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Evaporation and Diffusion

  1. Jul 21, 2010 #1
    Hello all,

    I am reading through Stephen Turns' An Introduction to Combustion. The third chapter is essentially a crash course on mass transport. In it, he talks about "the Stefan Problem" as it pertains to diffusion and Fick's Laws. I am understanding most of it, but I am realizing that I had really never given much thought to the phenomenon of evaporation. I am not really sure that I understand why it occurs?

    Clearly, water can evaporate away without reaching it's boiling point. So there a difference between evaporation and vaporization (right?). If I am understanding the text, than it seems that if we place a liquid, denoted Liquid A, in a graduated cylinder, then at the liquid-air interface, there will exist some gaseous A. I am just not clear of the mechanism that causes this gaseous A to exist?

    Any thoughts on this?
  2. jcsd
  3. Jul 21, 2010 #2


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    Water molecules on the surface are being held down by hydrogen bonding with the molecules below it. They are also being kicked about by the thermal energy in the liquid. The RMS size of the kick depends on the temperature, but at any given temperature, a specific molecule will experience a distribution of kick strengths. Occasionally, it experiences a kick strong enough to free it from the inter-molecular forces, which makes it separate from the body of the liquid.

    That's a simplified microscopic picture of evaporation.
  4. Jul 21, 2010 #3
    That actually is the best description I have found! It makes great sense to me and I think with that picture in mind, I can move forward in the text and make some progress. I probably have some lingering questions about the stefan problem itself, but I will post back for that. Thanks Gokul :smile:
  5. Jul 21, 2010 #4
    Ok. I do have another question. The text says that typically, the gas-phase mass fraction of the diffusing species A at the liquid-vapor interface, YA,i, is unknown. It says that we can determine YA,i by assuming that equilibrium exists between the liquid and vapor phases of A. With this assumption and assumption of ideal gases, the partial pressure of species A on the gas side must equal the saturation pressure associated with the temperature of the liquid:

    PA,i = Psat(Tliq,i).

    Two questions:

    1.) What kind of equilibrium? This looks like a force balance to me where the equal areas have cancelled. Are the escaping (evaporating) molecules not accelerating? I think they are.

    2.) Why is the liquid A considered to be staurated? Is it just a thin "layer" that we are considering to be saturated? I would not think that it is the whole tube.

    Sorry if these seem silly, but this really is a crash course for me! :redface:

    EDIT: Picture added for clarity.

  6. Jul 24, 2010 #5
    Any thoughts with regard to post #4 anyone?
  7. Jul 24, 2010 #6


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    Oops, sorry - missed this before. Don't have a lot of time now, but it's clear from #4 that there are some fundamental misconceptions that need to be cleared up.

    The equilibrium described here is a chemical equilibrium, not a mechanical equilibrium (no force balance).

    You need to learn what the term "saturation vapor pressure means." Which means you have to understand the nature of the dynamic equilibrium between the liquid and vapor phases. I recommend a quick read through the phase diagrams and solutions chapters in any standard Physical Chemistry text.
  8. Jul 24, 2010 #7
    Interesting. I will look around; I only have a"General Chemistry" text ... perhaps that is the same as Physical Chemistry? Either way, I have learned about saturation points in thermodynamics (from an 'engineering' perspective, however). I will review that and look into a chemistry text.

    I was under the impression that a "saturated liquid" was one that was 'about to' turn gaseous, though I realize that is a rather qualitative description. And the saturation points are fixed by T and P. For a certain T, there is but one P_sat and conversely.
  9. Jul 24, 2010 #8


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    A Gen Chem text will work too. T and P define the state of a gas, not a liquid. P_sat, the saturation vapor pressure, is the pressure of the vapor above a column of liquid that is in equilibrium with the liquid at some given temperature, T. If you increase T, you shift the equilibrium towards the vapor phase, turning more liquid into vapor, and thereby increasing the vapor pressure.
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