WOLFRAM|DEMONSTRATIONS PROJECT

Diffusion-Controlled Evaporation of an Aerosol Droplet

​
A
DOP
DBP
DBS
B
H
2
He
Ar
Air
CO
2
CO
N
2
CH
4
O
2
T (K)
296
P (atm)
1
R
0
(μm)
1
t (s)
0.1
surface area versus time
Diffusion-controlled evaporation of aerosol droplets in an ambient gas is important in various engineering and scientific fields, such as premixing air and fuel, ink-jet printing, spraying of pesticides, biochemical assays, and atmospheric pollution. For isothermal, quasi-steady evaporation, Maxwell [1], showed that the time rate of change of the droplet radius
R
is given by
dR
dt
=-

AB
P
vap
Mw
A
/(
ρ
A
RTℛ)
,
where

AB
is the binary diffusion coefficient for the vapor molecules of species
A
in a surrounding continuous phase
B
,
P
vap
is the vapor pressure of species
A
,
Mw
A
is the molecular weight of species
A
, and
ρ
A
is its density. The quantities
T
and
ℛ
are the temperature of the surrounding phase and the universal gas constant, respectively. Under isothermal conditions the surface area
A
of the evaporating drop is given by
A=
A
0
-4π
S
AB
(t-
t
0
)
, where
S
AB
=2

AB
P
vap
Mw
A
/
ρ
A
ℛT
.
The binary diffusion coefficients can be predicted from the kinetic theory of gases using the Chapman–Enskog theory with a Lennard–Jones (6-12) potential [2]. The vapor pressure of species
A
at temperature
T
can be related to a reference temperature
T
0
by applying the Clausius–Clapeyron equation:
P
vap
(T)=
P
vap
(
T
0
)exp-
Δ
H
vap
ℛ
1
T
0
-
1
T

,
where
Δ
H
vap
is the heat of vaporization of species
A
.
In this Demonstration you can select an aerosol compound
A
from a family of commonly used plasticizers that have low vapor pressures: DOP (dioctyl phthalate), DBP (dibutyl phthalate), and DBS (dibutyl sebacate). The necessary thermodynamic properties for the plasticizers are taken from [3]. You can also select species
B
for the surrounding gas phase. Using the sliders, you can specify the temperature
T
, the pressure
P
of the surrounding gas phase, the initial aerosol droplet radius
R
0
, and the evaporation time
t
. Then using the pull-down menu you can view: (1) a plot of
A
versus
t
; (2) an image of the drop (relative to its initial size) at a specified evaporation time
t
; and (3) the droplet properties displayed in tabular form at time
t
. Note:
t
max
in the droplet properties table denotes the evaporation time such that
R(
t
max
)=0
. To accommodate the wide range of
t
max
values for different diffusion experiments, the evaporation time slider is reset to
t=0.1
when any of the other controls are changed.