Heat and Mass Flow of Superfluid Helium (He II, Superfluidity) in Porous Media
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It is a well-known fact that the transport of the Newtonian components of liquid helium
in capillaries follow that of a classical fluid. The question is whether the transport
in porous media also follow that of a classical fluid. If so, whether the characteristics
of porous media, like the Darcy permeability, can be measured at room temperature and be
applied to low temperature.
Murakami had reasonable success in correlating mass flow in porous media with a modified
Blake-Kozeny Equation used for classical fluids.
Yuan proposed a modified Ergun equation which agrees with the Blake-Kozeny equation
for small Reynold's numbers and deviates at high Reynold's number for various temperatures
(see above figure).
where Kp is the permeability, e is the porosity,
r is density, S is entropy, and subscript n stands for
The modified Ergun's Equation is expressed as Equation 1
Kp in Equation (1) is the Darcy permeability as defined by the first
term of Eq (1) or by the Darcy law as follow
Denner (1977) measured the low temperature permeability of a glass plug and found
that it agrees with the room temperature permeability.
Likewise Yuan (1985) draws the same conclusion with a bronze sintered plug.
Yuan found that each porous medium is characterized by a constant permeability value
(see Figure below) if the fountain pressure is correlated with the normal fluid velocity,
thus proving that the heat and mass transport of the normal components of He II follow
that of a classical fluid.
"Channel Size Influence on the Heat Flux Density at Zero Net Mass
Flow in the Non-Linear Transport Regime Between 1.2 K and 2.1 K", in the
proceedings of the 17th Internationaler Kongress Fur Kaltetechnik, 1987,
vol. A, p. 72. (With T.H.K. Frederking, J.M. Lee and G.S. Sun.)
"Darcy Law of Thermo-Osmosis for Zero Net Mass Flow at Low Temperatures",
in Proc. of ASME-JSME Thermal Engineering Joint Conference, Honolulu, Hawaii,
March 1983, vol. 2, p. 191. (With T.H.K. Frederking.) (With I.E. Spradley.)