which he showed to have improved properties over the Knudsen equation. Skorov
et al. (2011) subsequently used this to investigate, numerically, artificially generated
layer structures. This equation shows that a range of solutions for the same mass flux,
q f , can be arrived at by balancing the internal pressure and the ratio of the length to
the pore radius. In other words, the equation shows the increase in internal pressure
required to maintain an identical surface production rate when the subliming source
is moved deeper into the nucleus.
Equation (3.105) is shown in Fig. 3.37 and the proportionalities seen in the
equation are evident. Temperature has no effect if the external boundary is vacuum
while the flow rate is almost directly proportional to the internal pressure and
inversely proportional to the ratio of the tube length to its radius. The mass flow
rate has been converted to molecular flow rate to allow comparison with Fig. 2.28.
The use of this equation is nonetheless complex for several reasons. For example,
the surface boundary pressure may not be strictly vacuum. The temperature will then
play a role. The temperature itself within the surface layer is not linear with distance
and the temperature of the gas at the surface will depend upon how well the gas
accommodates to the layer temperature. The layer itself loses heat to the gas in this
process which also needs to be accounted for. Hence, conserving energy in a
computation of this sort requires significant care. The key point here is that the
temperature of the gas at the surface is not necessarily that of the free sublimation
temperature although how far it can deviate from this temperature in a real case has
not been established.
3.4.8 Effects of Porosity on Small Scales
At local scales, variations in porosity may have quite important effects. Christou
et al. (2020) have demonstrated, again using tomographic scans of real highly porous
materials to initialise their calculations, that if the porosity of a layer changes along
Fig. 3.37 Plot of
Eq. (3.105) for three cases.
Solid line: Internal pressure
of 0.1 Pa going to vacuum
for an internal temperature
of 200 K and an external
temperature of
300 K. Dashed line: As the
solid line but for an internal
pressure of 0.001 Pa. The
external temperature has no
effect
246
3 Gas Emissions Near the Nucleus
et al. (2011) subsequently used this to investigate, numerically, artificially generated
layer structures. This equation shows that a range of solutions for the same mass flux,
q f , can be arrived at by balancing the internal pressure and the ratio of the length to
the pore radius. In other words, the equation shows the increase in internal pressure
required to maintain an identical surface production rate when the subliming source
is moved deeper into the nucleus.
Equation (3.105) is shown in Fig. 3.37 and the proportionalities seen in the
equation are evident. Temperature has no effect if the external boundary is vacuum
while the flow rate is almost directly proportional to the internal pressure and
inversely proportional to the ratio of the tube length to its radius. The mass flow
rate has been converted to molecular flow rate to allow comparison with Fig. 2.28.
The use of this equation is nonetheless complex for several reasons. For example,
the surface boundary pressure may not be strictly vacuum. The temperature will then
play a role. The temperature itself within the surface layer is not linear with distance
and the temperature of the gas at the surface will depend upon how well the gas
accommodates to the layer temperature. The layer itself loses heat to the gas in this
process which also needs to be accounted for. Hence, conserving energy in a
computation of this sort requires significant care. The key point here is that the
temperature of the gas at the surface is not necessarily that of the free sublimation
temperature although how far it can deviate from this temperature in a real case has
not been established.
3.4.8 Effects of Porosity on Small Scales
At local scales, variations in porosity may have quite important effects. Christou
et al. (2020) have demonstrated, again using tomographic scans of real highly porous
materials to initialise their calculations, that if the porosity of a layer changes along
Fig. 3.37 Plot of
Eq. (3.105) for three cases.
Solid line: Internal pressure
of 0.1 Pa going to vacuum
for an internal temperature
of 200 K and an external
temperature of
300 K. Dashed line: As the
solid line but for an internal
pressure of 0.001 Pa. The
external temperature has no
effect
246
3 Gas Emissions Near the Nucleus