This is the way that Glen Gruby explained sand filters in his term paper writen in BASIC in 1987.
Filtration of suspended solids is a widely used method in water purification systems. There are many types of filters in use for different processes but granular column filters are most common for drinking water purification.
The principle behind their use is that particles suspended in the liquid are transported to the media by flow through the column and bed and are trapped in the media pores.
There are three types of granular filters commonly used: slow sand, rapid sand, and multimedia. Slow sand filters consist of fine sand, supported by gravel. They capture particles near the surface of the bed and are usually cleaned by scraping away the top layer of sand that contains the particles.
Rapid sand filters consist of larger sand grains supported by gravel and capture particles throughout the bed. They are usually then cleaned by backwashing water through the bed to 'lift out' the particles.
Multimedia filters consist of two or more layers of different granular materials, with different densities. Usually, anthracite coal, sand, and gravel are used. The different layers combined may provide more versatile collection than a single sand layer. Because of the differences in densities, the layers stay neatly separated, even after backwashing. There are four major mechanisms by which particles attach to filter media: diffusion, inertia, interception, and hydrodynamics.
Diffusion towards media granules occurs for very small particles, such as viruses. Particles move randomly about within the fluid, due to thermal gradients. This mechanism is only important for particles with diameters < 1 micron.
Attachment by inertia occurs when larger particles move fast enough to travel off of their streamlines and bump into media grains.
Interception of particles is common for large particles. A streamline may lie very close to the media surface. If a large enough particle follows the streamline, it will hit the media grain and be captured. Hydrodynamic attachment, due to local turbulences and pressure fluctuations gets small particles caught up in eddies to spend a lot of time in the filter bed and eventually get captured.
For this reason also, small particles that are not captured generally take longer time to pass through the bed than do larger particles. Head losses are inherent in granular filters. As a fluid passes through a filter bed, head loss increases. As particles build up in the bed, head loss increases until the filtering flow rate is inefficiently slow. At this point, the bed is usually backwashed.