedes the diffusion of ions with the same charge as the fixed groups and accelerates the penetration of ions with the opposite charge. A biofilm matrix contains an excess of fixed negatively charged groups---phosphate--and carboxytic acid-groups at the surface of microorganisms. How-
Mass transfer mechanisms in a biofilm kS
I
I
I
for ex#ertmenta/ results see table l+2, coL 5,14 + 17
I
i ..a
o Sodium ion
~o 1.0 _o~
o
~
05 - theo.r.e!!cal_J/
o
• I
~__-
premct,on
influenced by the diffusion potential
~'
•- -
o
[
o
0.2
I
0.4
l
2" ONiBi0" D~IrBio
•
I:;
0.6
to
0.8
ion
x Bromide
Ci Average concentration of the observed ion i [ Ionic strength D~'Bi~ Measured diffusion coefficient in the biofilm
c~
Oo
1377
2" DNao
DNIBrBi ° : D~N,1Bio + DBrBi o
ONeBro =
• DBro
DNao+DBr °
{-1
q/t
Fig. 18. Effect of ionic strength on ion diffusivities within a biofilm. Increasing ionic strength relative to the concentration of the observed ion, lowers the diffusion potential and decreases the influence of electrostatic forces on the molecular diffusion of the different ions. To eliminate the influence of the mechanical resistance of the biofilm matrix, the quotient D,~o/D,~* is standardized with the ratio
DNaBrmo/D,',iaBro.
ever, three factors speak against the formation of a donnan potential; Negatively charged groups are not uniformly dispersed in the biofilm matrix but are concentrated at the surface of the microorganism's membranes. An electrical double layer of about 5-10 nm thickness (depending on ionic strength) can neutralize the excess negative charge. In the pores between the microorganisms, where mass transfer occurs, the effect of the negatively charged groups is therefore negligible. Parallel to a donnan potential, an osmotic pressure gradient would be formed by penetration of water molecules into the matrix (the ionic strength in the matrix is higher than outside which results in swelling of the matrix). It is unlikely that the biofilm matrix could resist the osmotic pressure. Mobile prozozoa may destroy portions of the exopolysacchride matrix and produce big pores for mass transfer. Experimental results also lead to the conclusion that a possible donnan potential may be neglected. Salt diffusion in a system without background elec-
"7
I
for experimental results see tame 1.3, col I+20 t.5 I I x
z N t.O ~
x
...........
%
bromide
a - - 0~,g.
2.~.1:~
.....
,!0
The mechanical structure of the biofilm matrix of 1.8-2.6~ TS reduces the molecular diffusion to about 60-50~o of the value in pure water. Mass transfer effects by electrostatic forces between ions (diffusion, donnan potential) are negligible at the ionic strength of waste water and tap water. Only in experiments with a very low ionic strength and bivalent ions must the influence of the diffusion potential on mass transfer be considered.
T
for experimental results see tame 1+3, cot 4,25+27 o Sodium ion I I x Bromide ion
1.5
--
i o kC _ o o . . . . . . . . . o ~ x x
x>
/~ (~
no backgroundelectrolyte
~J0
CONCLUSIONS
x Sodium-
E)
9 ~,o.5
trolyte should be lowered by a donnan potential. In the experiments (Fig. 19), no effect is evident for concentrations higher than 5.10 -4 M. Diffusion of a positively charged ion must be accelerated ( ~ 50~) and, respectively, diffusion of the negatively charged ion is reduced ( ~ 30~), if the concentration of fixed, negatively charged groups is equal to the ionic strength in a system with background electrolyte (Siegrist, 1985). In the experiments (Fig. 20), no effect is visible for ionic strengths higher than 1.5.10 .3 M. For wastewaters and tapwaters, the ionic strength is frequently higher than 10-3M, therefore the influence of a possible small donnan potential is negligible.
[
~oI ~~m~0"5
~.o
Sodium bromide cone. CNaBr [10 -3 MI
Fig. 19. Salt diffusion (D~,m) in the biofilm without background electrolyte in relation to the sodium bromide concentration. To eliminate the influence of the mechanical resistance, the quotient DN.,,/DNje, o must be standardized with the ratio DGI~kJDGI~ .
CNaB,
Oi~io Measured - diffusion coef o ficient by considering the effect of diff. potential (see equ. 12),
I I 0~ 5 1o 15 Ionic strength I [10 "3 M]
Fig. 20. Diffusion of bromide and sodium ion in the biofilm with background electrolyte in relation to the ionic strength. To eliminate the influence of the mechanical resistance of the biofilm, the quotient D~/Dio must be standardized with the ratio DNaBr~jD~,B,~.
13"78
H. S1EGRtSTand W. GuJER
Depending on the roughness of the biofilm surface and the flow conditions in the water film above, eddy diffusion may reach into the biofilm matrix near the surface. The appearance of advection in the upper part of the biofilm has the following consequences; no external mass transfer resistance, higher mass transfer in the upper part of the biofilm, the biofilm surface that is active for mass transfer may be higher than the supporting area of the biofilm. This leads to the conclusion, that besides the diffusion coefficient in the biofilm matrix, it is equally important to know the conditions at the biofilm surface (eddy diffusion, external mass transfer, mass transfer effective biofilm surface). Acknowledgement--We would like to thank Dr James
Bryers for a helpful review of the manuscript.
REFERENCES Characklis W. G. (1981) Fouling biofilm dcvelopment--a process analysis. Biotechnol. Bioengng 23, 1923-1960.
