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Sustainable Development
I am fond of telling people that a Maxwell-Boltzman distribution curve (bell shaped curve) can explain almost everything from behavior of any group of people or the behavior of a group of ants or marbles. In the case of the Delta T, it is very specifically since distribution curves were used by each of them to represent a plot of the range of energies of particles in a gaseous state.
We like to think of things simply, that is, it is considered an acceptable simplification to say “The water is 57 degrees” as opposed to saying “The temperature reading on the thermometer is 57 degrees and the likely range of the temperatures for 95% of the molecules is between 34 degrees to 150 degrees with a standard deviation being between 55 and 59 degrees with less than 3% of them achieving enough energy to escape the liquid state.” It’s easier to say the first and defer to the apparent temperature than to be highly accurate and very complicated but correct according the physicists (apologies to any physicists reading this).
While we continue to use common analogies when describing the functioning of the Delta T unit, a more accurate description of the closed loop system ensues in light of distribution curves.
First, a distribution curve is best described as a bell shaped curve with the apex being the most probable energy level (heat, kinetic energy, or speed) of a particle, but with molecules distributed along the entire curve. While at ambient temperatures, only those molecules at the far right side of the curve, say a portion of the 99.99th percentile, have sufficient energy at any one time to leave the liquid state and enter the gas state. Some molecules at the left side have so little energy that they could actually enter the solid state (form ice) except that they are so few of them they cannot achieve the solid state because you would need two and sufficient time to form the solid in an environment where thousands are bombarding it, which, of course, changes its energy state. (This actually starts to happen at about 34F when water starts to expand as sufficient molecules form ice to overcome those shrinking the water by cooling and coming closer together. Odd, but true, water shrinks slightly as it cools from, say, 200F to 34F then starts to expand until ice if fully formed.)
Sliding the distribution curve to the right (heating the water) increases the number of molecules that can leave the liquid state for the gas state when they reach the surface of the liquid, so, if I sprayed the water and collected the spray in a bucket, we would say the temperature dropped, when in reality, most of what was done was the loss of higher energy molecules to the gas state. But even at boiling point, the curve is not yet to the point where even half of the water can escape as a gas at any given time.
Likewise reducing the temperature moves the distribution curve to the left and more and more molecules are available to form a solid and do so under normal conditions. Conversely, there are still molecules at the surface that have sufficient energy to leave the liquid state and evaporate.
Each gas has a different distribution curve at a given temperature and the higher the temperature (that is, the more energy/speed that is present in the molecules) the longer the energy distributions curve, conversely, the less energy in the water, the narrower and taller the curve. Curves mostly grow to the right as temperature increases, while the slopes become less steep.
Water molecules are constantly moving back and forth between the three states of vapor, liquid, and solid. When more energy is present, more molecules are leaving a liquid surface than when it is at a lower energy state, say, when the water or gas is cooler.
As one heats gas or liquids, there is as net loss of water from the liquid state and a net increase in the gas state. As you cool water, the opposite occurs, there is net condensation. When this happens in the atmosphere, clouds form. Note that until rain occurs, the amount of water in the air is the same, the cooling merely changes the state of the water, not the amount of water in the volume of atmosphere, that is, the water starts to condense as it looses energy forming a cloud. (Another oddity, the air becomes more dense as water is condensing into clouds for the very reason the water condenses, the mass has lost energy, even though condensation releases energy, one would think it would heat the air, which it does, except that the fact that water is condensing shows the mass has lost sufficient energy, the other gasses also loose energy and become more dense, even as tons of water fall from the sky in the form of rain, this, downward convection, with either stops at the adiabat or penetrates that boundary and causes a cold heavy down draft.)
Over many a snow covered peak you will see a cloud directly overhead if there is a mild breeze. This cloud occurs because the air flowing over the surface cools and the water condenses onto dust particles as a cloud, it also picks up evaporated water from snow or gaseous water from the surface which then condenses onto dust particles because of the reduced pressure. (This is called altocumulus standing lenticularis, or a Lenticular cloud for short.) As the air drops back down to lower elevation on the leeward side of the mountain, this condensation evaporates, going back into solution and can no longer be seen. The moisture actually passes over the location, so the "cloud" forms in one spot then moves to another where it evaporates, but the shape is determined by the mound of air passing over the hill or mountain, so it looks stationary. The cloud is stationary, but the moisture changes position. It's complicated.
