I previously calculated (in Fast sea salt evaporator) that the enthalpy of vaporization of water (2.26 MJ/kg) and terrestrial mean insolation (180–280 W/m² at temperate latitudes) make solar evaporation a relatively inefficient method of desalination: 80–120 mg/m²/s of water. This also makes sea salt production relatively inefficient. Indeed, these efficiencies are so low that even normally abundant solar thermal energy only permits their use in niche cases.
By comparison, the Sorek reverse-osmosis desalination plant forces water through semipermeable membranes at 7.1 MPa, producing drinking water at a total cost of US$0.58/kℓ. 7.1 MPa × 1 kg/ℓ is 7.1 kJ/kg, or 0.0071 MJ/kg, about 320 times less energy than the enthalpy of vaporization. 7.1 kJ/ℓ works out to 2.0 kWh per kiloliter, which costs between US$0.08 and US$0.24 at 4¢ to 12¢ per kWh, current US electrical prices. By contrast, 2.26 MJ/kg works out to 630 kWh/kℓ, which would be US$25 to US$75 per kiloliter, compared to Sorek’s US$0.58. (The reason solar desalination happens at all is that you don’t have to buy the energy.)
However, vaporizing water once with solar energy is a silly way to do things. When that water condenses, it releases its enthalpy of vaporization again. If you could harness that heat released in condensation to vaporize more water, even a few stages of the process would improve the efficiency of the system dramatically, although 17 stages would be needed to bring it closer to Sorek’s consumption. However, 5 stages would reduce the energy consumption to 450 kJ/ℓ, or, say, increase to 500 mg/m²/s.
A tricky problem is that you need to deliver this condensation heat into water that is cooler than the condensing steam or water vapor, for example by running the steam through coils cooled by water that is evaporating. It would be sufficient, if perhaps not necessary, for the coolant water to be boiling — but at a lower temperature. This approach requires that each successsive stage of the desalination apparatus operate at a successively lower pressure — exponentially lower: 85 kPa for 95°, 70 kPa for 90°, 58 kPa for 85°, 47 kPa for 80°, 39 kPa for 75°. The water thus produced needs to be pumped out of these partial-vacuum chambers against this pressure — 62 kPa for the 75° chamber. While this is less than 1% of the pressure used in the Sorek reverse osmosis plant, and therefore will not add a significant energy cost, it still represents machinery that adds significant complexity to the apparatus.
I suspect that this quintuple-acting vacuum cascade approach will make solar water distillation sufficiently more inexpensive to permit its use in a wide variety of settings where it is currently too expensive.
Update: this method is called "multi-stage flash distillation" and is currently in widespread use; reverse osmosis typically uses less energy, as described above, so few new MSF plants are being built. The margin is sufficiently large that you can desalinate a larger amount of water per sunlight joule even by powering a reverse-osmosis plant from photovoltaic panels.