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# Determining Solvent Evaporation Rates Faster with Science based Tool

Steven Abbott – Jun 3, 2019

TAGS:  Science-based Formulation      Solvents When selecting a solvent, we must attend to its solubility characteristics as defined by Hansen Solubility Parameters, to its cost, its green credentials, its odor and its toxicity. But even if we have all these factors right, the solvent might be too volatile or too involatile for our purposes. So, for every solvent, we need to know about its vapor phase characteristics.

Scientifically, we need to know only two:

1. Its vapor pressure at any given temperature, and
2. Its flash point - the temperature at which the vapor can, in principle, burn when ignited by a spark

The flash point is, in general, a fact about a solvent and has to be found by measurement. It is of significance to a formulator because the safety restrictions on a flammable liquid (flash point < 37.8°C) are much more stringent than those of a combustible liquid (37.8° < flash point < 93.3°C) which are more stringent than a solvent with a flash point greater than 93.3°C.

## Calculating the Key Parameters

If we know how the vapor pressure of a solvent depends on temperature, then we can deduce three key parameters of significance to the formulator:

1. Vapor Pressure at 25°C, VP25 – This helps to define Volatile Organic Compounds
2. Boiling Point, BPt – The temperature near to and above which we cannot conveniently use the solvent as a liquid
3. Evaporation Rate – How fast the solvent will evaporate in given air flow. More usually described as Relative Evaporation Rate (RER) with respect to a standard solvent such as n-butyl acetate, nBuAc.

For any solvent, the vapor pressure VP can be calculated at temperature T using the three Antoine Constants, AA, AB, AC via:

log10VP = AA-AB/(T+AC)

• From this equation we automatically get VP25.
• The BPt is found from the value of T that gives VP=1 atm.
• And the RER (defined at 25°C) is basically 100.

VP25(Solvent)/ VP25(nBuAc) (plus a correction for the ratio of their molar volumes) because the rate of evaporation is proportional to the vapor pressure.

If, therefore, you need to select between different solvent options:

• First, ensure that you have the required flash point
• Then, find whether your VP25 fits your VOC requirements, that the process is comfortably below the BPt, and that the RER is suitably large (if you need to remove solvent) or small (if you want it to stay around)

A table of solvents can provide all those data – with one big confusing issue which is the large variety of numbers used for RER. At SpecialChem the standard will be nBuAc = 100. In many cases, you will find nBuAc=1. So, acetone is 560 at SpecialChem and might be 5.6 on another site. Even worse is that some solvents are quoted in terms of evaporation of ether and with an inverted scale based on time to evaporate rather than the rate of evaporation.

If we use nBuAc=100 then diethyl ether is a super-high 2574. If we use the ether scale with ether=1 then nBuAc=25.74 because it will take that much longer to evaporate. Formulators need to know about this confusion because although most of the time it is not too hard to work out if a value is based on nBuAc=1 or nBuAc=100 if the figures are quoted in terms of ether it is hard (because the scale is inverted) to check that the values make sense.

## Real-world Evaporation Rates

A question a formulator might reasonably ask is “How long will it take to evaporate 1g of solvent at this temperature?” For multiple reasons, there is no easy answer. We need to break the question down into bite-sized chunks. 1. We first need to know the vapor pressure at that temperature. If T=25°C, then we use the VP25 value. At any other temperature, we need to know the Antoine Constants and do the calculation.

2. We need to know the thickness of the layer. 1g spread over 1m2 is a much thinner layer that will evaporate 10000 times faster than if it was spread over 1cm2. To put it another way, using the rough assumption that all densities are equal to 1 (we will shortly see why we are allowed to do this), then from a simple formula we can estimate the number of µm/minute that will be evaporated away, taking into account that 1μm is equivalent to 1g/m2. We need only evaporate 1μm of liquid if it is spread over 1m2, and we need to remove 10000μm (i.e. 1cm) if it is spread over 1cm2.