Harremors P. (1978) Biofilm kinetics. In ~Vater Po/lution Microbiology (Edited by Mitchell R.L Vol. 2, pp. ~2-109. Wiley, New York. Helferich F. (.1959) lonenaustaucher, Band I. Ver!ag Chemic. Weinheim. Jansen J. and Kristensen G. H. (1980) Fixed film kinetics-denitrification in fixed films. Rep. 80-59, Department of Sanitary Engineering, Technical University of Denmark. Lakshminarayanaiah N. (1969) Transport Phenomena in Membranes. Academic Press, New York. Matson J. V. and Characklis W. G. (1976) Diffusion into microbial aggregates. Water Res. 10, 877-885. Onuma M. and Omura T. (1982) Mass transfer characteristics within microbial systems. War. Sci. Technol. 14, 553-568. Picologlou B. F., Zelver N. and Characklis W. G. (1980) Effect of biofilm growth on hydraulic performance. J. Hyd. Dic. Am. Soc. cir. Engrs 106, 733-746. Pipes D. M. (1974) Variations in glucose diffusion coefficients through biological flocs. M.S. thesis, Rice University, Houston, Tex. Riemer M. (1979) Kinetics of denitrification in submerged filters. Ph.D. thesis, Department of Sanitary Engineering, Technical University of Denmark. Siegrist H. (1985)Stofftransportprozesse in festsitzender Biomasse. Ph.D. thesis, Swiss Federal Institute of Technology, Zurich. Williamson K. and McCarty P. L. (1976) Verification studies of the biofilm model for bacterial substrate utilization. J. Wat. Pollut. Control Fed. 48, 281-296.
0043-135,4:85 $3.00+0.00 Copyright ~ 1985 Pergamon Press Ltd
MASS TRANSFER MECHANISMS IN A HETEROTROPHIC BIOFILM H. SIEGRIST a n d W. GUJER Swiss Federal Institute for Water Resources and Water Pollution Control (EAWAG), 8600 Diibendorf, Switzerland
(Received July 1984) Al~'tract--The diffusion coefficients of three different chemical species in naturally grown, heterotrophic biofilms have been measured and a simple model of mass transfer in a biofilm matrix is developed. The mechanical structure of the biofilm matrix reduces the molecular diffusion to about 50-80~o of the value in pure water. Depending on the roughness of the biofilm surface and the flow conditions eddy diffusion increased the mass transfer into the biofilm near the surface. The influence of the diffusion potential and the donnan potential on ions have been evaluated by comparing the diffusion coefficients of a positively and a negatively charged ion and a neutral molecule in experiments with different background electrolyte concentrations. Mass transfer effects by electrostatic forces are negligible at the ionic strength of waste water and tap water.
Key words--biofilm, mass transfer, diffusion coefficient, diffusion potential, donnan potential, advection, external mass transfer, eddy diffusion
NOMENCLATURE A = cross-sectional area of the hole in the plastic piece supporting the membrane (Fig. 1) (ML -3) C~(t) = concentration in the small compartment of the experimental reactor at time t (Fig. 3) (ML -~) Cl(0) = Ct at the beginning of an experiment (ML -3) C~(tr) = C~ at the end of an experiment (ML -3) Cl(O) + Cl(te) (ML -3) C~,v,r~ concentration in the large compartment of the experimental reactor, practically independent of time (ML -3) D~=diffusion coefficient of the freely movable particle i (L-'T-i) D~' = diffusion coefficient of the ion i influenced by the diffusion potential [see equation (12) and Table I, col. I0] (L-'T -I) D o = diffusion coefficient in pure water (L2T -I) D m = diffusion coefficient of the membrane (L2T - ~) DB~ = apparent diffusion coefficient over the entire biofilm (L-T -I) D~io= average diffusion coefficient in the biofilm matrix close to the membrane (no eddy diffusion effects, see ddifr) (L2T -t) d~, at., = thickness of the effective laminar layer on both sides of the membrane system (Fig. 4) (L) dBio = average thickness of the biofilm (Fig. 2) (L) d, aay = part of the biofilm in which eddy diffusion predominates (L) drier=part of the biofilm in which molecular diffusion predominates (L) d m = thickness of the membrane (L) dw~t = water film thickness with the same mass transfer resistance as the corresponding biofilm [equation (6)1 (L) 1 = ~ Z Z,c~; ionic strength (ML -3) J = specific flux through the membrane system (ML--'T -I)
kt, = mass transfer coefficient for the component i of a certain layer n (LT -I) K~= mass transfer coefficient for a whole system of different effective layers for the component i (LT -I) KI = overall mass transfer coefficient for the membrane system with biofilm (LT -I) K2 = overall mass transfer coefficient for the membrahe system without biofilm (LT -~) ksio = Ds~o/de~; mass transfer coefficient for the biofilm (LT -l) V = volume of the small cell (Fig. 3) (L 3) z~= charge of the ion i gdry wt. P = 100"gwet w - - -~- -, average density of the biofilm ( ~ TS).
LNTRODUCTION T h e substrate u p t a k e rate o f m o s t biofilm systems is limited by mass transfer. Therefore, it is i m p o r t a n t to characterize the mass transfer m e c h a n i s m s a n d diffusion coefficients in the biological matrix. M o s t biofilm models use a fixed diffusion coefficient over the entire biofilm depth. Nevertheless, J a n s e n a n d Kristensen (1980) report diffusion coefficients o f m o r e t h a n 100K of the value in pure water. This suggests t h a t processes o t h e r t h a n molecular diffusion influence mass transfer. H a r r e m o ~ s (1978) a n d Riemer (1977) o b t a i n e d different ratios for the diffusion coefficients o f m e t h a n o l a n d nitrate in a denitrifying biofilm as c o m p a r e d to values in pure water. It appears, therefore, that ions are influenced by electrostatic forces t h a t m a y decrease or increase their molecular diffusion.
1369
[370
H. SmoaJs-r and W. GUJER
~
/ E
~ ))"r'~"~ !
