Nonconducting particles

If a conduc tor particle and a nonconduc tor particle are just separated from contac t with a charged plate, the conductor particle will be repelled by the charged plate and the nonconducting particle will be neither repelled nor attracted by it. 

The electrozone sensing technique, also called the Coulter principle, was originally developed for biomedical applications for counting blood cells. This method counts and sizes particle based on changes in the electrical resistance caused by nonconductive particles suspended in an electrolyte. It presently finds uses in a wide variety of industries, including the food, environmental, coatings, ceramics, and metals industries. 

Nonconducting particles of the mixture are acted upon by induction so that they acquire equal and opposite charges, the total net charge being zero. On the other hand, conducting particles present in the mixture permit the flow of electricity, with the result that they assume a charge of the same polarity as the plate or cylinder. An electrode of polarity opposite that of the plate or cylinder will therefore attract the conducting particles. 

A simple expression for the electrophoretic velocity of a uniformly charged nonconducting particle is the Smoluchowski equation [1]... 

A comparison of these expressions is given in Table I. This table shows the increase in the mixture resistance due to the presence of nonconducting particles or droplets, - Rj, divided by the fluid resistance as a function of the dispersed-phase concentration. R and Rj are the mixture and fluid resistances, respectively. Maxwell s (68) and Bruggeman s (74) relations give... 

Operation. The operation of the probe relies on the variation of the slurry resistivity as the solids concentration changes. To understand the probe s principle, assume the probe is surrounded by a conducting liquid such as tap water then if a potential is applied across the field electrodes (of the order of 5 V), a small current flows from one field electrode to another. The value of this current, for a fixed probe geometry and applied signal, depends on the total resistance of the medium surrounding the field electrodes. If nonconducting particles (e.g., sand particles) are added to this fluid, then the resistivity of the mixture will increase. As the solids concentration is increased, the mixture resistivity increases, and consequently the field circuit current diminishes. 

The velocity of migration of the particles (/Tg) under unit applied potential can be determined microscopically with a timing device and an eyepiece graticule. For nonconducting particles, the Henry equation is used to obtain 5 from /Tg. This equation can be written in the form... 

The maximum charge that can be acquired by a spherical, nonconducting particle in a uniform electric field was determined by Pauthenier " and is... 

The electrostatic attraction forces of electrical conductors and of insulators with excess charges are smaller than the van der Waals forces. However, the influence of roughness is less pronounced and disappears completely for nonconducting particles facing a plane with an opposite charge of the same density. 

Charged particles influence the net conductivity in several ways (1) the presence of particles having dielectric constant and conductivity different from those of the medium affects the local electrical field and the conditions for ion transport (e.g., nonconducting particles act as obstacles to the electromigrating ions and polarize the incident electric field) (2) the inaeased ionic concentration in the diffuse ion... 

The contribution of the particle surface conductivity (effect (2)) for a thin EDL can be accounted for phenomenologically in a similar way, and the final result for nonconducting particles reads ... 

In analyzing the electrophoretic motion of a nonconducting particle where the Debye length is small compared with the characteristic particle dimension, say the radius, we may neglect curvature effects in the diffuse part of the double layer and treat the particle surface as locally plane. The electric field may therefore be considered to be applied parallel to the surface, and the analysis carried out in Section 6.5, in which electrical and viscous forces were balanced to determine the electroosmotic velocity for a fixed surface, applies here unchanged. Therefore in a reference frame in which the particle is stationary, from Eq. (6.5.5) we may write... 

This is just the Helmholtz-Smoluchowski equation, as might have been expected, since electrophoresis is just the complement of electroosmosis. Its derivation shows that the electrophoretic velocity of a nonconducting particle is independent of the particle size and shape for a constant surface potential when the Debye length is everywhere small compared with the characteristic body dimension. Note that Eq. (7.2.6) differs from the Huckel large Debye length result (Eq. 7.2.2) only by the factor. ... 

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