Suspensions Containing Charged Particles

Electrostatic interactions are present in materials that contain ions. These include aqueous solutions of acids, bases, salts, polyelectrolytes (i.e., charged polymers), as well as colloidal suspensions of charged particles or droplets. Although fluids containing charged surfaces and mobile ions maintain electroneutrality overall, locally there are often eharge imbalances. 

Keep in mind that Eqs. (8-14) are only valid for small Kr, when the electrophoresis retardation (electric-field-induced movement of ions in the electric double layer, which is opposite to the direction of particle movement) is unimportant [41J. This limitation is inherent to the Hiickel equation. Practically, a colloidal suspension always contains charged particles dispersed in a medium with surfactants (or electrolytes) of both polarities. In this case the Poisson s equation must be used for deriving the surface charge density and Zeta potential relationship. Under the Dcbyc-Hiickel approximation, i.c., the small value of potential, zey/ kgT, where v is the potential and z is the valency of ion, a simple relationship between the surface charge density and Zeta potential can be easily obtained [7], The Poisson s equation simply says that the potential flux per unit volume of a potential field is equal to the charge density in that area divided by the dielectric constant of the medium. It can be mathematically expressed as ... 

Gl) have also derived a similar modified equation for the case of a drop of conducting liquid surrounded by a gaseous suspension of both neutral and charged particles, enclosed in a spherical container. 

In this experiment the optical and electrical transients were recorded simultaneously for a dispersion containing relatively high particle concentration. The current-time curve reveals that in the initial movement, two species transit the cell at different times. Clearly both cannot be due to the movement of the particles across the cell the simultaneous optical measurement demonstrates that the motion of the charged particles is contributing only to the second maximum. The first peak is due to excess ions in the suspension, presumably the charge control agent which is put in specifically to assure proper charging of the suspended particles. 

If photons of sufficient energy are incident on a semiconductor, excess electrons and holes are created in the semiconductor conduction and valence bands respectively. Further, if the semiconductor is fabricated to contain one or more p-n junctions, the chemical potential of the excess carriers can be converted into a flow of charges resulting in an electric current. This current can then be used to power the direct electrolysis of water. Alternatively, the excess charge carriers can migrate to the semiconductor surface where they initiate chemical reactions and produce H2 and/or 02 in the surrounding medium either in a PEC or in a suspension of semiconductor particles. 

Another important application is water suspensions of charged colloids in the form of ore particles such as silica and silicate. These systems can be destabilized by addition of surfactants followed by a separation of the ore by froth flotation procedure. This is of great importance for the mineral industry, while it permits large-scale and economic processing of crushed ores, where the desired mineral is separated from the non-mineral containing... 

Consider a concentrated suspension of charged spherical soft particles moving with a velocity 17 in a liquid containing a general electrolyte in an applied electric field E. We assume that the particle core of radius a is coated with an ion-penetrable layer of polyelectrolytes with a thickness d. The polyelectrolyte-coated particle has thus an inner radius a and an outer radius b = a + d. We employ a cell model [4] in which each particle is surrounded by a concentric spherical shell of an electrolyte solution, having an outer radius c such that the particle/cell volume ratio in the unit cell is equal to the particle volume fraction 4> throughout the entire dispersion (Fig. 22.1), namely. 

For charged particles, the net charge contained by the solvent must balance that carried by the particles. Suppose, in addition to these counterions, there is a concentration Ub of a symmetric electrolyte, where is the number of ion pairs per unit volume of suspension the concentration of ion pairs in the liquid phase is = nb/(l—0). The inverse square Debye length from both contributions then works out to be (Russel et al. 1989)... 

In Figure 2 are represented the electro-optical effect a, the electrophoretic mobility Ue, and the relaxation time r of the particle disorientation after the switching off of the electric field as a function of the initial polyelectrolyte concentration. One observes that the a and r variations correspond to the variation of f/e, i.e., the electrostatic attraction of the polyelectrolyte to the oppositely charged surface, which is the main driving force for the adsorption, governs the electro-optical behavior and stability of the suspension containing this polyelectrolyte. 

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