~
Membrane (5art0r=us membrane filter with printed btack network) stuck over a central h01e in a plastic support which is mounted with a d0ubte sidedtape on the
disc of a rotat,og
:~~
biotogia( contactor. "----Waterlevel
""
~
Fig. 1. Sketch o f the rotating biological contactor used to grow the biofilm directly on membranes
t~
,@Filament
,//
f
f
/ / /.~ Water / /
';
f;,
/ ; / - F e r r i c oxid, //" particles
o, l dBio
the biofilm
Fig. 2. Schematic view of the biofilm. Ferric oxide particles are necessary to mark the surface of the biofilm.
-
Br0mide eteetr0de
Reference electrode Biofiim Membrane Ptastic support with central hote Smal compartment (V :75mr) Large compartment (V:120Oral)
Fig. 3. Two-compartment reactor to observe mass transfer.
with activated sludge and fed with either a synthetic waste water (20 mg l-i peptone and 13 mg 1- I meat extract, Exp. BI-B7) or diluted primary effluent ( ~ 1 0 0 m g C O D I -t, Exp. A1 + A 2 ) . The dilution rate was 2 h -t, the rotational speed 120 rpm and the temperature 20°C. After 3-6 days the membranes with the plastic support were taken out of the reactor and the biofiim thickness was measured with the microscope. The biofilm water interface was marked with small particles o f ferric oxide (Fig. 2). The bottom of the biofilm was visible to a thickness o f 500/~m by ~the printed black network on the membrane. The difference in thickness was read on the microscope micrometer. To estimate the real biofilm thickness, the micrometer reading was multiplied with the quotient of the refractive index o f water and air (n,,=/n=i r = 1.34).
Mass tramfer experiments
EXPEltliVlEN'rAL SYSTEM ~ £V.4gLUATION OF THE M E A S U l t ~
Biofilm growth Heterotrophic biofilms were grown directly on membranes which were mounted over a cemrai hole in a piece o f plastic. A rotating biological contactor =erred as a laboratory reactor (Fig. I). The reactor has been inoculated
Mass transfer was observed in a two-ceil system for the three, chemical species bromide ion, sodium ion and ,glucose (Fig. 3). At t = O, a large pulse inp~,t o f the diffusing species was injected into the larger compartment o f the diffurdon cell. Concemration within the large compartment stayed euentially constant throughout the experiment (experimental conditions, see Table I). I n ~ e small ceil, t h ¢ ~
of bromide ion concentration with time was observed with a bromide electrode. The ¢onzerttration of sodium ion and glucose were measured in samples taken at the beginning
Table 1. E~porinumtal condition= and me~ured valueJ Col.
1
2
3
NaBr
Gluc
KNO3
Ct(0)
=0
C~=
Exp.
C2 10-3 M
= 10-2 M
C= = l0 -3 M
[ [6] 10-3 M
BI B2 B3 114 B5 B6
10.0 10.0 10.0 1.0 1.0 20.0
2.0 2.0 2.0 4.0 4.0 4.0
200 200 0 2.0 !.0 5.0
B7
4.0
4.0
0
BI-B7 A1 A2 AI +A2
1.0 1.0
4.0 4.0
0 2.0
4
5
6
C~
t
7
8
9
Measured mass transfer ~ient
11
Corrected ratio
ratio
§
front column S
(~/0)
f~
205 205 5.0 2.5 1.5 15.5
0.0~ 0.024 1.00 0.20 0.33 0.68
2.0 1.4 2.0 2.5 2.2 2.3
0.5 0.6 s 0.5 t 0.5 0.6 0.7
1:0.580:0.343 1:0.603:0.420 1:0.938:0.473 | :0.363 1:0.832:0.414 1:0.864:0.508
5 5 4 1 1 6
1:0~38:0.33 t:0.60:0.40 1:0.94:0.45 1: - - :0.36 1:0.83:0.41 1:0.86:0.48
0.73 0.75 0.97 -0.91 0.92
2
1.00
1,9
0.8
1: I. 120:0.412
3
I : I. 12:0.40
1.06
2.6 2.6
0.6 0.5 0.5 0.5
l: 1.003:0.363 1:0.837:0.357
1 I
1: 1.00:0.36 1:0.84:0.35
1.00 0.91
!.00 0.20
(~) D~a,.'D~,~,'Dc.,~. =~
¶
I
0.5 2.5
D~=,:D~=,:D~
10
Dr~,am,~
tp = Density of the biofilm (.~rs). ok, ~f = ~ = Reduction factor. §Diffusion of the ions decreau~ by the activity coeffm/ent aad the ionic =trength (SieIrist, 1985).
,~ D ~ ' D ~ ~ N = ~ = ~'D*Nalb + D " " Mass transfer coefficient ratios are used be~mt¢ difftulion ¢odkiemu ~ with increasingbiofdm thickn¢~. BI-B7--biofilm grown with peptone and meat extract; AI + A2~bio~lm grown with primary effluent. ¢~
M a s s transfer m e c h a n i s m s in a biofilm
1371
Table 2. Effect of the diffusion potential (Fig. 17) Col.
12
13
D ~r~o
DNaB¢o
D ~k.=../D~
D ~.=,,
D~.~
D ~,b./DN.,
D~o Values in pure water
Dn°sq~/ Ds°~.o
D ~ o ~ / Dr~.~,,
Values from col. 12+ 13
DN°Ik~ Values from cot, 10 + II (Table 1)
DN~
Exp.
