Journal of Contaminant Hydrology 152 (2013) 12–17

Contents lists available at SciVerse ScienceDirect

Journal of Contaminant Hydrology
journal homepage: www.elsevier.com/locate/jconhyd

Bacteriophage PRD1 batch experiments to study attachment,
detachment and inactivation processes
Gholamreza Sadeghi a,b, Jack F. Schijven b,c,⁎, Thilo Behrends d,S. Majid Hassanizadeh b, Martinus Th. van Genuchten b,ea

Department of Environmental Health Engineering, Zanjan University of Medical Sciences, Zanjan, Iran
Department of Earth Sciences, Utrecht University, P.O. Box 80021, 3508 TA Utrecht, The Netherlands
Expert Centre for Methodology and Information Services, National Institute of Public Health and the Environment (RIVM), P.O. Box 1, 3720 BA Bilthoven, The NetherlandsdDepartment of Earth Sciences — Geochemistry, Utrecht University, P.O. Box 80.021, TA 3508 Utrecht, The NetherlandseDepartment of Mechanical Engineering, COPPE/LTTC, Federal University of Rio de Janeiro, UFRJ, Rio de Janeiro, RJ 21945-970, Brazilbca r t i c l e

i n f oArticle history:
Received 18 March 2013
Received in revised form 11 June 2013
Accepted 13 June 2013
Available online 22 June 2013
Keywords:
Colloids
Bacteriophage PRD1
Batch experimenta b s t r a c t
Knowledge of virus removal in subsurface environments is pivotal for assessing the risk of viralcontamination of water resources and developing appropriate protection measures. Columns
packed with sand are frequently used to quantify attachment, detachment and inactivation rates ofviruses. Since column transport experiments are very laborious, a common alternative is to performbatch experiments where usually one or two measurements are done assuming equilibrium
is reached. It is also possible to perform kinetic batch experiments. In that case, however, itis necessary to monitor changes in the concentration with time. This means that kinetic batch
experiments will be almost as laborious as column experiments. Moreover, attachment anddetachment rate coefficients derived from batch experiments may differ from those determinedusing column experiments. The aim of this study was to determine the utility of kinetic batch
experiments and investigate the effects of different designs of the batch experiments on estimatedattachment, detachment and inactivation rate coefficients. The experiments involved various
combinations of container size, sand–water ratio, and mixing method (i.e., rolling or tumbling bypivoting the tubes around their horizontal or vertical axes, respectively).
Batch experiments were conducted with clean quartz sand, water at pH 7 and ionic strength of
20 mM, and using the bacteriophage PRD1 as a model virus. Values of attachment, detachment
and inactivation rate coefficients were found by fitting an analytical solution of the kinetic
model equations to the data. Attachment rate coefficients were found to be systematicallyhigher under tumbling than under rolling conditions because of better mixing and more
efficient contact of phages with the surfaces of the sand grains. In both mixing methods, moresand in the container yielded higher attachment rate coefficients. A linear increase in the
detachment rate coefficient was observed with increased solid–water ratio using tumbling
method. Given the differences in the attachment rate coefficients, and assuming the same
sticking efficiencies since chemical conditions of the batch and column experiments were thesame, our results show that collision efficiencies of batch experiments are not the same as
those of column experiments. Upscaling of the attachment rate from batch to column
experiments hence requires proper understanding of the mixing conditions. Because batch
experiments, in which the kinetics are monitored, are as laborious as column experiments,
there seems to be no major advantage in performing batch instead of column experiments.
© 2013 Published by Elsevier B.V.

