| Compressed-gas dusters spray a gas such as difluoroethane (DFE) to remove dust from electronics. When gas exits the valve, liquid DFE in the container vaporizes to maintain vapor-liquid equilibrium. The energy to vaporize the liquid is obtained by cooling the remaining liquid; the container is modeled as adiabatic in this Demonstration. Decreasing the liquid temperature decreases its saturation pressure, which lowers the driving force, and thus the gas flow rate decreases. For smaller "initial volume fractions of liquid" (change with the slider), the liquid cools faster. Select a plot (volume, moles, temperature, or pressure) using the buttons to display how that property changes with time. Animate the duster by clicking the play button next to "spray gas." Spray continues until the temperature reaches -5°C (if stop at -5°C is selected); otherwise the spray stops at the time selected by the "time sprayed" slider when "adjust stopping time" is selected. In either case, the black dot(s) show the conditions of the duster on the plot. The liquid and vapor DFE are assumed to be in equilibrium at all times. As the spray time increases, the adiabatic approximation becomes less accurate. |
Details:
The total volume of the can 
is 0.375 L, and the initial volume of liquid in the can 
is:
,
where 
is the initial volume fraction of liquid.
Initially all contents are at room temperature (300 K), and the pressure inside the can is the saturation pressure 
at 300 K. The Antoine equation is used to calculate :
,
where is in bar, 
is temperature (K) and 
, 
and 
are Antoine constants.
The total moles 
are equal to the liquid moles 
plus the vapor moles 
:
,
,
,
where 
is the liquid molar density (mol/L), 
is the ideal gas constant ([L bar]/[mol K]), and 
and 
are the liquid and vapor volumes at any time.
The liquid volume is found by rearranging the equation for total moles:
,
with 
.
From an unsteady-state mole balance:
at 
, 
,
where 
is time (s), 
is a constant (mol/[bar s]) and the air pressure outside of the can is 1 bar.
From the energy balance:
at , 
, where 
is the heat of vaporization (kJ/mol), and 
is the liquid heat capacity (kJ/[mol K]).