# Still water droplet evaporation rate (help using Maxwell's formula please)

• zoofog
In summary, I am trying to find a reference point to develop a better equation for drops of water vapor. I am also trying to learn more about the evaporation rate of drops of water.
zoofog
So I've observed the animal I am studying dry it's self (a survival mechanism called anhydrobiosis) to avoid freezing (laseration by ice crystals). Life forms given time produce a number of protectants in order to survive. Trehalose a sugar is produced to 2-4%. This will act as an antifreeze to aprox minus 4 C. Additionally Trehalose appears to act as a water substitute protecting structures from failing due to dehydration. Protein molecules deprived of water will fold into new incompatible structures collapsing the house of cards that is life. I am trying to write a paper for publication and I want to master this equation ( I = 4 Pi D R (c1-c2)). I have spent day's trying but still do not have a clear idea. Examples I have found use it as a reference point and mostly a starting point to add variables ( velocity and heat flows ) formulated with advanced calculus most of all fail because the added variables are unstable in nature and then the next researcher starts again with Maxwell. You get a sense of the genius of Maxwell by leaving the obvious ( velocity and heat) out. I am not a genius and am unable to read around the advanced calculus content of these journal articles. I just want a sense of the maximum evap rate as a percent of drop mass. One could also call it initial evap rate. My drops (the organism) temperature, diameter and concentration of solutes will immediately change with the evaporation. My biggest problem with the formula has to be with the dissociation coefficient. I have read "the quantity of gas traveling one cm through one cm x cm. Then I'll see 1 m x 1m so in that case is the travel distance a meter or still one cm through orifice of area x. Not mentioned is the units of the quantity ( example grams, moles etc ). I saw something like D = 0.022 + (0.134 c1-c2). Density effects D. D for water is different than for methane etc. I think it's different for different temperatures. I want to carefully get the correct D, conserve my units so the final answer makes sense and is correct. I don't want to be forced to print a retraction. Most of the work that I could find using this rarer Maxwell formula is for metereology and some evaporator uses, spray use or to explain other phenomonom like sailors being pelted with dry salt crystals while at sea.

I googled this topic: See https://www.tandfonline.com/doi/pdf/10.1080/02786828408959006
Equation (3) is a better form of Maxwell's formula. The effusion rate (number per second per unit area) ## R=\frac{n \bar{v}}{4} ## is a well-known result that can be derived with some calculus.(##n ## is the concentration=number of particles per unit volume). I don't know that you have your units right in the OP, but again see equation (3). The ## 4 \pi R^2 ## in that formula is the surface area of the droplet. (3) makes complete sense.

I googled this topic: See https://www.tandfonline.com/doi/pdf/10.1080/02786828408959006
Equation (3) is a better form of Maxwell's formula. The effusion rate (number per second per unit area) ## R=\frac{n \bar{v}}{4} ## is a well-known result that can be derived with some calculus.(##n ## is the concentration=number of particles per unit volume). I don't know that you have your units right in the OP, but again see equation (3). The ## 4 \pi R^2 ## in that formula is the surface area of the droplet. (3) makes complete sense.
Thank you ever so much. It will take me time (as probably days) to digest and use the new search terms to learn what I can on my own before asking for more help. Thanks again. I was mistified why circumference and not surface area was in my equation.

I looked at the Seaver (1983). I wish I could understand it fully (or even partially). I forgot calculus it came easily and went just as easily (40 years ago). Seaver though is developing a formula for drops smaller than 2 microns and Seaver confirms any drop larger is Maxwellian (ie yields best correlation to experimental data). Taking your lead of Seaver's equation (3) I am reading Fuchs (1959) rendition that in part is available on Google books and I'll see where it takes me. Fuch's is good about symbols and in conserving units and actually provides a Maxwell gas law combo equation that will let me input my partial pressures without the risk of deriving the wrong equation on my own. Algebra I am still sound on and Fuchs first chapter is Algebraic.

## 1. What is Maxwell's formula for calculating the evaporation rate of still water droplets?

Maxwell's formula for calculating the evaporation rate of still water droplets is given by the equation: J = Avp, where J is the evaporation rate (in kg/m2/s), A is the surface area of the droplet (in m2), v is the vapor pressure of the liquid (in Pa), and p is the mass transfer coefficient (in m/s).

## 2. How is Maxwell's formula used to calculate the evaporation rate of still water droplets?

To use Maxwell's formula, you will need to measure or estimate the surface area of the droplet, the vapor pressure of the liquid, and the mass transfer coefficient. Once you have these values, you can plug them into the formula to calculate the evaporation rate. It is important to note that this formula assumes ideal conditions and may not be accurate for all situations.

## 3. What factors can affect the evaporation rate of still water droplets?

The evaporation rate of still water droplets can be affected by various factors, including temperature, humidity, air flow, and the properties of the liquid itself (such as surface tension and viscosity). These factors can impact the vapor pressure and mass transfer coefficient, which in turn affect the evaporation rate calculated using Maxwell's formula.

## 4. Can Maxwell's formula be used for all types of liquids?

No, Maxwell's formula is specifically designed for calculating the evaporation rate of still water droplets. It may not be accurate for other types of liquids, as their properties and behavior may differ from water. In these cases, different formulas or methods may need to be used to calculate the evaporation rate.

## 5. Are there any limitations to using Maxwell's formula for calculating the evaporation rate of still water droplets?

Yes, there are some limitations to using Maxwell's formula. As mentioned before, it assumes ideal conditions and may not be accurate for all situations. Additionally, it does not take into account any external factors that may affect the evaporation rate, such as impurities in the liquid or the presence of other substances in the surrounding environment. It is important to use caution and consider these limitations when using Maxwell's formula.

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