1. Introduction⁎ Corresponding author at: Department of Earth Sciences, Utrecht University,
P.O. Box 80021, 3508 TA Utrecht, The Netherlands.
E-mail address: jack.schijven@rivm.nl (J.F. Schijven).
0169-7722/$ – see front matter © 2013 Published by Elsevier B.V.
http://dx.doi.org/10.1016/j.jconhyd.2013.06.002

Both groundwater and surface water may become contaminated with pathogenic viruses from various fecal sources (Yates

G. Sadeghi et al. / Journal of Contaminant Hydrology 152 (2013) 12–17

et al, 1985). There is worldwide interest in the removal ofviruses by soil passage; either for the protection of groundwatersupplies, or for treatment of surface water for drinking water.
Major processes determining virus removal during soil passage
are attachment to and detachment from soil grains, as well
as virus inactivation. These processes depend on a range ofenvironmental conditions, as explained in several recent reviews(Bradford et al., 2004; Foppen and Schijven, 2006; Jonczyk et al.,2011; Sen, 2011; Sen and Khilar, 2006).
Three types of experiments are typically conducted toobtain parameter values for virus attachment, detachment
and inactivation: batch, column and field experiments. Each
type of experiment has its characteristic spatial and temporalscales with certain advantages and disadvantages. A majoradvantage of field studies is the fact that the actual situation is
being investigated, which may involve 1-, 2-, or 3-dimensionaltransport depending upon local hydrologic conditions. Field
studies involving pathogens, or even harmless indicator microorganisms like bacteriophages, are often not allowed because ofsafety regulations. Commonly, field studies are laborious and canbe very expensive. Physico-chemical heterogeneities further add
to the complexity of field-scale studies and may necessitate
sampling at multiple locations (see e.g. Pang, 2009; Ryan et al.,
1999; Schijven et al., 1999, 2000).
Column experiments offer the advantage that permission
from local authorities is not required, and that the transportand removal processes can be studied under well-defined
physico-chemical conditions. Column experiments are often
used to support field studies. However, because of spatial andtemporal variations in field conditions, an extensive series ofcolumn experiments may be required in order to encompass
field heterogeneities. Also, a large number of samples still may
be needed for accurate parameter estimation, thus renderingcolumn experiments laborious (Lewis and Sjöstrom, 2010). An
additional challenge is the appropriate upscaling of parametervalues from the column to the field scale (Pang et al., 2003). For
these reasons, most column studies are aimed at understanding
removal processes rather than obtaining parameters applicableto the field scale (e.g. Bradford and Bettahar, 2005; Sen and
Khilar, 2006; Stevik, 2004).
Batch experiments can be performed with or without soil.
A batch experiment with only water may be used to determine
inactivation rates of viruses in the water phase. Rate parameters are then obtained from measurements of the decreasing
virus concentration as a function of time. To study attachment
and detachment processes, batch experiments are carried out
in which a suspension of viruses is agitated with a known
quantity of solid material (e.g., a field soil or quartz sand).
While agitating the containers, virus particles simultaneously
attach onto and detach from the solid grains. Both free andattached virus particles may become inactivated, leading to a
gradual decrease in the number of infectious virus particles.
Because of inactivation, a true steady-state equilibrium will
never be reached, but rather a quasi-equilibrium situation(Grant et al., 1993).
Initially, in a batch experiment, free virus concentrations
decline rapidly with time because of attachment and inactivation. Eventually a quasi-equilibrium distribution of viruses
between the solid surfaces of the sand and the water isobtained because of reversible adsorption. Because attachment
and detachment are kinetic processes, for modeling purposes13

