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Expect simple filtration by gravity to use less energy than distillation (where you have to take the material to its gaseous state) so it will be cheaper, but if you're considering reverse osmosis (a hi-tech form of filtering) against solar-powered distillation (in a solar still), the running costs of R-O are large, the running costs of a solar still are small.

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Q: Distillation and Filtration which is cheaper?
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