Dn,aR~ Values from col, l0 + I I (Table 1)
Values in pure water
Values from col, 15 + 16
1.06 1.04 0.81 -0.86 0.84 0.74
0.79 0.80 0.97 -0.92 0.93 1,06
0.78 0.85
1.00 0.92
B[ B2 B3 B4 B5 B6 B7 BI-B7 AI A2 AI + A 2
1.36 1.33 1.03 -I. 10 1,08 0.95
0.78
1.00 1.10
0.78
14
15
and at the end o f each experiment. S o d i u m was a n a l y s e d by a t o m i c a b s o r p t i o n a n d the glucose by a dissolved o r g a n i c c a r b o n analyser. Mass transfer t h r o u g h the m e m b r a n e w a s observed b o t h with and w i t h o u t biofilm. The m a s s transfer coefficient was c a l c u l a t e d based on the c h a n g e o f the c o n c e n t r a t i o n with time, the v o l u m e o f the small cell (V),
16
1.22
1.22
17
0.96 0.98 I. 18 -1.12 1.14 1.29 1.22 1.12
the area o f the hole in the s u p p o r t of the m e m b r a n e (A) a n d the c o n c e n t r a t i o n difference between the large a n d the s m a l l cell [according to e q u a t i o n (1)1.
vdC= dt = A "j = A "K(C 2 - C,).
(1)
Table 3. Effect of the donnan potential (Figs 18 and 19) Col.
Exp. BI
B2 B3 !t4 B5 B6 B7 BI-B7 AI A2
18
19
DN^nR~o DGn=csi.
DGI~
Values from col, 10 + 11 (Table 1)
D~.gro Values in pure water
--
20
DNtIk~ao/DN°BrO DGIa¢L,o/DGIu=o Values from from col. 18 + 19 i
-2.16 ---2.65
0.42 s
0.92 --
1.13
2.78 --
0.421
Col.
21
Exp.
Coefficient to consider the influence of the diffusion potential [from equation (12)] for* Br Na
1.18 -22
23
Corrected ratios from col. 10 + 21
DB,~o:Dn=~:DG~=~.:DN=e,m,
1.007 1.007
0.994 0.994
1:0.57:0.33 1:0.59:0.40
0.73 0.74
B3 B4 B5 B6 B7
1.28
0.82 0.96 0.93 0.87 0.82
1:0.60:0.35 I: - :0.35 1:0.72:0.38 1:0.64:0.41 I:0.72:0.31 I:0.65:0.36 1:0.64:0.28 1:0.77:0.34 1:0.70:0.31 I:0.66:0.35
. . 0.84 0.78 .
1.07 1.17 1.28
BI-B7 AI 1.28 0.82 A2 1.04 0.96 A I + A2 BI-B7 and Al + A 2
25
Dl,~
BI B2
1.04
24
. 0.87
. .
. .
26
DN,,.,
D~.~
27
DN,,~./DN~
Dn.~b o Values from cot. 22 + 23
D~,~JDN, tk.o Values from col. 13 + 24
Values from col. 22 + 23
DN=a,tJDN, ~ Values from col. 16 + 26
1.38 1.35
1.07 1.04
0.79 0.80
0.96 0.97
0.86 0.82
1.05 1.00
0.89
1,08
. . 1.19 1.28 . . 1.15
. .
. .
. . 0.93 I.O0 . . 0.90
--
+0.07_.+0.04 Literature values
1:0.64:0.33
*Ci in equation (12) is assumed to be (C a+ C~)/2. This corresponds with the assumption that within the biofilm the effecUve concentration C~ is equal to the average concentration in the two reactor compartments.
tDn.~,, = 2 D ~ " DN.~o values from col. 22.
DBrLo+ DN.~
1372
H. SIEGRISTand W. GUJER =
~"
=~
Exp.
=,.
~
= ...a
Averaae ! ~".':"":".': ~I ' D ~• o ' , DM a.... t n u s i~o n coefflc ent I/..-.'..: :
dl = 0
for
I
I
I
I
I I
i
~E u
a) with biofdm
D~a .
I0 , IO.
0 60 064
l~ 0 ~*0 033 -
~:
q~,o3 : 2. Io" M 4-
b) without
08r •
CNa8¢ : 5" 10"3 M C~ : I0 -2 M
~o
dBio > 100 ym
*astewater
Exp (table l, ¢o(.10) Theory ([>>CNaBr)
8-
Thickness i ~:.-":!' ".": i.:, of the kl~l :d~iio' dM tayer I 1:'. ?."
B2
Biofllm grown on synthettc I0 I I
• SOdKlm ion - Brom*de ion
.'~.
biofilm
-=
Fig. 4. Schematic view of the membrane system.
For Cz>>C~we obtain Kg
0 ~J
V Q(t)-Q(O)
(2) A-t C , - C l=,=.~ The mass transfer coefficientsfor sodium ion and glucose were obtained from equation (2). Mass transfer coefficients for bromide ion were computed with a leasts squares iteration program, which employed approx. 10 bromide measurements for each experiment. An overall mass transfer coefficient can be evaluated from the average diffusion coefficient and the thickness of each layer of the exlmdmental system (Fig. 4) by equation (3). I
d,
I
From the difference of the reciprocal mass transfer coefficients of the membrane system with (K l) and without biofilm (K2), one gets the inverse mass transfer coefficient of the biofilm, kaio: 1
l
I
daio
(4)
K l K2 ke,o /)nio The thickness of the apparent laminar subtayer at the side of the biofilm (d0 decreases with increasing mulllmess of tl~ biofilm surface. If the laminar sublayer disap~ars completdy (d~, > 100/am), the turbulent water layer reaches the surface of the biofilm, resulting in the following change of equation (4), ]
1
d~i o
d2
Bmfitm thickness
[pro]
Fig. 5. Results of an experiment with a h ~ back~ound electrolyte concentration (I>>C~). Since ionic strength is much higher than the observed salt coacentration (NaBr), electrostatic effects are negligible and the ratios of the diffusion coefficients of the different components are equal to the ratios in pure water. Experiments were made at different KNO 3- a n d NaBr-concentrations and different KNO3/NaBrratios because mass transfer of ions is influenced by the concentration of the background electrolyte (potassium nitrate, KNO3) and the observed salt (sodium bromide, NaBr). Figures 5-8 show the difference of the reciprocal values of the mass transfer coefficient with and without biofilm ( 1 / K I - I/K2) vs the m e a s u r e d biofilm thickness. Figures 5 and 6 are the results of Exp. B3 10
(5)
KI K2 D,,io DO From experimental evaluations [observing the overall mass transfer coefficient(K2) with increasing stirring rate] and order of magnitude estimations the laminar sublayer thickness at the side of the large cell was estimated at less than 30/~m. Consequently, the influence of this phenomenon upon the biofilm resistance is at most 15*, therefore equation (4) was used for data evaluation.
dBm
8.