one needs to obtain values of the attachment and detachment
rate coefficients, rather than only the equilibrium distribution
coefficient. The distribution coefficient as such is of little use
unless augmented with a kinetic rate coefficient.
To determine virus concentrations in the water phase, waterand sand need to be separated. This is relatively easy to do in caseof coarse sand since the grains will settle quickly as soon as
shaking of the container ends, after which a sample from thesupernatant water can be taken. In case of medium- and finetextured materials, centrifugation is required to separate waterand soil. Because of these sampling issues, and to maintainsaturated conditions, batch experiments usually make use of aseries of containers (tubes) that are sampled only once.
Usually only equilibrium batch experiments are carriedout. Samples in that case are taken only at the beginning of anexperiment and at the end when equilibrium is assumed
to be reached. The equilibration time is often assumed to be
30 min to 8 h (Schijven and Hassanizadeh, 2000). Suchexperiments can be used only to estimate the distribution
coefficient. For this reason, only few values for attachment
and detachment rate coefficients from batch studies areavailable. Unfortunately, the results of batch experiments canvary drastically when performed under different experimental conditions, such as the solid–water ratio and the methodof agitation (Schijven and Hassanizadeh, 2000). It is therefore
not always clear whether results of batch studies can be used
to predict virus removal under transport conditions.
In this paper, we investigate whether the gap between
batch and column experiments for studying virus attachment, detachment and inactivation can be bridged. The
container size, solid–water ratio, and the mixing method
were varied in order to determine their effect on attachment,
detachment and inactivation. The batch experiments wereconducted with the bacteriophage PRD1 as a model virus. In
previous work (Sadeghi et al., 2011), attachment, detachment and inactivation were studied in saturated sandcolumns for a range of pH and ionic strength values. Since
we used the same coarse sand and bacteriophage, values of
the rate coefficients from the batch and column experiments
can be compared immediately.
2. Material and methods
2.1. Experimental set-up and measurements
The bacteriophage PRD1 was used as a model virus in all
experiments. PRD1 is an icosahedral phage with a diameterof 62 nm and an isoelectric point between pH 3 and 4,
implying that the phage is negatively charged at pH values
between 5 and 8 (Loveland et al., 1996). PRD1 may beconsidered a worst-case model virus because of its low
inactivation rate between 10 and 23 °C (Blanc and Nasser,
1996). Because of its larger size, PRD1 is of interest as arepresentative of rotaviruses and adenoviruses (Sinton et al.,1997). Its host bacterium was Salmonella typhimurium LT-2.
Host bacteria and the bacteriophage were obtained from the
National Institute of Public Health and the Environment(RIVM), Bilthoven, The Netherlands. For the soil we used
quartz sand (H31, Sibelcoo, Belgium) with an average grain
size of 0.44 mm. Potential impurities were removed following procedures adopted by Foppen et al. (2007) to clean sand.

14

G. Sadeghi et al. / Journal of Contaminant Hydrology 152 (2013) 12–17

Our sand for this purpose was heated to 850 ± 50 °C for 4 h,followed by acid washing with 12 N HCl for 48 h, andsubsequent rinsing with de-ionized water until the electricalconductivity of rinse water was less than 1 μS/cm. Prior touse, the sand was oven-dried for 24 h at 105 °C. A stock
solution of water with a pH of 7 and ionic strength (IS) of
20 mM was prepared using sodium salts (NaCl, NaHCO3),
similarly as for the column experiments of Sadeghi et al.
(2011) to enable direct comparisons of the batch and column
experiments. A seeding suspension with a PRD1 concentrationof 108 pfp/ml was prepared. All experiments were conducted
at a controlled room temperature of 11 (±1) °C.
For the inactivation experiments we used the stock
solution for all batch experiments without soil. The solution
was dosed with the same amount of PRD1 from the seedingsuspension. Samples were taken regularly over a 2-month
period to determine PRD1 concentrations according to ISO
10705-I (ISO, 1995), except for nalidixic acid since our hostbacteria S. typhimurium LT-2 was sensitive to this acid.
Two series of batch experiments with soil were performed,
each with a different mixing method. In each series, fourcombinations of solid–water ratios were used (see Table 1).
Two or ten grams of dried sand was placed into small and large
tubes (15 and 50 ml Greiner Bio-One Polypropylene Falcon
tubes, Cat No. 188271 and 227261). Subsequently, all tubes
were filled with the stock solution and then drained after a
few hours. Filling and drainage were repeated several times
during a one-week period until constant pH and ionicstrength values were obtained, as indicated by measurements after each replacement. The tubes were subsequently
inoculated with the same number of viruses (2.2 × 106
viruses). All tubes were gently filled completely so that no
air remained in the tubes upon their closure with caps. The
tubes were mounted onto two different agitators. For batch
series 1 we used an electrical rotor (Watson Marlow 505S)
that enabled us to roll the tubes horizontally at 4 rpm(Fig. 1a–1d). For batch series 2, the tubes were tumbled at
9 rpm (Fig. 2a–2d). A total of 104 tubes were prepared forsampling at 13 different times.
At various times, a tube from each batch experiment was
taken for sampling. This tube was left standing for one hourto allow the sand to settle. Its supernatant was then sampled
to determine the remaining virus concentration. All samples
were analyzed within 2 h of collection.

