Rapid-sand filtration requires some form of treatment prior to the actual filtration. This pretreatment can be achieved by coagulation and sedimentation. The water is treated with a coagulant which flocculates the particles, carrying most of the suspended matter to the bottom of the sedimentation tank. Most common coagulating agents contain Fe+2, Al+3, Fe+3, or Ca+2. The objectives of using such pretreatment are 1) it will increase the state of aggregation of the particles comprising the filter cake, and 2) it will help to maintain thefiltration rate while increasing the life of the filter bed [2].
Efficient filtration consists of both particle destabilization and particle transport. In order for the particles to be removed from the fluid, they should be "sticky', or more formally, destabilized. At their colloidally unstable state, the suspension particles no longer repel each other; instead they adhere to existing deposits [3]. This is based on the DLVO theory. The DLVO theory views the stability of colloids as arising from the electric charge of the particles and the consequent electrical repulsion between them. Opposing this repulsion are attractive forces of the universal van der Waals type. If the repulsion forces can be reduced sufficiently so that van der Waal's attractive forces become dominant, then particles colliding with each other will stick together to form more-or-less permanent aggregation [2]. The formation of "bridges" between particles through flocculation, adsorption of charged polymers, and charge-neutralization also support the explanation of attachment of particle suspensions.
Prior to the attachment of particles to the surface, the transport of suspended particles to the immediate vicinity of the solid-liquid interface must take place (i.e., to a grain of the media or to another particle previously retained in the bed). The capture mechanisms, which are characterized by dimensionless ratios are interception, inertia, gravity, diffusion and hydrodynamic.
Water flow through a filter follows Darcy's law. Darcy's law states that in all cases of filtration the flow is in the laminar range and that pressure drop is governed by the flow rate. Cleasby and Bauman at Iowa State University showed that even filters that are considerably clogged with deposits, which cause pressure drops that are many times greater than the one's for clean media, still obey Darcy's law [3]. Relationships between permeabilities and the geometry of the porous solid can therefore be explained using the Carmen-Kozeny equation.
The Carmen-Kozeny equation illustrates the calculation of the pressure drop, -dP necessary to maintain a fluid at a superficial velocity mus over a sufficiently large distance L (so that the flow is fully developed) in laminar flow where mu is the fluid viscosity and dg is the grain diameter.
Initially, particles attach to the filter surface and increase the surface area. However, after a certain head loss (-dP) is reached, filtration is minimal. At that point the fluid (water) moves through the channels that are formed and all available areas are clogged up. Thus, as time goes on the velocity keeps increasing but, at a certain point it will reach its steady point.