Biofilm grown on synthetic wastewater l I l, ] OBr : Ot~
Exp.(hd~e I. co1.10) l"ht~y (I:C~)
1.0 :
tO :
t
: 06|=: 0.9/* : 0.45 1.0 : 0.43
C-,Naef= 5.10 -3 M IE
CC~= 10"2M
u 6- CKN03= 0 *0
RESULTS AND DISCUSSION
Mechanical resistance of the biofilm matrix Prior to this work, diffusion coefficients have been evaluated using only particulate biomass filtered onto a membrane (Willlamson and McCarty, 1976; Matson and Characklis, 1976; Pipes, 1974; Onuma. and Omura, 1982). Williamson and McCarty (1976) obtained diffusion coeff~ients of about 80% of tha values in pure water. H o w e v e r , filtered,biomass does not have the same structure as a grown biofilm. The mass transfer effect of the rough surface of the grown biofilms may be lost.
Cy
--
o
6oo Biofilm thickness
dei e
[pml
Fig. 6. Results o f an experiment without background electrolyte. The only eharIed ~ ~ the ~
the bromide ion. Due to the law of ~ , the mass transfer coefacients are equal for both ions. With decreasing background electrolytethe diffusion~ t s of the ions approach the values of the salt diffusion coe~cient.
Mass transfer mechanisms in a biofilm
B7
Exp. B 1 -
Exp. At * A2
B~ofitm grown on synthetic wastewater 10
=
I
=
~..c
ion
. . . . Mass
+O 7,
B r omm
//"
transfer model
/<
./
/
I
i
/
/.~/
/• /~"
/'2
=
.
i
I/"
/
I •" 0.70:0.31 " /
theory 1 : 0 . 6 ~ ' . 0 . 3 3
-
I
m
.
~ ~ ~ ' ~- 2 ~
=
I
/
..<.
4-
Exp.
/~
" //
/
/
" ~ / ' ~
i
OBr : ON• : DGtuc
~ . / //"/
i" Sodium ion
6- "
I0
A
•
I " Glucose
~'
8=of•Ira grown with primary effluent
=
DBt:DNa : DGIuc . " I Ezp(taDle3,mt22} I : 0 8 5 : 0 3 6 o ] Theory (no electro0.64:033 o~ static effects) :
1373
4
.=-'"
""
t
,,..~Vr" 0
'
0
///~
(~,o--8o- 6oo,m)
i
i
i
i
1(20 2O0 300 Biofilm thickness dBio
i
4O0
5OO
o
6OO
[iJml
,do
360
26o
Biofitm thidmess
5bo
dBio
600
[Ijm]
Fig. 8. Summary of the results of the experiments AI and A2. To compare the values of all experiments we have taken into account the effects of diffusion potential [see equation (I 2)], ionic strength and activity coefficient. The corrected results agree with fictitious values that would be measured if all components were freely movable. The ratios of the diffusion coefficients of the different components are equal to the ratios of the freely movable components in pure water. Fig. 7. Summary of the experiments BI-B7.
two experiments (Fig. 5: CKNO~>>CN.B. Fig. 6:
CKNo,= 0). In Figs 7 and 8 all the results of the experiments B I-B7, respectively, A1 and A2 are combined by considering the effects of diffusion potential, ionic strength and activity coefficient (see later). In Figs 9 and l0 the results from all 3 species and all experi-
ments are combined. The differences of the reciprocal values of the mass transfer coefficient in Figs 7 and 8 are multiplied by the corresponding diffusion coefficient of each component in pure water:
(, l)
d w , t = D ~ o KI,
Exp.
Exp. B1- B7 Biofi{m
~Jrown
600
on
A
=
synthetic wastewater = =
(6)
A2
A1 *
600
i
Ill
500"
'
Biofilm grown with primary effluent i
t
l
" -
1
= //
•
400-
g2,
.'.
Mass transfer
500"
///1~//I /
.= = ~ / /
m,i
.
Mass transfer m o d e .l ~- a/ . , / ' / I , ----E="400-
/. //
,,
- 300-
300-
.o~
///
,~
•
200-
,~/
~,~/ /. /
eg
.
I00- 3 ~ " / d 8 ~ ° :
0-80
pm
100/
•
e II
" ],fiden in,rval .
.
of
the linear r~ression of aU v~es
/
/
o
0
.
100 8iofiim
.
200
.
thickness
.
300 dBi o
0 r
.
400
500
[ml
600
o
360 8iofilm thickness
dBio
6o0 [jlm]
Fig. lO. Summary of the results of the experiments A I and A2. To combine the values of all three components, one has to multiply the values of Fig. 7 with the diffusion coefficients in pure water of each component, dw= is a fictitious water film thickness that would yield the same mass transfer coefficient as the observed biofilm. With increasing biofilm thickness, the average diffusion coefficient in the biofilm matrix increases too due to eddy diffusion in the upper part of the biofilm.
Fig. 9. Summary of the results of the experiments B I - B 7 .
t374
H. SIEGRISTand W. GUJER
1.5 I
B,ofdm 9r0waOn
.4°°t
~, , Y
d primary effluent I
0
100
I
I
I
I
t
200
300
400
500
600
~,
|
Biofilm thickness dora [/jrn]
o i]/ /
0
Fig. 11. Mean apparent diffusion coefficient over the entire biofilm in function of the biofilm thickness. (A) As pr~lict~l by transforming equation (4) D ~ = d s ~ / ( t / K l - t/K2); (B) as predicted by transforming equation (5) D~o= dmo/(I/Kl - IlK2 + dtlDo).