2.2. Conceptual model
In a batch experiment with water, sand and virus particles,
the governing equations describing changes in the virus concentrations in the water phase and attached to the sand grains,
as a function of time, are:dC
M
¼ −katt C þ k det s S−μ l C
Vw
dt

ð1Þ

dS
V
¼ katt w C−k det S−μ s S
Ms
dt

ð2Þ

where t is time [T], C is the number of free viruses per volume ofwater [L−3], S is the number of attached viruses per mass ofsand grains[M−1], Ms is the dry mass of sand [M], Vw is thevolume of water [L3], katt and kdet are the attachment anddetachment rate coefficients [T−1] and μl and μs are theinactivation rate coefficients, of free and attached viruses,
respectively [T−1]. Subject to the initial conditions that C(t =0) = C0 and S(t = 0) = 0, the analytical solutions for C andS were derived using the DSolve command of Mathematica(8.0.4) (Wolfram, 2012). They are as follows:C ðt Þ ¼

β1 expð−β4 t Þ þ β2 expð−β5 t Þ
2β3

ð3Þ

Sðt Þ ¼

β6 expð−β4 t Þ þ β7 expð−β5 t Þ
2β3

ð4Þ

where
β1 ¼ C 0 ðkatt þ μ l −k det −μ s þ β3 Þ−2k det

Ms
S
Vw 0

β2 ¼ −C 0 ðkatt þ μ l −k det −μ s −β3 Þ þ 2k det

Ms
S
Vw 0

ð5Þ
ð6Þ

β3 ¼

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
β8 2 −4β9β4 ¼

β8 þ β3
2

ð8Þ

β5 ¼

β8 −β32

ð9Þ

ð7Þ

Table 1
Experimental conditions and estimated attachment, detachment and inactivation
parameter values.
Conditions

Parameter values

Experiment

Ms
g

Vw
Ml

Ms/Vw
g/ml

C0
pfp/ml

katt
h−1

kdet
h−1

μs
h−1

1a
1b
1c
1d
2a
2b
2c
2d

2
2
10
10
2
2
10
10

55
15.3
52
12.3
55
15.3
52
12.5

0.036
0.13
0.19
0.81
0.036
0.13
0.18
0.80

4.18 × 104
1.30 × 105
5.02 × 104
1.72 × 105
3.45 × 104
1.41 × 105
3.39 × 104
1.37 × 105

0.19
0.086
0.21
1.2
0.59
1.1
0.74
2.1

0.026
–
0.014
0.00140.000027
0.000370.00091
0.0036

0.007
0.007
0.007
0.007
0.007
0.066
0.066
0.066

All experiments were performed at pH 7 and ionic strength 20 mM; in series 1,
the tubes were rolled at 4 rpm; in series 2, the tubes were tumbled at 9 rpm.

Fig. 1. Evolution of PRD1 concentration in experimental series 1 (rolling at afrequency of 4 rpm). Symbols are observed virus concentrations and lines
are fitted model results.

G. Sadeghi et al. / Journal of Contaminant Hydrology 152 (2013) 12–17

Fig. 2. Evolution of PRD1 concentration in experimental series 2 (tumbling ata frequency of 9 rpm). Symbols are observed virus concentrations and lines
are fitted model results.

