Figure that the solar heated evaporator surface is 10 cm (4 inches) above the sea surface. In the last post, a 0.1 mm (100 micro-meter) diameter capillary was found to lift seawater 29.1 cm. We only have to lift it 10 cm, so we have (19.1 cm)(1024 kg/m3)(9.8 m/s2) pressure available to overcome viscous friction. Poiseuille's formula tells us that the quantity of water pumped per second is proportional to the fourth power of the radius times the pressure difference divided by (viscosity)(length). Surface tension and viscosity of sea water are about the same as the respective values for fresh water. I used 1.0E(-6) m2/s for the kinematic viscosity. Multiply that by the density to get the viscosity used in the denominator of Poiseuille's formula. The result is that a single capillary tube transports 4.59E(-11) m3/s.

I assumed a 27C ambient air temperature and 60% relative humidity for the area around Sydney, Australia, where we might want to place evaporator rafts to enhance the humidity of air coming from the Coral Sea. I assumed various evaporator surface temperatures and calculated the radiation, convection, and evaporation loss. At a surface temperature of 45C the sum of the losses equalled the solar input that we might expect at noon on December 21 at the 34 deg S latitude of Sydney. The evaporation rate is 1.72E(-4) kg/s per square meter of evaporator surface. This is fresh water, so we have to pump a slightly greater mass of sea water to supply it. But then we divide by the greater density of sea water to compute the volume flow. The result is that we must pump 1.72E(-7) m3/s for the 1 m2 panel. Dividing by the flow per tube, we require 3750 capillary tubes, which is an array of slightly more than 61 rows and 61 columns.

The only way I know to get 0.1 mm holes 10 cm long is to heat a larger diameter glass tube and pull it down to the required inner diameter. The largest practical outer diameter would enhance ruggedness and ease of handling. The evaporator module would have a hollow plastic tube rectangular frame around the outside with a tubular X-brace to resist diagonal forces. This sealed tubular frame would provide the flotation and rigidity for a thick panel. The glass capillary tubes could be cemented into holes drilled in the panel. There must be some type of ribbing to protect the long capillary tubes during rough handling and impacts from objects. There's a lot to do here. The first step is to get some capillary tubing, put it in water, and see if it pumps.

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