/
,Ldaiff-~ ,
100
,
i
,
200 300
,
,.
400 500
Biofdm thickness d0io [~rn]
Fig. 13. Mass transfer modell: thickness of the part of biofllm that is dominated by eddydiffusion (dm~), respectively, molecular diffusion a~) in function of the thickness of the biofilm (dmo= d~y + da~r).
The calculated effective water film thickness has the same mass transfer coefficient as the corresponding biofilm (Do/dw,t = D~/dmo). Figures 9 and 10 relate interpretation of this phenomenon is, that the lamithe calculated value (d,=) to the measured biofilm nar sublayer becomes ineffective as the surface roughthickness (d~o). ness of the biofilm protrudes into the turbulent flow If the average diffusion coefficient (Da~o) in the region. Apparently the small external mass transfer biofilm were constant, one would obtain a linear co¢ffacient for thin biofilms caused by the laminar relation between D~t and dmo. ExperimentalI results in water layer (d0 becomes negative with increasing • , Figs 9 and 10 indicate, however, the average diffusmn biofilm thickness. coefficient in the biofilm matrix (Da~) increases with increasing biofilm thickness. The observed value of Mass transfer model Dmo varies from a tow 40% to a high 140% of the Instead of assuming a negative external mass t t W corresponding value in pure water. This apparent fer coefficient, one may assume a fraction of the increase of the diffusion coefficient can be explained biofilm matrix close to the biofiim surface, where by eddy diffusion in the biofilm matrix close to the mass transfer is dominated by eddy diffusion. The biofilm surface (see Fig. 11). The irregularities and concentration gradient through this biofilm layer is filaments of the biofilm surface penetrate through the practically zero because the eddy diffusivity is much laminar waterfilm layer. Therefore the turbulent zone higher than molecular diffusivity (Fig. 12). reaches the surface of the biofilm and produces eddy The thicknes of the biofilm layer that is influenced diffusion in the biofilm matrix near to the surface. by eddy diffusion (a~r) depends on the surface This effect becomes visible by the moving of the morphology roughness of the biofilm and fluid flow filaments in the current. Picologlou et aL (1980) and conditions above the biofflrn surface. While the~ two Characklis (1981) showed in their experiments that parameters are very important, the following at~roxthe friction factor of a circular tube increases strongly imations are only valid for the system described in if the wall growth reaches a certain thickness. Their this paper. If we assume a constant diff~u!ion coefficient in the part of the biofilm layer whe,re molecular diffusion predominates (d,~f) we can write, 1 I based .on the above data, for the biofilm grown on synthetic substrates, the following (Fig. 13): ~srge to tl~ sinai ¢141
a,aay = 0.6 (d~o - 100/~m) L~iofilm
Mass transfer I
[= I: .~
LIRIImr
~
_~ ~
l l~l~
deddy ddiff T d~ 'a~2" Fig. 12. Simple model of mass transfer through the membrane and biofitm system.
(7)
and ddi~, = 100/zm+ 0.4(dmo- 100/~m).
(8)
The molecular diffusion co¢ttlcient in the lower portions of the biofilm matrix is assumed al~i'ox 60°,/. of the value in pure water. With increasing bJofilrn thickness, the average apparent diffusion c ~ t ~ t would increa~ because of increasing importance of eddy diffusion in the upper part of the biofilm. For a biofilm grown on primary effluent we get similar
Mass transfer mechanisms in a biofilm
1375
Fig. 14. Scanning electron micrograph of the biofilm grown on synthetic waste water,
Fig. 15. Scanning electron micrograph of the biofilm grown with primary effluent.
results
significant relation between the mechanical resistance of the biofilm and biofilm density. Despite this, experimental results suggest the diffusion coefficient may slightly depend on biofilm density and is about 50-80% of the value in pure water for a biofilm density of about 2% TS. Biofilm density decreases slightly with increasing biofilm thickness. For Fig. 16 we used the average density of two or three measurements with different biofilm thickness, in each experiment. Biofilm density can be influenced by the following factors:
dd~er 0.4 (dBio -- 100/~m). =
(9)
The molecular diffusion coefficient in the biofilm matrix is about 50% of the value in pure water. The difference in the relative influence of eddy diffusion may be explained by looking at the structure of the two biofilms. A biofilm grown on synthetic wastewater has a more compact layer near the membrane and a light structure with filaments at the top of the biofilm. The light layer and the filaments can be removed by a water jet. The layer below can only be taken away with the finger. A biofilm grown with primary effluent has a more compact structure over the entire biofilm, there are only a few filaments at the top of the film. Because of these differences in the structure of the observed biofilms, eddy diffusion is more active in the former biofilm than in the latter (see Figs 14 and 15). Advection in the upper part of the biofilm has the following consequences for biofilms thicker than 100/a M: there exists no external mass transfer resistance, the concentration gradient of the substrate is smaller than for mass transfer by molecular diffusion only. All these effects increase the substrate uptake of the biofilm in the case of substrate limitation. Jansen and Kristensen (1980) estimate in a rotating drum system exceptionally high mass transfer coefficients which, in light of the above work, may likely be due to the contribution of eddy diffusion.
the the the the
fraction of exopolysaccharides in the biofilm, inorganic fraction, fraction of protozoa, worms and insects, types of microorganism that predominate.
Therefore it may be quite difficult to obtain a well defined relationship between diffusion resistance and biofilm density.
Mechanical resistance in relation to the molecular size of the chemical species As seen in Fig. 17, the relative magnitude of the diffusion coefficients of glucose, sodium and bromide
for experimenta/ resu/ts see tabl~ I, col 6 + ?