β6 ¼ S0 ðk det þ μ s −katt −μ l þ β3 Þ−2katt

Vw
C
Ms 0

β7 ¼ −S0 ðk det þ μ s −katt −μ l −β3 Þ þ 2katt

ð10Þ

Vw
C
Ms 0

ð11Þ

β8 ¼ katt þ k det þ μ l þ μ S

ð12Þ

β9 ¼ katt μ S þ k det μ l þ μ l μ S :ð13ÞEqs. (3) and (4) show that the concentrations of both free
and adsorbed viruses eventually approach zero because ofinactivation.
2.3. Data analysis
The main parameters in Eqs. (3)–(4) are C0, Ms, Vw, katt, kdet,
μl, and μs. Values of C0, Ms, and Vw were measured directly. In allcases, the value of μl was set equal to 0.007 h−1. This value wasdetermined from batch experiments without sand, assuming
first-order kinetic inactivation.
Coefficients katt, kdet and μs were determined by fitting
Eq. (3) to observed concentration data. To that aim, thefollowing log-likelihood function was used (Hogg and Craig,1995):
L½katt ; k det ; μ s  ¼ −2

n
X
i¼1

"

 pﬃﬃﬃﬃﬃﬃ ð log C Þ2
10 t
ln s 2π þ
2s2

#
ð14Þ

where i is the i-th observation out of n observations, Ct is
the concentration as a function of time as given by Eq. (3)and s is the normal distributed random error. Parameter values
were obtained by minimizing the log-likelihood function using
the numerical optimization option of Mathematica (8.0.4)(Wolfram, 2012).
Note that the log transform of the virus concentration
was used in the optimization. This was essential since theconcentration values covered several orders of magnitude.
Without the log transformation, the optimization would be
biased almost exclusively towards values at the beginning of
the experiments when virus concentrations are still high. For
comparison, kinetic parameters were also optimized using
concentrations that were not log transformed. For someexperiments we obtained very similar values for katt and kdet

15

irrespective of the transformation. In several experiments,
however, the optimized values differed considerably. Thiswas especially the case for experiments that reached quasiequilibrium. When the concentrations were not log transformed,
the optimized model then did not capture the transition between
initial and quasi-equilibrium phase very well. For this reason,
only the optimized parameters for the log transformed concentrations are reported here.
In the initial phase of a batch experiment, the decrease inaqueous phase concentrations is mainly controlled by katt andμl. But later, when quasi-equilibrium is reached, the decreasein concentration of free viruses is determined by inactivationof both attached and free viruses. For experiments where thevirus concentration decreased below the detection limit
before quasi-equilibrium was reached, it was not possible toestimate a value for μs. For those experiments, μs was set equal
to the liquid phase inactivation coefficient of 0.007 h−1, in
which case only katt and kdet needed to be estimated.
First, we carried out an optimization in which the objectivefunction (Eq. 14) consisted of the sum of all eight log-likelihood
functions (one for each experiment). In this way, values of therate coefficients (katt, kdet, and μs) could be estimated separately
for each experiment. Next, similar log-likelihood functions
were defined whereby parameter values of different experiments (or groups of experiments) were assumed to be thesame. Using the log-likelihood deviates (the same as thelikelihood ratios), we could then determine whether thoseassumptions were correct. If the log-likelihood between
models differed less than the 95-percentile of a χ2-value,with the degree of freedom equal to the difference in thenumber of parameters between models, then the model withthe least number of parameters was used. We further used
multivariate regression analysis to investigate in what manner
the batch rate parameters were related to the parameters Ms
and Vw.
3. Results
Figs. 1 and 2 show observed and calculated virus concentrations versus time for all eight batch experiments. As
explained in the previous section, the model was fitted to the
log-transformed bacteriophage concentrations. The fitted parameter values are presented in Table 1.
In all experiments, concentrations of free viruses dropped
rapidly at the beginning (Figs. 1 and 2). Depending upon the
Ms/Vw ratio, concentrations changed by up to four orders ofmagnitude within the first 10 h of the experiments. This time
period reflects the initial phase in which changes in the virus
concentrations are predominately caused by an imbalance
between the rates of virus attachment and detachment.
During the second phase, rates of virus attachment anddetachment are almost balanced and the system reaches
quasi-equilibrium with respect to virus attachment. In thisquasi-equilibrium phase, the decrease in free virus concentration is predominately due to inactivation. Quasi-equilibrium
was not reached in experiment 1b (Fig. 1).
When estimating the rate coefficients for each of the eightbatch experiments separately, it became apparent that valuesof μs could be estimated for experiments 1d, 2a, 2b, 2c and 2d
only, where quasi-equilibrium was established. In the case ofexperiments 1a and 1c, quasi-equilibrium was just reached,16

