# Definitions of flux

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```					    1.7 TRANSPORT OF FLUIDS
IN SOLIDS
•   1.7.1 Permeation
•   1.7.2 Capillary suction
•   1.7.4 Osmosis
•   1.7.5 Electro-osmosis
Definitions of flux
If the flux q is defined as the amount of fluid
flowing per second:
q = AV m3/s
where A is the cross sectional area of material
through which the fluid is flowing. If Q is the
total amount flowing in a time T
Q = qT = ATV          m3
Seepage Velocity
Consider a porous solid with a porosity e. The cross
sectional area available for the fluid to flow in will
be Ae. If the actual velocity (the seepage velocity) of
the fluid in the pores is vs
AV = Aevs
thus:
V = v se         m/s
It may be seen that when the porosity = 1 (e.g. when
a fluid is flowing in a pipe) V = vs
Coefficient of permeability
The         coefficient       of
permeability          (hydraulic
conductivity) k has the units of
m/s is defined from:
V = k (h1 - h2) m/s     h1
x
where the fluid is flowing
through a thickness x (m) with
pressure heads h1 and h2 (m)
on each side.                           h2

x
Intrinsic permeability
The intrinsic permeability K has the units of
m2 and is defined from the equation:
V = K (p1 - p2) m/s
e     x
where e is the viscosity of the fluid (= 10-3 Pas
for water) and p1 and p2 are the pressures on
each side in Pa .
Relationship between
permeabilities
The pressure from a fluid p =  g h where:
g = 9.81 m/s2 ,  = density = 1000 kg/m3 for
water and h = fluid head in m
Thus k (h1 - h2) = K ( g h1 -  g h2)
x          e       x
Thus k =K  g
e
High pressure permeability
measurement
Water
outlet

Hydraulic
oil
Drainage
Plates
Perforated
disc                            Concrete
Sample

Water inlet
The High Pressure Through Flow Cell
Permeability of concrete
1.7 TRANSPORT OF FLUIDS
IN SOLIDS
•   1.7.1 Permeation
•   1.7.2 Capillary suction
•   1.7.4 Osmosis
•   1.7.5 Electro-osmosis
Wetting and non-wetting surfaces

Water on a wetting surface

Water on a non-wetting surface
Capillary Suction
Capillary
tubes
h
h

The height of the column of water in a fully wetting capillary is
h=      2s      m
rg
where: s is the surface tension (= 0.073 N/m for water)
r is the radius of the capillary
 is the density of the fluid (= 1000 kg/m3 for water)
g is the gravitational constant = 9.81 m/s2
“Ink bottle” pore
1.7 TRANSPORT OF FLUIDS
IN SOLIDS
•   1.7.1 Permeation
•   1.7.2 Capillary suction
•   1.7.4 Osmosis
•   1.7.5 Electro-osmosis

A concrete structure which has been
contaminated with de-icing salt heats up in
sunlight

Hot (fast moving)   Cold (slow
particles           moving) particles
1.7 TRANSPORT OF FLUIDS
IN SOLIDS
•   1.7.1 Permeation
•   1.7.2 Capillary suction
•   1.7.4 Osmosis
•   1.7.5 Electro-osmosis
Osmosis

Concrete
Solution with                 Solution with
high salt                     low salt
concentration                 concentration
1.7 TRANSPORT OF FLUIDS
IN SOLIDS
•   1.7.1 Permeation
•   1.7.2 Capillary suction
•   1.7.4 Osmosis
•   1.7.5 Electro-osmosis
Damp proofing with electro-osmosis

Copper plate (positive
voltage)

Floor
Earth rod

Brick wall – water in
it has positive charge
Ground
level
Footing

```
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