This is a common misunderstanding about clouds and air masses. The rate at which water molecules form liquid (condensate) or form gas (evaporate) is determined by the pressure of the water vapor not by the temperature of the air per se. That pressure changes by the amount of energy in the vapor itself. Molecules can escape from liquid more readily than from the solid ice (or snow) so most (not all) water molecules that are ice, leave the solid state and enter into the liquid state before they leave the liquid state and enter the gaseous state. (Some solids, like carbon, go directly to the gaseous state. This is called sublimation, as is the opposite direction, moving from gas to a solid. Some ice molecules also sublimate directly to gas, this happens when things are subjected to freeze drying.)
In the Delta T, we are interested in the water vapor condensing in the condensation chamber, but the air movement is not related to this condensation, rather, it too is independently cooled in the same process and that cooling makes the air dense, which, of course, makes it fall because it becomes gravimetrically enhanced. If the water vapor was actually suspended or dissolved in the air, condensation would lighten the air as the water was removed and cause the air to rise, that is, it would be gravimetrically minimized, and heating the water and air would cause it to sink because it was gravimetrically enhanced.
When Doug says, “We make a cloud, then ring it out,” this is what he is referring to.
Sinking Clouds
Think about it this way, are clouds found clinging to the ground or floating in the air? Since they are high in the air it is obvious that the water molecules are not attached to the air, say, onto the nitrogen or oxygen molecules. Rather they are all in the gaseous state behaving the way gases do until the water leaves the liquid state, precipitating onto a dust particle (just like a snowflake) and that small particle is suspended in the moving gas molecules of all types, including water vapor, as a colloid until and unless it gains enough size to fall by gravity toward the ground, or receives enough energy to evaporate again.
Have you ever seen a cloud evaporate? In that case, the condensed water in these small particles gained enough energy to completely evaporate. Remember, this happens at 20,000 feet or more where it is quite cold, yet the energy was sufficient for the water to leave the liquid state and enter the gas state, commonly thought to occur at 212oF. (At least enough water did evaporate to make the cloud “disappear,” that is, not reflect enough light for your eyes to detect.)
A distribution curve can describe this by saying that sufficient energy was present to move the curve toward the warm side and evaporation exceeded condensation, or we could say that the vapor pressure was low in the cloud. If a cloud passes over dry air this happens because the dry air has very low vapor pressure, the could disappears as it converts from a colloidal solution of liquid particles back into the gaseous state.
This is the same process that occurs in our Delta T. When we talk about heating air we are really saying we are heating the salt water to the point that heat is being transferred into the air entering the evaporation chamber warming the air and evaporating significant amounts of water into the mixture, likely raising the humidity to +300% relative humidity. The warming air expands and rises moving this water vapor up to the condensation chamber where, at places, there are flat cold surfaces, and water condenses returning that small spot to <100% relative humidity.
The Independent States
Air does not dissolve water; it merely co-suspends a mixture of independent gasses that includes water vapor. The individual particles rarely interact accept during collisions of gas molecules which is reasonably rare. These collisions form the individual gas pressures, the sum of which is measured when gas pressure is measured. Each gas creates a different and independent pressure gradient (again, a Boltzman distribution). Dalton proved by his 1802 paper that the pressure of a gas is independent of the amount of other gases present. Atmospheric gas is mostly empty space; each gas acts individually as if it alone existed except for the interactions with the other gases which thermodynamically tend to equalize their kinetic energy (heat) by collisions yet each gas continues to act in a manner specific to the type of gas it is.