G. Sadeghi et al. / Journal of Contaminant Hydrology 152 (2013) 12–17

and μs was estimated but with low certainty. For experiment1b, quasi-equilibrium was not reached and, hence, only kattcould be estimated. In the likelihood ratio test, the estimatedvalues of μs for experiments 1b, 1c, 1d and 2a were found
not to be significantly different from the default value of0.007 h−1 for free viruses. For experiments 2b, 2c and 2d,
however a much higher value of 0.066 h−1 (almost the samefor all three experiments) was estimated. Thus, depending
upon the experimental conditions, there are two very
distinctive estimates of μs. The higher value was obtainedfor Ms/Vw ratios equal to or greater than 0.13 g/ml, and fortumbling at 9 rpm.
4. Discussion and conclusions
Batch experiments can be used to obtain information onvirus attachment to sand grain surfaces. Results of this study
show that the method of mixing has a very substantial effecton virus attachment. We believe that complete mixing of thesand and water was not achieved in the rolling experiments
since much of the sand remained in the lower part of thetube, while water was occupying the remainder of the tube.
In this case, viruses had to move (by diffusion and someadvection) from the water-only region to the water–sandregion before they could attach. Much better mixing wasachieved by tumbling the tubes. More complete mixing
implies fewer mass transfer limitations and hence more
immediate physical contact between the free viruses insolution and the sand grains. For experiment 1d, underrolling conditions, virus attachment was of a similar order ofmagnitude as for the tumbling experiments. This may beascribed to the high sand–water ratio, which provides more
surfaces for attachment and a better distribution of the sandwithin the tube, and hence better mixing leading to more
complete attachment.
Fig. 3 presents katt values as a function of Ms/Vw, wherea linear relation between Ms/Vw and katt is apparent. A
multivariate regression analysis showed that the increase in
katt due to an increase in Ms/Vw was the same for both seriesof experiments. In the case of experiment series 1, theintercept was not significantly different from zero (Table 2).
This is important because if there is no sand in the container,
there cannot be any attachment to sand. The linear trend forexperiment series 2, however does not go through the origin.
There is a steep rise from 0 to about 0.6 h−1in the Ms/Vw
value range of 0–0.036 g/ml. So, the relationship is nonlinear.
In both series of experiments, more sand in the container
leads to an increase in katt.
Fig. 4 presents kdet values as a function of Ms/Vw. The data
here also seem to indicate a linear relationship, but withdifferent trends for the two series of experiments. Multivariate regression analysis revealed a significant correlation
with Ms/Vw, whereas in series 2, the opposite trend wasfound. Series 1 exhibited a decrease in kdet with increasing
Ms/Vw, whereas the opposite occurred for series 2. In thelatter case, the intercept was not significantly different fromzero. Again, obviously, there cannot be detachment from thesand if there is no sand in the container. For series 1, the highkdet values at low solid–water ratio are questionable. The
estimates for those experiments (1a and 1c) were inaccurate
because of a very gradual transition from the kinetic phase to

Fig. 3. Attachment rate coefficient katt as a function of Ms/Vw.

