Transport of Escherichia coli strains isolated from spring water - Transport of Multiple Escherichia Coli Transport in Saturated Porous Media - page 83

6.2.5 Segment sticking efficiency and bacteria fraction retained

To verify the distribution in cell affinity for collector surfaces, sticking efficiencies within
column segments were computed for a fraction of cells retained in a column slice as
(Lutterodt et al., 2009a, Chapter 2 of this thesis, Martin et al., 1996):

2 d M

Α = −

c

ln

i

(6.1)

( ) 0

i

3 1 − Θ Η L M

i i − 1

d is the median of the

where

Α is the dimensionless sticking efficiency of a column slice i ,

Η is the single collector contact efficiency (-), Θ is the

grain size weight distribution (m),

total porosity of the sand (-), and

L is the length of the column slice i , i.e. the distance (m)

between two sampling ports.

M − is the total number of cells entering slice i , obtained from
the breakthrough curve determined at the upper sampling port of slice i and M is the total
number of cells, obtained from the breakthrough curve determined at the lower sampling port
of slice i using (Kretzschzmar et al., 1997):

1

t

= ∫

(6.2)

M q C t dt ( )

i

0

where q is the volumetric flow rate (ml/min), C is the cell suspension (# cells/ml) and t is
time (min). The Tufenkji-Elimelech (TE) correlation equation (Tufenkji and Elimelech,
2004a) was used to compute Η. Thereto, 1055 kg/m 3 was assumed for the bacteria density,
while the Hamaker constant was estimated to be 6.5×10 -21 J (Walker et al., 2004).
The number of retained bacteria in a quartz sand column slice, F , as a fraction of the total
number of bacteria cells injected in the column was calculated as (Lutterodt et al., 2009b,
2011; Chapters 4 & 5 ):

M − M

F =

i i − 1

(6.3)

i

M

0

where

M is the total number of E. coli cells in the influent suspension.

6.3 Data analysis

A power-law distribution was used to assess the degree of association between F and Α and
the coefficient of determination ( R 2 ) was applied to evaluate the goodness of fit. Fitting was
considered excellent when R 2 > 0.90, and for 0.8 ≤ R 2 ≤ 0.9 fit was considered good and
when R 2 <0.80 fit is considered weak. With these power-law equations the minimum sticking
efficiencies were calculated. In order to do this,

F was assumed to be 0.001% of the initial

E. coli mass introduced into the column.