There is another method that produces fully purified water in one step, and that is distillation. A solar still can be built by digging a hole, putting an empty pan in the bottom, setting a bucket full of impure water into the middle of the pan, and then setting a peaked clear plastic sheet over top. This will evaporate the water out of the impurities, collect and condense it inside the plastic, and let it drip down into the empty pan. The problem with this method is that it is very slow and produces relatively little water.
In 1904, Allen Hazen showed that the efficiency of a sedimentation process was a function of the particle settling velocity, the flow through the tank and the surface area of tank. Sedimentation tanks are typically designed within a range of overflow rates of 0.5 to 1.0 gallons per minute per square foot (or 1.25 to 2.5 litres per square meter per hour). In general, sedimentation basin efficiency is not a function of detention time or depth of the basin. Although, basin depth must be sufficient so that water currents do not disturb the sludge and settled particle interactions are promoted. As particle concentrations in the settled water increase near the sludge surface on the bottom of the tank, settling velocities can increase due to collisions and agglomeration of particles. Typical detention times for sedimentation vary from 1.5 to 4 hours and basin depths vary from 10 to 15 feet (3 to 4.5 meters).[6]:9.39–9.40[7]:790–1[8]:140–2, 171
Ozone has been used in drinking water plants since 1906 where the first industrial ozonation plant was built in Nice, France. The U.S. Food and Drug Administration has accepted ozone as being safe; and it is applied as an anti-microbiological agent for the treatment, storage, and processing of foods. However, although fewer by-products are formed by ozonation, it has been discovered that ozone reacts with bromide ions in water to produce concentrations of the suspected carcinogen bromate. Bromide can be found in fresh water supplies in sufficient concentrations to produce (after ozonation) more than 10 parts per billion (ppb) of bromate — the maximum contaminant level established by the USEPA.[14] Ozone disinfection is also energy intensive.
Slow sand filters may be used where there is sufficient land and space, as the water flows very slowly through the filters. These filters rely on biological treatment processes for their action rather than physical filtration. They are carefully constructed using graded layers of sand, with the coarsest sand, along with some gravel, at the bottom and finest sand at the top. Drains at the base convey treated water away for disinfection. Filtration depends on the development of a thin biological layer, called the zoogleal layer or Schmutzdecke, on the surface of the filter. An effective slow sand filter may remain in service for many weeks or even months, if the pretreatment is well designed, and produces water with a very low available nutrient level which physical methods of treatment rarely achieve. Very low nutrient levels allow water to be safely sent through distribution systems with very low disinfectant levels, thereby reducing consumer irritation over offensive levels of chlorine and chlorine by-products. Slow sand filters are not backwashed; they are maintained by having the top layer of sand scraped off when flow is eventually obstructed by biological growth.[10]
Boiling: Bringing water to its boiling point (about 100 °C or 212 F at sea level), is the oldest and most effective way since it eliminates most microbes causing intestine related diseases,[21] but it cannot remove chemical toxins or impurities.[22] For human health, complete sterilization of water is not required, since the heat resistant microbes are not intestine affecting.[21] The traditional advice of boiling water for ten minutes is mainly for additional safety, since microbes start getting eliminated at temperatures greater than 60 °C (140 °F). Though the boiling point decreases with increasing altitude, it is not enough to affect the disinfecting process.[21][23] In areas where the water is "hard" (that is, containing significant dissolved calcium salts), boiling decomposes the bicarbonate ions, resulting in partial precipitation as calcium carbonate. This is the "fur" that builds up on kettle elements, etc., in hard water areas. With the exception of calcium, boiling does not remove solutes of higher boiling point than water and in fact increases their concentration (due to some water being lost as vapour). Boiling does not leave a residual disinfectant in the water. Therefore, water that is boiled and then stored for any length of time may acquire new pathogens.

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This is my second RO-PH90 system. Simply one of the best systems on the market, in my opinion. Uses genuine Dow filmtec reverse osmosis membrane. As anyone familiar with RO knows, filmtec membranes are the gold standard and rank among the elite in rejection rates. This is not your generic RO bought in a hardware store, although some large chains carry it. Input TDS = ~225 ppm, output TDS = ~15-20ppm. Does the job. Have not tested PH yet. Water tastes great as it does with my first system. Change your pre filters once per year or at the recommended %TDS interval and expect this RO membrane to last its full schedule of 3-5 years. This is very important. Incoming water pressure must be at least 50psi in my opinion, for this system to operate as intended. At 75psi, outgoing pressure is like a dream, even with 1/4'' stock tubing. ... full review
The addition of inorganic coagulants such as aluminum sulfate (or alum) or iron (III) salts such as iron(III) chloride cause several simultaneous chemical and physical interactions on and among the particles. Within seconds, negative charges on the particles are neutralized by inorganic coagulants. Also within seconds, metal hydroxide precipitates of the iron and aluminium ions begin to form. These precipitates combine into larger particles under natural processes such as Brownian motion and through induced mixing which is sometimes referred to as flocculation. Amorphous metal hydroxides are known as "floc". Large, amorphous aluminum and iron (III) hydroxides adsorb and enmesh particles in suspension and facilitate the removal of particles by subsequent processes of sedimentation and filtration.[6]:8.2–8.3