The Delta T
In the Delta T, the amount of vapor depends almost entirely on the temperature of the liquid and the temperature of the water vapor, not on the temperature of the air per se; however, there is always a relationship between the two because cold air would draw heat from the water vapor causing it to condense forming a fog if the loss of energy was sufficient to support this, however, in our case, it is the warmed water that is warming the air and water causing an increase in water vapor pressure also so the energy is primarily in one direction.
In the condensation side of the loop, the condensing devices are a heat sink that draws energy out of both the water vapor and the air vapor creating product water and dense air.
Where’s the Bell?
The bell shaped curve represents a plot of the range of energies of particles in any gaseous state, both the air gasses and the water gasses. The evaporation chamber moves this curve to the right and lengthens it toward evaporation temperatures by adding energy to the liquid water as well as the gaseous water causing more water molecules to leave the liquid state than enter it.
When we move to the condensation side we slide the distribution curve to the left and shorten it causing many of the water molecules to leave the gas state and enter the liquid state (and far fewer leave the liquid state and enter the gas state). Thus we have net condensation.
Vapor Pressure
Now let’s talk about vapor pressure. The higher the vapor pressure the easier it is for a given molecule to leave the gas state and enter the liquid state, the lower the pressure, the easier it is for water to leave the liquid state and enter the gas state. When our cold air leaves the condensation loop is has very low water vapor pressure helping more water molecules leave the liquid state because of this low pressure, in essence creating a pressure vacuum literally drawing water out of the liquid. What is happening here is the attempt to create equilibrium between the now low water vapor pressure air and the high water vapor pressure liquid water drawing the water out. From a distribution curve then, we can describe exactly the same situation describing both the energy in the water and the vapor pressure, each moving the distribution curve the same direction at the same time.
What is commonly called “saturation” occurs when the rate of condensation and evaporation are equal, that is, at a given spot, there is no more net water moving from one state into the other. Some call this 100% relative humidity, but this is also dependent on the shape and texture of the surface and, if the shape is correct, and there is no dust, relative humidity can reach 300% or more. Relative humidity at the ground, where it is dusty, rarely exceeds 100%, and saturation would require pure liquid water.
Relative humidity is actually the ratio of the amount of water vapor actually present in the air to the greatest amount possible at the same temperature, or, the vapor pressure of the water vapor divided by the equilibrium vapor pressure times 100%, consequently, at 100% relative humidity there is no net movement of water from liquid to vapor and vise versa, thus the misnomer “saturation,” in common parlance, the inability to hold more of something.
Without the dust as a solute particle, which causes water to nucleate and condense because of equilibrium conditions, conditions here on earth could become quite uncomfortable with the desert reaching 200% or 300% relative humidity before the water began to condense on the ground and other surfaces.
This is actually what occurs in the Delta T precisely because the dust from the outside air is excluded from the unit so the gas mixture contains much more water vapor and when it reaches the condensation side, it condenses precipitously.
A problem evaporation desalination has had to date is the misunderstanding of this type of condensation loop, supposing it is more efficient to boil water causing a greater percentage of water molecules to leave the water state and drive the reaction in the desired direction as opposed to merely increasing the efficiency of the evaporation probability. You certainly do achieve a higher water output if you ignore the cost of the fuel used to drive the process, or if fuel is free, however, these processes have never been able to reach the competitiveness of other desalination techniques, as costly as these are also.
Misunderstanding what happens in evaporation leads to false conclusions about the best method for providing the correct circumstances to promote evaporation.
Boiling merely provides sufficient heat to move the distributions curve to the right a little more than water just a few degrees cooler, but radically increases surface exposure allowing more molecules to escape because it is only at the surface that water escapes into the gas state. The bubbles in boiling water bring more evaporated molecules to the top because the vapor pressure inside the water reaches the state where the vapor resists collapse both by the water pressure above and to the sides, and by heat loss to adjacent water molecules causing the molecules to revert to the liquid state. The various vapor molecules accumulate because this conserves energy, they form a bubble, then, because they are significantly less dense, they rise to the surface releasing the flow vapor to the atmosphere.
This constant loss of the highest energy particles causes a tremendous drain on the total energy of the system and explains why these systems have captured only a small fraction of the market.
So you had to ask a Professor?
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