~ 1.0
I
l
o Biofilm grown with primary effluent
x
_~ o.'.
O'B,° Averoge diffusion c o e f h -
The mechanical resistance of the biofilm matrix-in relation to the biofilrn density The following considerations are valid only for the lower part of the biofilm in which only molecular diffusion is responsible for mass transfer. Unfortunately, the density differences between the different experiments are too small to obtain a
x Biofilm grown on synthetic waste water
in the blof drn mQtfix trent
t~
i I
o~ Density
I 2
~
[% rs]
close
fO the
rnernbrone {no eddy dlff )
Fig. 16. Reduction of the molecular diffusion coefficient in the biofilm in relation to the biofitm density.
1376
H. SIEGRISTand W. GUJER
r~
e~
~ 2.0
%
Dq = D,'Dj(I - :uzj)
for experimental results see tmNe 1.3, co17+22 T=
for biofilms
20 *C I
grown on synthetic waste water ( B I - B ? )
.I:Zl
"' 1.0 E
~
•~, 0 0
Dj
x Average values
o
f
1.0
~
o Average values for biofilms grown with primary effluent (AI + A2)
2.0
Diffusion in pure water Do [lO-Scrn 2 S"-1"1
Fig. 17. The average diffusion coctficient of glucose, sodium and bromide ion in relation to the values in pure water after considering the effects of diffusion potential [see equation (12)], ionic strength and alteration of the activity coefficient (Siegrist. 1985).
- -
:,/2j" D i
valid for ions with different charges. If there is a background electrolyte at a constant concentration in the system, the diffusion potential decreases with increasing concentration of the background electrolyte. Diffusion coefficients of the oppositely charged ions (i and j) in the system can be related to the quotient of the concentration of the observed ion and the ionic strength by the following equation (Siegrist, 1984).
D;/O,
= l + : ~ ( D J - O,). c_~ 2" D ..... ~, t
the pores of the biofilm may have the same physical size as the diameter of the chemical species, thus mechanical resistance for the larger particles would be higher than for the smaller ones, bioturbation (movement of protozoa and higher organisms) could increase the diffusion coefficient in the biofilm for all three observed species by the same amount. As seen from scanning electron micrographs (Figs 13 and 14) the size of the pores is much bigger than the size of the glucose molecule. An alteration of the diffusion coefficient due to bioturbation cannot be detected.
Z D;~'Ci
Z D,:~'Ci 2"1
The average diffusion coefficient does not change noticeably with ionic strength if the diffusion of the ion pair is of the same order of magnitude as that of the background electrolyte. In the above experiments, sodium bromide and potassium nitrate were used, which have about the same salt diffusion coefficients. Therefore, a linear relation between the gradient of D*/Di and the ratio of cJl (Fig. 18) is expected. As shown in Fig. 18, theoretical prediction and experimental results correspond quite well. For biofilm systems with an impermeable support at the back of the film, the following equation (Siegrist, 1985) can be written: D?/D, = 1 +
z~(Dj- D,)
(13)
flux of inert ions (background electrolyte) is zero.
Diffusion potential Molecular diffusion of neutral components is essentially not altered by effects other than the mechanical resistance of the biofilm matrix. However, the movement of ions is influenced by electrostatic forces. Consider a system with only two oppositely charged ions with different independent mobilities. Because of these different mobilities, one should obtain different fluxes for the ions along an equal concentration gradient. However, this is impossible since, due to the law of electronentrality, a diffusion potential would be formed, lowering the molecular diffusion of the quicker ion and increasing the diffusivity of the slower ion. One thus obtains for opposite ions the same diffusion coefficient called salt-diffusion Fq (Lakshminarayanaiah, 1969), where Du=D~*=D~=
(12)
background electrolyte at a constant concentration D..... *c= Z :~'C,
ion in the biofilm matrix are about the same as in pure water. This relationship could be affected by the following mechanisms:
(,l ! )
2.D,.Dj D, xDj
(10)
valid for ions with equal charge (no background electrolyte)
For wastewaters, the concentration of the observed ion is frequently less than 20% of the ionic strength, therefore the influence of the diffusion potential may generally be neglected. Only for a system with low background electrolyte concentrations, with large differences between the diffusion coefficients and bivalent ions, should the effect of the diffusion potential be taken into account.
Donnan potential If a solid matrix contains regularly dispersed, fixed, negatively or positively charged groups in em:ess, a donnan potential will be formed at the surface of the matrix (Hdferich, 1959). The donnan potential impedes the diffusion of ions with the same charge as the fixed groups and accelerates the penetration of ions with the opposite charge. A biofilm matrix contains an excess of fixed negatively charged groups---phosphate--and carboxytic acid-groups at the surface of microorganisms. How-
Mass transfer mechanisms in a biofilm kS
I
I
I
for ex#ertmenta/ results see table l+2, coL 5,14 + 17
I
i ..a
o Sodium ion
~o 1.0 _o~
o
~
05 - theo.r.e!!cal_J/
o
• I
~__-
premct,on
influenced by the diffusion potential
~'
•- -
o
[
o
0.2
I
0.4
l
2" ONiBi0" D~IrBio
•
I:;
0.6
to
0.8
ion
x Bromide
Ci Average concentration of the observed ion i [ Ionic strength D~'Bi~ Measured diffusion coefficient in the biofilm
c~
Oo
1377
2" DNao
DNIBrBi ° : D~N,1Bio + DBrBi o
ONeBro =
• DBro
DNao+DBr °
{-1
q/t
Fig. 18. Effect of ionic strength on ion diffusivities within a biofilm. Increasing ionic strength relative to the concentration of the observed ion, lowers the diffusion potential and decreases the influence of electrostatic forces on the molecular diffusion of the different ions. To eliminate the influence of the mechanical resistance of the biofilm matrix, the quotient D,~o/D,~* is standardized with the ratio
DNaBrmo/D,',iaBro.
