Re: [math-fun] California water crisis
Allan: The wicking "space cup" for the astronauts might be slightly relevant: https://www.wired.com/2015/01/coffee-cup-designed-let-astronauts-sip-espress... A Coffee Cup Designed to Let Astronauts Sip Espresso in Space Liz Stinson Design 01.27.15 6:30 am "The cupÂs shape is oddÂ-a little like a plastic baby bootÂ-and was determined by mathematical models. Every curve and geometric shape is designed to encourage the controlled movement of liquid. YouÂll notice a pointed corner in the center of the cup; this strange bit of design is what makes it possible to drink liquids in low gravity. The corner essentially acts like a wick, using surface tension to guide liquid toward your mouth. As soon as an astronaut touches her mouth to the lip of the cup, a capillary connection is formed and the liquid travels up the vessel and forms sippable balls of coffee." At 12:39 PM 4/22/2015, Allan Wechsler wrote:
I have a blue-sky invention, that I have been cherishing in the back of my mind for a decade or so, that is relevant to this discussion.
It's a simple nanotech application -- actually within reach with present methods.
I call it "black tape" because I imagine that is what it would look like. The tape would be coated with a substance, to be designed that would capture ambient water molecules and transport them preferentially in one direction (probably it would be marked with arrows every few centimeters to show the transport direction). When the tape was wetted anywhere, the downstream end would soon start to drip water. The transported water would be reasonably pure, because the surface coating would not be designed to transport, say, salt. One would dip one end in salt water, and the other end would soon start producing fresh water.
There is a minimum energy requirement for desalination, independent of the technology, based on thermodynamics. The osmotic pressure of seawater is 30 atm = 3 MPa. This is the minimum pressure required to force water molecules from seawater through a membrane to pure water on the other side. Thus the minimum process energy is 3 mJ/m^3. Any other process, such as evaporation or freezing, has the same minimum energy cost, since this depends only on the initial and final thermodynamic states. This value assumes the source to be an infinite reservoir with constant salinity as water is extracted. Reverse osmosis requires prefiltering to remove crud that would clog the critical filter. Thus there is an investment in the source brine. If a fraction x of the water has been extracted, the brine salinity is greater by a factor 1/(1-x), and the osmotic pressure is greater by the same factor, assuming the brine sufficiently dilute for van't Hoff's law to hold. To extract a further dx of water requires effort dx/(1-x), and so the effort to extract a total fraction f of the water is int(dx/(1-x),x=0 to f) = -log(1-f). This gets f units of water, so the minimum energy requirement is greater by a factor of (-log(1-f))/f. For example, if half the water is extracted, discharging brine at twice the salinity, the energy required is greater by 2 log 2 = 1.38, or 4.14 MJ/m^3 = 1.15 kWh/m^3. According to [ http://en.wikipedia.org/wiki/Desalination ], reverse osmosis requires 3-5.5 kWh/m^3, just for the reverse osmoses, and excluding the energy needed to operate the facility. -- Gene
During the 197x Energy Crisis, there was an article in Science pointing out the osmotic pressure difference between fresh water & sea water was equivalent to a 900 foot dam. The authors had a proposal to extract some of that as usable energy, building some dam-like gadget at the mouth of a river. Points in favor: sizable new energy source, tolerable cost, known physical chemistry. Against: serious eco-damage, possible membrane issues. Rich ------- Quoting Eugene Salamin via math-fun <math-fun@mailman.xmission.com>:
There is a minimum energy requirement for desalination, independent of the technology, based on thermodynamics. The osmotic pressure of seawater is 30 atm = 3 MPa. This is the minimum pressure required to force water molecules from seawater through a membrane to pure water on the other side. Thus the minimum process energy is 3 mJ/m^3. Any other process, such as evaporation or freezing, has the same minimum energy cost, since this depends only on the initial and final thermodynamic states.
This value assumes the source to be an infinite reservoir with constant salinity as water is extracted. Reverse osmosis requires prefiltering to remove crud that would clog the critical filter. Thus there is an investment in the source brine. If a fraction x of the water has been extracted, the brine salinity is greater by a factor 1/(1-x), and the osmotic pressure is greater by the same factor, assuming the brine sufficiently dilute for van't Hoff's law to hold. To extract a further dx of water requires effort dx/(1-x), and so the effort to extract a total fraction f of the water is int(dx/(1-x),x=0 to f) = -log(1-f). This gets f units of water, so the minimum energy requirement is greater by a factor of (-log(1-f))/f. For example, if half the water is extracted, discharging brine at twice the salinity, the energy required is greater by 2 log 2 = 1.38, or 4.14 MJ/m^3 = 1.15 kWh/m^3. According to [ http://en.wikipedia.org/wiki/Desalination ], reverse osmosis requires 3-5.5 kW h/m^3, just for the reverse osmoses, and excluding the energy needed to operate the facility. -- Gene
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Dear Minerva, I don't feel good about your making my hypothetical flyer into an issue between us. As an issue between us, I do not feel that this is what I consider a favor. So let's forget about your doing a flyer for me. I'm sure it would be better than anything I could come up with, but it has become more of a negative than a positive. Also, I'd love to see you again soon, but I feel that we've come to the point where we need to see a counselor. Please let me know if you want to see a counselor, too, and we can proceed from there. xoxox, Dan
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Dan Asimov -
Eugene Salamin -
Henry Baker -
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