Kinetic theory approach for the determination of rate of evaporation
The problem of liquid evaporating/condensing from/to its surface is of importance in a wide
variety of engineering applications.
These can be classified into naturally occurring processes and those that came out of
technological advancement. Of the naturally occurring processes the important problems are
loss of water due to evaporation in dams, evaporation from moist material to dry it,
condensation in droplets required for cloud formation etc. The processes which became
important due to technological advancement are evaporation in freeze drying processes,
evaporation and condensation required to produce thin films using vacuum coating
techniques, drying processes required at ordinary temperatures and pressure to prevent
chemical degradation at high temperature and the evaporation process which produce the
cooling effect in evaporative cooling towers.
The problem in which continuum concepts are valid are analysed using the Fick's
Diffusion model. It involves the experimental determination of the diffusion coefficient in
each case. Cases where evaporation took place under free molecular regime could not be
analysed using the Fick's model.
In the present study a Kinetic Theory approach is made to analyse the problem. The
analysis is made in two stages. In the first stage, the evaporation from a free liquid surface to
its own vapour is studied. In the second stage the study is extended to the case where noncondensable
gas is also present along with the vapour. The analysis is carried out using the
Boltzmann transport equation. The collision terms in the equation are obtained using the
model suggested by Bhatnagar Gross and Krook and now known as the BGK equation. The
numerical schemes are developed for both the cases and solutions are obtained for the net rate
of evaporation. The distribution of temperature, pressure and molecular number density are
also plotted for the region close to the interface.
The evaporation coefficient introduced in the theoretical model is obtained by comparison
with experimental data. Experiments are conducted with water as the fluid and nitrogen as the
The correlations are made and the results are presented. The evaporation coefficient was
found to be in the range 0.0005 to 0.0007 for the single component case and for the twocomponent
case it is found to be in the range 0.0009 to 0.00135. These values can be used for
engineering design applications