quasi-equilibrium, and the limited number of observations in
the quasi-equilibrium stage.
Notice that the kdet value of experiments 1d and 2d forrolling and tumbling, respectively, was similar for the highest
solid–water ratio case. This again can be attributed to the
distribution of sand in the water phase. The linear increase in
the value of kdet with increasing solid–water ratio during
tumbling may be ascribed to an increase in hydrodynamic
forces or higher collision frequencies between sand particles.
This would facilitate virus detachment at the higher solid–
water ratio. Also, with the tumbling method of mixing, alarger value of μs was obtained. This was specially so forhigher Ms/Vw ratios. This suggests that hydrodynamic forces
may be damaging virus particles for those conditions.
Another important finding relates to the time required forreaching quasi-equilibrium. Fig. 2 demonstrates that this timeis shorter for larger solid–water ratios. For experiment 2a, theequilibrium time was about 20 h, but for experiment 2d only
about 4 h. This also means that for batch experiments withviruses, soil and water, it is important to collect samples during
both kinetic and quasi-equilibrium phases of an experiment.
Moreover, to accurately determine kdet as well as μs, a sufficientnumber of samples during the quasi-equilibrium phase isrequired.
The variability in kinetic parameters as a function of Ms/Vw
ratio and agitation method indicates that obtaining kinetic
parameters of virus removal in porous media from batch
experiments is not straightforward. Our study suggests that
performing kinetic batch experiments is as laborious as column
experiments with regard to set up, operation, sampling andparameter estimation.
Another important question is how to upscale results ofbatch experiment to column and larger scales. In this regards,
we compared our batch results with parameter values
obtained from column experiments at the same conditions,
i.e., pH 7 and ionic strength of 20 mM (Sadeghi et al., 2011).
Table 2
Regression analysis of katt, kdet as a function of Ms/Vw.
katt

Intercept (h−1)
Slope (h−1 g−1 ml)
R2

kdet

Series 1

Series 2

Series 1

Series 2

0
1.59
94.3%

0.67
1.59

0.024
−0.02994.4%

00.0046

G. Sadeghi et al. / Journal of Contaminant Hydrology 152 (2013) 12–17

17

The authors thank Jan Gerritse, Alette Langenhoff, and Fredericke
Langenhoff of the Geo Environment Research Laboratory forfacilitating the experimental work. We also acknowledge partial
support by CAPES-Brazil.

References

Fig. 4. Detachment rate coefficient kdet as a function of Ms/Vw.

The value of katt from those experiments was 0.21 h−1,which is lower than all katt values obtained from the batch
experiments under tumbling conditions. Given the fact thatthe chemical conditions were the same, the sticking efficiency of the column and batch experiments may be assumed tobe the same too. This implies that hydraulic conditions incolumn and batch experiments differ. Thus, the probability ofcollision of virus particles with the sand grains in batch
experiments is much higher than in a sand column. This may
seem contradictory to the fact that Ms/Vw ratios in column
experiments are almost always higher than in batch experiments. However, the solid phase in column experiments is
stationary and hence the frequency of collision of viruses
with soil grain surface is lower. This should be the main
reason why katt values are lower in column experiments.
Another important shortcoming of kinetic batch experiments isthat they do not provide any information about the possible
dependence of kinetic rate coefficients on the flow velocity,
since there is no flow. Column experiments, however, may bedesigned to provide such information.
The usual practice of determining distribution coefficientsfrom batch experiments is questionable for viruses. Suchexperiments are commonly based on one single measurement of the virus concentration after only a few hours, thus
assuming that equilibrium is reached and that virus inactivation is negligible. Our results show that much longer times
are needed for quasi-equilibrium to be reached. Inactivationin that case cannot be neglected anymore. Hence, the proper
way of performing batch experiments with viruses requires
determining virus concentrations for an extended period oftime, and evaluating all attachment and inactivation rate
coefficients. This means that well-executed batch experiments are as laborious as column experiments. As such, we
conclude from our study that there are no major advantagesof doing batch experiments for viruses as compared tocolumn experiments.
Acknowledgments
The first author acknowledges the Iranian Ministry of
Health and Medical Education for support of his PhD studies
at Utrecht University. Pieter J. Kleingeld is greatly acknowledged for his technical support. Dineke van de Meent andHelen de Waard of the Geochemistry Laboratory are highly
acknowledged for their support during experimental work.

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