Colloidal Systems - Surface and Colloid Chemistry: Principles and Applications - page 153

that divalent ions are 60 times as effective as monovalent ions, and trivalent ions are
several hundred times more effective than monovalent ions. However, ions that spe-
cifically adsorb (such as surfactants) will exhibit different behavior.
Based on these observations, in the composition of washing powders, multivalent
phosphates are used, for instance, to keep the charged dirt particles from attaching
to the fabrics after having been removed. Another example is wastewater treatment
where, for coagulation purposes, multivalent ions are used.
Streaming potential : The interface of a mineral (rock) in contact with an aqueous
phase exhibits surface charge. The currently accepted model of this interface is the
EDL model of Stern. Chemical reactions take place between the minerals and the
electrolytes in the aqueous phase, which results in a net charge on the mineral. Water
and electrolytes bound to the rock surface constitute the Stern (or Helmholtz) layer.
In this region, the ions are tightly bound to the mineral, while away from this layer
(the so-called diffuse layer), the ions are free to move about.
Since the distribution of ions (positive and negative) is even in the diffuse region,
there is no net charge. On the other hand, in the Stern layer, there will be asymmet-
ric charge distribution, and thus one will measure from zeta-potential data that the
mineral exhibits a net charge.

7.3 KInetIcS oF coaGulatIon oF colloIdS
Colloidal solutions are characterized by the degree of stability or instability. This
is related to the fact that both kinds of properties in everyday phenomena need to
be understood. The kinetics of coagulation is studied using different methods. The
number of particles, N p , at a given time is dependent on the diffusion-controlled
process. The rate is given by

−d N p /dt = 8 π D R N p 2 (7.27)

where D is the diffusion coefficient, and R is the radius of the particle. The rate can
rewritten as

−d N p /dt = 4 k B T/3 v N p 2 = k o N p 2 (7.28)

where D = k B T /6 π v R , the Einstein equation is applied, and k o is the diffusion-con-
trolled constant.
In real systems, both stable colloidal systems (as in paints, creams) and unstable sys-
tems (as in wastewater treatment) are of interest. It is thus seen that, from DLVO consid-
erations, the degree of colloidal stability will be dependent on the following factors:

1. Size of particles; larger particles will be less stable.

2. Magnitude of surface potential.

3. Hamaker constant ( H ).

4. Ionic strength.

5. Temperature.