Introduction - Transport of Multiple Escherichia Coli Transport in Saturated Porous Media - page 3

where C is the mass concentration of suspended bacteria in the aqueous phase (# of cells/ml), t is
time (s), D is hydrodynamic dispersion coefficient (cm 2 /s), v is velocity (cm/s), S is total retained
bacteria concentration (#cells/gram sediment ) bul Ρ is the bulk density (g/ml), x is the distance
traveled (cm) and Θ is the volume occupied by the fluid per total volume medium (-). The first,
second and third terms on the right hand side of equation (1.1) represent transport by
hydrodynamic dispersion, advection and particle deposition, respectively. The retained bacteria
fraction is given by a first-order kinetic term expression:

∂ S Θ

Ρ

(1.2)

= k C

a

∂ t

bulk

where k (s -1 ) is the attachment rate coefficient. For steady state conditions and negligible
hydrodynamic dispersion and for continuous particle injection at concentration C (at x=0) and
time, t , the solution to equations (1.1) and ( 1.2 ) for a column initially free of particles is
described by:

k

( )

C x = C

0 exp

−

a

x (1.3)

v

and

t Θ

Ρ

k

( ) ( )

S x =

0 a

C x (1.4)

bulk

Equation (1.3) describes the colloid filtration theory (Yao et al., 1971, Iwasaki, 1937). Yao et al.
(1971) described the attachment rate coefficient (s -1 ) as related to the single collector contact

k

efficiency (

Η) (-) and the dimensionless sticking (collision) efficiency ( Α ) by the following

expression

3(1 − ΘΑΗ ) v

k =

0

(1.5)

a

2 d

c

where d is the mean grain (collector) diameter (cm). The collision efficiency ( Α ) represents a
percentage or fraction of colloids that successfully strike and stick to a collector surface.

The experimentally determined single collector removal efficiency (SCRE), Η (-) and the
attachment efficiency are also obtained under negligible hydrodynamic dispersion at steady state
over total transport distance as

2 d C

c

Η = − ln (1.6)

3 (1 − Θ ) L C

0