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Submitted on 1 Jan 1978
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THERMOROTATION EFFECTS IN SUPERFLUID 4HE
E.J. Yarmchuk, W. Glaberson
To cite this version:
E.J. Yarmchuk, W. Glaberson. THERMOROTATION EFFECTS IN SUPERFLUID 4HE. Journal
de Physique Colloques, 1978, 39 (C6), pp.C6-168-C6-169. �10.1051/jphyscol:1978674�. �jpa-00218354�
JOURNAL DE PHYSIQUE Colloque C6, suppl2inent au no 8, Tome 39, aolit 1978, page C6-168
THERMOROTATION EFFECTS I N S U P E R F L U I D 4
HE
E.J Yarmchuk and W.I. Glaberson
Department of Physics Rutgers University, New Bmnswick, New Jersey 08903
Rdsum6.- On a observd des contre courants thermiques perpendiculaires 2 un rdseau de lignes de vor- tex en accord avec les Bquations 1 deux fluides de Hall pour un superfluide en rotation.
Abstract.- Temperature gradients associated with thermal counter-flow transverse to an array of vor- tex lines have been observed and are consistent with Hall's two-fluid equations for the rotating su- perf luid
.
Thermal counterflow transverse to an array of differences were measured in both clockwise and parallel vortex lines causes the lines to move at counterclockwise rotations and the components of the some angle with respect to the counterflow direction. temperature gradients parallel and perpendicular to The angle is determinedvby the condition that the the heat current were obtained.
frictional force on each line, proportional to Parallel components of the temperature gra-
-f -f + -+
IvL - vnl
where VL is the line velocity and V the n dient are shown in figure I as a function of heater normal fluid velocity, is just balanced by the Ma- power.gnus force on the line, proportional to
1 3 ~ -
-fvs 1
where
?
is the superfluid velbcity. Because the chemical potential difference between two points in the liquid is proportional, as per the Josephson condition, to the rate at which the phase differen- ce "slips" and hence to the rate at which vortices pass between the points /I/ the vortex motion (rela- tive to V -+ ) leads to a chemical potential gradient at some "Hall" angle with respect to the counter- flow direction. The Hall / 2 / two-fluid equationscan be solved explicitly for temperature and pres- 1 2 3 4 sure gradients in terms of the mutual friction coef-
ficients.
Our experimental arrangement involves a glass
channel of rectangular cross-section, closed at one Fig. 1 : Temperature gradient versus heater power for the non rotating channel and for the channel end with the other end open to a pumped helium bath. rotating at 10 rad/s.
A resistive heater is placed near the closed end and
the channel is rotated about a vertical axis, per- Note that (a) the temperature gradients in the li- pendicular to the heat current. The channel investi-
gated was of large aspect ratio, the height being 1 mm, the width I cm, and the length 5-1/2 cm. Tem- perature sensors were aluminium films, held in their superconducting transition regions, evaporated onto one of the glass channel walls. The sensors were placed in the middle of the channel, approximately
1 cm apart, and separated on a line at an angle of
Q, 45 O with respect to the channel axis. The sensi- tive thermometric technique required in these ex- periments is described elsewhere 1 3 1 . Temperature
near (non turbulent) regimes are larger when rota- ting, (b) the critical heater power, associated wih onset of turbulent counterflow, is larger when ro- tating and (c) turbulent onset is characterized by a relatively smooth deviation from linearity when not rotating and a sharp change of slope when ro- tating. A plot of the linear regime slopes versus rotation speed for both the parallel and perpesidi- cular components of the temperature gradient are shown in figure 2. The solid lines are fits to the data using a solution to Hall's two fluid equations
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1978674
for a channel of infinite aspect ratio. The values References of the mutual friction coefficients obtained from
this fit are in excellent agreement with those pre- / I / Anderson, P.W., Rev. Mod. Phys. =(1966)298 viously measured / 4 / .
0 2 4 6 8 1 0
OMEGA (RAD/S)
Fig. 2 : Dependence of the temperature gradients on rotation speed.
A unique solution to Hall's two-fluid equa- tions can only be obtained by introducing a bounda- ry condition on the tangential component of V or + curl + V
.
We chose to speqify that the components of curl V perpendicular to the rotation axis are zero +s at the boundaries for the purpose of fitting the data. Progress towards the experimental determina- tion of the appropriate boundary conditions for V -+is expected from our extension of this experiment to channels of different aspect ratios and to mea- surements of chemical potential gradients.
/2/ Hall, H.E., Liquid Helium, International School of Physics "Enrico Fermi" Course XXI, edited by G. Careri (Academic Press, New York)1963,P.326 /3/ Yarmchuk, E.J. and Glaberson,W.I., to be publi-
shed
/4/ Lucas,P., J. Phys. C : Solid St. Phys.
