Although many well-controlled experiments have been conducted to measure the static properties of systems near criticality, few experiments have explored the transport properties in systems driven very far away from equilibrium as the transition occurs. Here we propose to measure the thermal gradient across the superfluid (HelI)--normal fluid (HeI) interface in microgravity conditions as a function of the heat flux Q used to make the measurements. Microgravity conditions are required (1) to avoid the hydrostatic pressure variation along the height of the helium column (a concern for Q<0.1pW.cm-2), (2) avoid convection in He-I for Q> 3pW-cm -2 in our apparatus, and (3) to increase the Q = 0 interfacial width from its value of a few tens of microns on Earth to about a millimeter in orbit. New technologies described in this paper are under development for this experiment, which is in definition for Space Shuttle flight.
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