ever, three factors speak against the formation of a donnan potential; Negatively charged groups are not uniformly dispersed in the biofilm matrix but are concentrated at the surface of the microorganism's membranes. An electrical double layer of about 5-10 nm thickness (depending on ionic strength) can neutralize the excess negative charge. In the pores between the microorganisms, where mass transfer occurs, the effect of the negatively charged groups is therefore negligible. Parallel to a donnan potential, an osmotic pressure gradient would be formed by penetration of water molecules into the matrix (the ionic strength in the matrix is higher than outside which results in swelling of the matrix). It is unlikely that the biofilm matrix could resist the osmotic pressure. Mobile prozozoa may destroy portions of the exopolysacchride matrix and produce big pores for mass transfer. Experimental results also lead to the conclusion that a possible donnan potential may be neglected. Salt diffusion in a system without background elec-
"7
I
for experimental results see tame 1.3, col I+20 t.5 I I x
z N t.O ~
x
...........
%
bromide
a - - 0~,g.
2.~.1:~
.....
,!0
The mechanical structure of the biofilm matrix of 1.8-2.6~ TS reduces the molecular diffusion to about 60-50~o of the value in pure water. Mass transfer effects by electrostatic forces between ions (diffusion, donnan potential) are negligible at the ionic strength of waste water and tap water. Only in experiments with a very low ionic strength and bivalent ions must the influence of the diffusion potential on mass transfer be considered.
T
for experimental results see tame 1+3, cot 4,25+27 o Sodium ion I I x Bromide ion
1.5
--
i o kC _ o o . . . . . . . . . o ~ x x
x>
/~ (~
no backgroundelectrolyte
~J0
CONCLUSIONS
x Sodium-
E)
9 ~,o.5
trolyte should be lowered by a donnan potential. In the experiments (Fig. 19), no effect is evident for concentrations higher than 5.10 -4 M. Diffusion of a positively charged ion must be accelerated ( ~ 50~) and, respectively, diffusion of the negatively charged ion is reduced ( ~ 30~), if the concentration of fixed, negatively charged groups is equal to the ionic strength in a system with background electrolyte (Siegrist, 1985). In the experiments (Fig. 20), no effect is visible for ionic strengths higher than 1.5.10 .3 M. For wastewaters and tapwaters, the ionic strength is frequently higher than 10-3M, therefore the influence of a possible small donnan potential is negligible.
[
~oI ~~m~0"5
~.o
Sodium bromide cone. CNaBr [10 -3 MI
Fig. 19. Salt diffusion (D~,m) in the biofilm without background electrolyte in relation to the sodium bromide concentration. To eliminate the influence of the mechanical resistance, the quotient DN.,,/DNje, o must be standardized with the ratio DGI~kJDGI~ .
CNaB,
Oi~io Measured - diffusion coef o ficient by considering the effect of diff. potential (see equ. 12),
I I 0~ 5 1o 15 Ionic strength I [10 "3 M]
Fig. 20. Diffusion of bromide and sodium ion in the biofilm with background electrolyte in relation to the ionic strength. To eliminate the influence of the mechanical resistance of the biofilm, the quotient D~/Dio must be standardized with the ratio DNaBr~jD~,B,~.
13"78
H. S1EGRtSTand W. GuJER
Depending on the roughness of the biofilm surface and the flow conditions in the water film above, eddy diffusion may reach into the biofilm matrix near the surface. The appearance of advection in the upper part of the biofilm has the following consequences; no external mass transfer resistance, higher mass transfer in the upper part of the biofilm, the biofilm surface that is active for mass transfer may be higher than the supporting area of the biofilm. This leads to the conclusion, that besides the diffusion coefficient in the biofilm matrix, it is equally important to know the conditions at the biofilm surface (eddy diffusion, external mass transfer, mass transfer effective biofilm surface). Acknowledgement--We would like to thank Dr James
Bryers for a helpful review of the manuscript.
REFERENCES Characklis W. G. (1981) Fouling biofilm dcvelopment--a process analysis. Biotechnol. Bioengng 23, 1923-1960.
Harremors P. (1978) Biofilm kinetics. In ~Vater Po/lution Microbiology (Edited by Mitchell R.L Vol. 2, pp. ~2-109. Wiley, New York. Helferich F. (.1959) lonenaustaucher, Band I. Ver!ag Chemic. Weinheim. Jansen J. and Kristensen G. H. (1980) Fixed film kinetics-denitrification in fixed films. Rep. 80-59, Department of Sanitary Engineering, Technical University of Denmark. Lakshminarayanaiah N. (1969) Transport Phenomena in Membranes. Academic Press, New York. Matson J. V. and Characklis W. G. (1976) Diffusion into microbial aggregates. Water Res. 10, 877-885. Onuma M. and Omura T. (1982) Mass transfer characteristics within microbial systems. War. Sci. Technol. 14, 553-568. Picologlou B. F., Zelver N. and Characklis W. G. (1980) Effect of biofilm growth on hydraulic performance. J. Hyd. Dic. Am. Soc. cir. Engrs 106, 733-746. Pipes D. M. (1974) Variations in glucose diffusion coefficients through biological flocs. M.S. thesis, Rice University, Houston, Tex. Riemer M. (1979) Kinetics of denitrification in submerged filters. Ph.D. thesis, Department of Sanitary Engineering, Technical University of Denmark. Siegrist H. (1985)Stofftransportprozesse in festsitzender Biomasse. Ph.D. thesis, Swiss Federal Institute of Technology, Zurich. Williamson K. and McCarty P. L. (1976) Verification studies of the biofilm model for bacterial substrate utilization. J. Wat. Pollut. Control Fed. 48, 281-296.