Solvent Evaporation
Quick Start
Solvent evaporation depends on parameters specific to each solvent, plus air temperature and velocity. A simple model gives an evaporation time for a chosen thickness of solvent, a more academic model lets you see how the quick model works.
Solvent Evaporation
A common requirement is an "approved" formula for calculating evaporation rates from a pool of liquid. There is a formula approved by the US Environmental Protection Agency, which, while recognising that it's a simplified approximation, is acceptable given that an accurate calculation is impractical for most purposes.
The evaporation rate, R in g/m²/s depends on air speed U in m/s, MWt M in g/mole, the vapour pressure P in mm/Hg calculated from Antoine Coefficients that are commonly provided in mm/Hg, T °C units, and on the temperature TK in Kelvin:
`R = 0.282U^0.78M^0.667P/T_K`
P is calculated using the Antoine AA, AB, AC coefficients you see for each solvent:
`P = 10^(("AA"-"AB"/("AC"+T)))`
Now the more academic app which shows in more detail what is going on. The calculation method is the same, but for simplicity the quick model assumes that L=1000.
Flat Plate Evaporation
We often need to know the evaporation rate of a solvent on a flat plate with a steady air flow above it. This is rather difficult to calculate from first principles, but some well-known approximations are good enough given the uncertainties in, say, measuring the rate.
The calculation uses a set of dimensionless numbers. Based on the air velocity, U, the temperature T and length of the plate L, then basic parameters such as the kinematic viscosity of air, ν, diffusion coefficient of the solvent in air, D (itself a complicated dependency on MWt and MVol of the solvent) we have:
| Reynolds Number | Re | UL/ν |
| Schmidt Number | Sc | ν/D |
| Sherwood Number | Sh | kL/D |
The key number is Sh because it contains the mass transfer coefficient, k. It is calculated from the other two via:
`Sh = 0.664Re^0.5Sc^0.333`
So we get k from:
`k=(ShD)/L`
From k we can calculate the moles of solvent evaporated per unit width along the length L, given a molar concentration c at the surface and assuming that the air is solvent-free:
`Evap = k.L.c`
The molar concentration c depends on the vapour pressure, VP, the temperature T and the universal gas constant R:
`c = "VP"/(RT)`
The mass evaporated is simply the molar rate multiplied by the moelcular weight, Evap*MWt. Finally, we can calculate the vapour pressure if we know the Antoine Constants of the solvent:
`log_10(VP) = "AA"-"AB"/(AC+T)`
There are many different units used in Antoine. Here pressure is in mm Hg and T is in °C. Why? Because the most common Antoine databases use them.
A few details remain. The air properties assume dry air - the calculated evaporation rates for moist air are not significantly different at this level of approximation. The kinematic viscosity of air changes with temperature; a simple polynomial is used to calculate it. The diffusion coefficient of the solvent in air can be calculated from T, MWt and the molar volume, MVol via a formula not shown here. The solvent values of MWt, MVol, AA, AB, AC are extracted from the values shown in the combobox for each solvent.
