Opening
A mixture is a togetherness that does not have to last. Rice with a few stones, flour with a dropped pin, seawater with salt you would like to keep, curd that can become butter. Separation is the art of sending each substance to a different place. The method is never a guess from a list. It is a reading of the difference.
When the pieces are large enough to see
Handpicking separates solids by differences you can see: size, colour, or shape. Stones out of rice, a spoiled grain out of a handful. It works when the unwanted piece is few and large enough for fingers. It is a poor plan for a sack of sand mixed with salt. The fingers would die of boredom before the mixture did.
Threshing separates grain from stalks by beating the stalks so the grains fall free. Farms do it with sticks, or with animals walking over the harvest, or with machines. The difference used is simple. The grain lets go of the stalk when it is struck.
Winnowing separates lighter husk from heavier grain by wind, or by air you blow. The grain falls close. The husk rides farther. Standing on a windy day with a basket is an old experiment that still works. The difference is weight in the air, not colour.
Sieving separates solids by particle size. A sieve is a mesh with holes of a chosen size. Fine flour passes. Coarse bran stays. Sand can be taken out of a mix of pebbles. If both substances have the same size of piece, a sieve is useless. The holes cannot take sides in a tie.
When one partner will not mix, or will
Sedimentation is the settling of a heavier insoluble solid to the bottom of a liquid. Muddy water left alone grows a clearish layer on top and a mud layer below. The solid was never dissolved. It was only floating and then tired.
Decantation is pouring that liquid off gently, so the settled solid stays. It is sedimentation's second step. Pour too fast, or too late in the glass, and you invite the mud back into the drink.
Filtration separates an insoluble solid from a liquid by passing the mixture through a filter: cloth, filter paper, a fine strainer. Tea leaves stay in the strainer. Sand stays in the cloth. Clearer liquid passes. Filtration cannot catch salt that has dissolved. Dissolved particles are smaller than any kitchen hole. People who try to strain salt water to get drinking water without removing the salt are hoping the cloth will do a job it was never built for.
Evaporation separates a dissolved solid by letting the liquid become vapour. Seawater in a shallow pan, under the sun, leaves salt. The water goes. The solid remains. You chose this method because the solid was soluble, so sieving and filtration had already failed.
Condensation can catch the vapour if you want the liquid back too. Vapour meets a cool surface, becomes liquid, and you collect it. Then you have both: salt in the pan, and water from the vapour. Evaporation alone keeps the solid and spends the liquid into the air. Adding condensation is how you stop spending it.
Churning separates butter from curd. The fat globules that were scattered join into butter you can lift out. In many homes, churning also helps separate cream from milk. The difference is that fat does not want to stay evenly hidden once you beat and rest it. It gathers.
Magnetic separation uses a magnet to pull a magnetic substance out of a non-magnetic one. Iron pins from flour, iron scrap from other waste. You already know the rule from the magnet journey. The magnet does not negotiate with plastic beads or with rice grains.
Check yourself
You have salt dissolved in water, and you want the salt. Which method, and why will a sieve fail?
Check yourself
Muddy water is left to stand, then the clear water is poured off. Name both steps.
Choosing in real kitchens and real fields
A single mixture may need a chain. Harvested stalks are threshed, then winnowed, then perhaps sieved. Salt from the sea is evaporated, and if the water is precious, condensed. Flour that has picked up a pin is magnetically separated, not winnowed. The pin and the flour may be similar in "not flying away." They are not similar to a magnet.
Oil and water are a different quarrel from sand and water. Oil floats and does not dissolve. You might decant, or use a separating arrangement that lets the heavier water out from below. The principle stays: use the behaviour that is not shared.
Turn this over
A friend says filtration will make seawater safe to drink. Where is the mistake, exactly?
PauseButter was inside the curd the whole time, invisible as butter. What other "hidden apartness" might be in a mixture you eat, waiting for the right motion to reveal it?