g v volumetric mass density of the water volumetric mass density of the particles in suspension diameter of the particles
In sedimentation zones the flow conditions are laminar. A place is available for the settling of sludges contained in the water to be filtered.
Although the total inner surface that is available for the formation of deposits in a filter sand bed is important, only a part of this is available in the laminar flow zones that promote the formation of deposits. Usually material with a volumetric mass slightly higher than that of water is eliminated by sedimentation during filtration. Such matter could be, for example, organic granules or particles of low density. In contrast, colloidal material of inorganic origin-sludge or clay, for instance—with a diameter of 1 - 10 /¿m is only partially eliminated by this process, in which case the settling velocities in regard to the free surface become insufficient for sedimentation.
The trajectory followed by water in a filter mass it is not linear. Water is forced to follow the outlines of the grains that delineate the interstices. These changes in direction are also imposed on particles in suspension being transported by the water. This effect leads to the evacuation of particles in the dead flow zones. Centrifugal action is obtained by inertial force during flow, so the particles with the highest volumetric mass are rejected preferentially.
Diffusion filtration is another contributor to the process of sand filtration. Diffusion in this case is that of Brownian motion obtained by thermal agitation forces. This compliments the mechanism in sand filtration. Diffusion increases the contact probability between the particles themselves as well as between the latter and the filter mass. This effect occurs both in water in motion and in stagnant water, and is quite important in the mechanisms of agglomeration of particles (e.g., flocculation).
The next mechanism to consider is the mass attraction between particles which is due to van der Waals forces. These are universal forces contributing to the transport and fixation mechanism of matter. The greater the inner surface of the filters, the higher is the probability of attractive action. Van der Waals forces imply short molecular distances, and generally play a minor role in the filtration process. Moreover, they decrease very quickly when the distance between supports and particles increases. Nevertheless, the indirect effects, which are able to provoke an agglomeration of particles and, thus, a kind of flocculation, are not to be neglected and may become predominant in the case of flocculation-filtration, or more generally in the case of filtration by flocculation. Electrostatic and electrocinetic effects are also factors contributing to the filtration process. Filter sand has a negative electrostatic charge. Microsand in suspension presents an electrophoretic mobility. The value of the electrophoretic mobility, or of the corresponding zeta potential, depends on the pH of the surrounding medium. Usually a coagulation aid is used to condition the surface of microsand. In filtration without using coagulant aids, other mechanisms may condition the mass more or less successfully. For instance, the formation of deposits of organic matter can modify the electrical properties of the filtering sand surfaces. These modifications promote the fixation of particles by electrokinetic and electrostatic processes, especially coagulation. Also, the addition of a neutral or indifferent electrolyte tends to reduce the surface potential of the filtering sand by compression of the double electric layer. This is based on the principles of electrostatic coagulation. The sand, as the carrier of a negative charge spread over the surface of the filter according to the model of the double layer, will be able to fix the electropositive particles more exhaustively. This has a favorable effect on the efficiency of filtration of precipitated carbonates or of floes of iron or aluminum hydroxide-oxide. Optimal adherence is obtained at the isoelectric point of the filtrated material. In contrast, organic colloidal particle carriers of a negative charge such as bacteria are repulsed by the electrostatic mechanism in a filter with a fresh filter mass. In this case, the negative charges of the sand itself appear unchanged. With a filter that is conditioned in advance, there are sufficient positively charged sites to make it possible to obtain an electrochemical fixation of the negative colloids.
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