## 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

_{Evap}

*Note that up to 5 March 2021 there was an error of dividing, rather than multiplying, by density so that evaporation times were too slow by a factor of ρ² which was OK for water but not for other solvents. I thank the user who found the bug.*

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 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^{0.5}Sc^{0.333}

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(VP) = AA-AB/(AC+T)

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.