Environmental Engineering Reference
In-Depth Information
the DLVO theory, according to which, interparticle
forces are regarded as the sum of electrostatic repul-
sion and van der Waals attraction.
The electrostatic repulsion force assumes that the
colloidal particles are charged, which has been estab-
lished by electrophoresis, when colloidal particles
move under the infl uence of an electric fi eld. In clay
sols, the particles move toward the positive elec-
trode, indicating that the clay particle is negatively
charged. On the other hand, ferric hydroxide sols are
positively charged, because the particles move toward
the negative electrode.
The charge on the colloidal particle is compen-
sated for in solution, because the whole hydrophobic
sol must be electrically neutral, like an ionic solution.
The idea of the electric double layer was used to
explain the internal balance of charges in a soil.
arises as to why the particle is charged; there are two
possibilities. Firstly, when the charge on the particle
originates from interior crystal imperfections such as
isomorphic substitution in clay minerals, the charge
per unit surface area (the charge density) is a fi xed
quantity, or a permanent charge. The second possi-
bility, whereby a particle does not have any interior
crystal imperfections, is that the surface charge can
be created by adsorption or chemical reaction of
species from the solution on the reactive sites of the
particle. This is called a variable charge.
The addition of an electrolyte to a stable hydro-
phobic sol changes the electric double layer confi gu-
ration, leading to compression of the diffuse
counter-ion atmosphere at the surface. The degree of
compression of the double layer is proportional to
the increase in electrolyte concentration. This effect
is determined mostly by the concentration and
valency of the counter ions, whereas the infl uence of
co-ions is comparatively small. This phenomenon is
based on the empiric Schulze-Hardy rule, which
established that counter ions with higher valency are
more effi cient fl occulating agents for hydrophobic
colloids (Atkins 1994).
3.2.2 The electric double layer
The electric double layer can be described as a charge
located on the surface of the particle and a counter-
ion charge in the surrounding liquid phase. The
counter-ions undergo two opposite tendencies: they
are attracted by the oppositely charged surface; and
they have a tendency to move away from the surface
toward the bulk solution, where their concentration
is lower. The two opposite tendencies (electrostatic
attraction and diffusion in the other direction) result
in an equilibrium distribution of the counter-ions
near the surface of the particle. This theory was fi rst
introduced by Gouy in 1910 and then Chapman in
1913, in a model that considers the diffuse character
of the counter-ion atmosphere and is referred to as
the diffuse layer or Gouy-Chapman layer. In the
diffuse layer, the non-uniform distribution of ions
with the same charge as the particle is also consid-
ered, because these ions are depleted from the region
near the surface owing to electrostatic repulsion.
Mathematically, the Gouy-Chapman layer uses
both electrostatic repulsion and diffusion (the
Poisson-Boltzmann equation) to obtain the exact
distribution of positive and negative ions as a func-
tion of distance from the surface. The average electric
potential is also computed: starting with a maximum
value at the surface and decreasing roughly exponen-
tially with distance from it.
The origin of the double-layer is therefore the
surface charge on the particle. The question then
3.2.3 Double-layer repulsions
The thermal kinetic energy of colloidal particles in a
hydrophobic sol gives rise to Brownian motion,
which can bring two particles so near each other that
their diffuse counter-ion atmospheres begin to
overlap, causing electrostatic repulsion. The repul-
sive potential energy is the amount of work required
to bring the particles from infi nite separation to a
given distance between them. From the DLVO
theory, it is possible to plot the repulsive potential
energy (
V
R
) as a function of distance, which gives a
roughly exponentially decreasing value of
V
R
with
increasing particle separation. Such plots are called
potential energy curves.
The range of repulsive infl uence is considerably
diminished by the increase in electrolyte concentra-
tion, owing to compression of the double layer.
3.2.4 van der Waals attractions
For fl occulation to occur, attractive forces must over-
come the double-layer repulsion. Attractive interac-
tions are attributed to van der Waals forces, which
