Transport of Escherichia coli in 25 m columns - Transport of Multiple Escherichia Coli Transport in Saturated Porous Media - page 66

t

= ∫ M q C t dt ( ) (5.2)

L

0

where q is the volumetric flow rate (mL/min), C is the cell suspension ( # cells/mL) and t is the
time (min).
To verify the distribution in cells 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, Martin et al., 1996).

2 d M

Α = −

c i

(5.3)

ln

( ) 0

i

3 1 − Θ Η L M

i i − 1

where

Α is the dimensionless sticking efficiency of column slice

i ,

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 equation (2). Also the number of retained bacteria in a
slice, as a fraction of the total number of bacteria cells injected in the column was estimated.
This fraction,

1

F , in each segment was calculated as (Lutterodt et al., 2009b)

M − M

F =

i i − 1

(5.4)

i

M

0

5.3 Data Analysis

5.3.1 Extrapolation of tracer breakthrough curves

Observed tracer breakthrough concentrations at 19 and 25.65 m were fitted with second order
polynomial and the coefficient of determination ( R 2 ) was applied to evaluate the goodness of fit.
R 2 -values greater than 0.9 were considered good. Equations generated from fitting were applied
to extrapolate data for the incomplete section of the curves. Tracer recoveries were then
computed from the extrapolated curves. The Pearson's mode skewness coefficient was applied to
measure the skewness of tracer breakthrough curves.