3. We need to know the air velocity. At zero velocity the rate of evaporation is very close to zero because molecular diffusion is amazingly slow. As the air velocity increases, evaporated molecules are swept away, allowing more to escape from the liquid.

4. We need to assume that the latent heat of vaporization (i.e. the energy needed to change a molecule from the liquid to gaseous state) can be provided by the surface beneath the film so that the temperature of the liquid does not fall, slowing the evaporation. Thermal conductivities of liquids are sufficiently large that for any reasonably conductive surface and any film below 100μm of a solvent evaporating at “normal” rates (ether might be an exception!), the temperature can be assumed to be that of the surface.

From that we can use a semi-official formula that is a “good enough” approximation to the effect of air velocity. Regulatory authorities know that a simple air velocity calculation cannot be accurate because factors such as surface roughness and turbulence play a big role in evaporation. They also know that a “good enough” formula that people can use is better than an ideal formula with parameters no one can measure. This approximation explains why we don’t need to worry too much about mass or volume concerns, i.e. we can assume that density is 1 g/cc or, more technically, that molar volume equals molecular weight, MWt.

Where, R is the rate of evaporation in μm/min/cm2, T is the temperature in °C, V is the air velocity in m/s (a typical lab value would be 0.5m/s) and the vapor pressure is expressed in mm.Hg because the most common Antoine Constants are expressed in those units. The formula is:

R = [42/ (8.31. (273+T))]. MWt.VPmm.HgV0.78

### Calculating Evaporation Rates of Solvents Made Easy!

For those who just want to get a time taken to evaporate a thickness of one of many typical solvents, I have a convenient app at https://www.stevenabbott.co.uk/practical-coatings/evaporate.php. That same app includes a much more complex calculation based on more fundamental physics.

Hopefully, you will not need to worry too much about absolute evaporation rates. But no formulator should choose a solvent without knowing Flash Point, VP25, BPt and RER!

3 Comments on "Determining Solvent Evaporation Rates Faster with Science based Tool"
Steven A Jun 19, 2019
Both comments are right - I should have emphasised that this was just a starting point. If you don't get the basic right then things won't work out - but if you get them right then the non-ideality effects and the diffusion limited effects have to be attended to next. The whole story of diffusion limited evaporation is interesting because it can be fairly well modelled with just three parameters: a "standard" diffusion coefficient, a concentration dependence of that coefficient and a temperature dependence. In the TopCoat drying software that I co-authored with colleagues from Rheologic we can do such calculations very well and can even calculated the transition from the constant rate (evaporation limited) to the diffusion-limited rate. Unfortunately, although we can do the calculations, almost no one knows the 3 constants for most systems. Interestingly, this means we have to go back to solubility parameters. To keep the polymer system "open" for as long as possible we need a great solvent for the system which is also slower evaporating. Hence we need a good HSP match coupled with a low RER. By admitting that we can't readily do the complex science (diffusion limited calculations) we have to fall back on a simpler science that works surprisingly well.
Giso P Jun 13, 2019
Even in the "wet" state, there is a set back, because the calculation of the vapor pressure is only valid for "ideal mixtures". It is an good approximation for low interacting systems. But keep in mind several solvents do strongly interact and even form azeotropes. With increased evaporation the interaction with the polymer binder comes into the game. In some cases an relative volatile solvent can act as slowly, or not at all (e. g. water), evaporating plastisizer.
Ian B Jun 12, 2019
Obvious comment, I know, but just a reminder that, whilst the coating is "wet", the above applies and the volatility is evaporation-controlled. However, once the coating begins to dry out then it can switch to a migration-controlled system i.e. cross-sectional dimensions etc. become important. As an example, iso-butyl acetate will evaporate faster than n-butyl acetate whilst the coating is wet. Once it begins to dry, iso-butyl acetate will appear to evaporate more slowly than n-butyl acetate as its migration to the surface is slower due to its larger cross section.