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Submitted on 1 Jan 1978
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EVAPORATION AND CONDENSATION IN 3He-4He MIXTURE SYSTEMS
S. Ohta, Y. Sawada
To cite this version:
S. Ohta, Y. Sawada. EVAPORATION AND CONDENSATION IN 3He-4He MIXTURE SYSTEMS.
Journal de Physique Colloques, 1978, 39 (C6), pp.C6-194-C6-195. �10.1051/jphyscol:1978686�. �jpa-
00218366�
JOURNAL DE PHYSIQUE Colloque C6, suppliment au no 8, Tome 39, aofit 1978, page C6-194
EVAPORATION AND CONDENSATION IN
3 ~ e - 4 ~ eMIXTURE SYSTEMS
S. Ohta and Y. Sawada
Research I n s t i t u t e o f EZectricaZ C o m i c a t i o n , Tohoku University, Sendai, Japan
R6sumC.- L1&vaporation et la condensation d'un mi5lange 3 ~ e - 4 ~ e ont dt6 i5tudiEes expdrimentalenent par une technique d'impulsion de chaleur. Une analyse fond6e sur un modSle de faible couplage entre les Ltats de surface et les excitations du liquide, consid6rL c o m e m6canisme d16vaporation et de condensation, donne des renseignements sur les Ltats de surface des atomes 3 ~ e qui s'accordent avec les mesures de tension superficielle.
Un calcul bas6 sur ce modSle donne une valeur de 0.31 pour le rapport des sections efficaces de capture des excitations du liquide, par les atomes 3 ~ e de surface et par les atomes 'He de surface, respectivement.
Abstract.- Evaporation and condensation of mixed 3~e-'~e system were studied experimentally using heat pulse technique. Analysis based on a weak coupling model of the surface state with the bulk excitations as an evaporation and condensation mechanism gave information on 3 ~ e surface trapped state which agrees with the surface tension measurements.
Calculation based on this model for the ratio of the cross section of surface 3 ~ e atoms for bulk excitations to that of surface 'He atoms gives 0.31.
Since Johnston and King's first experiment .ground state of the surface eigenstate and Anderson's proposal of. a model for evaporation
several experimental and theoretical studies have been made on the evaporation and condensation from Be 11. However, a microscopic mechanism of the eva- poration and condensation is still open to be un- derstood in many respects at the present stage. We present first experimental data on the evaporation and condensation at the liquid-gas interface of 3 ~ e - 'He mixtures at 1,58 K.
Evaporating atoms from liquid film covering on the heater were detected by a microphone to mea- sure the pressure variation of gas phase and also by a superconductor bolometer to measure the tempe- rature variation by the condensation. As shown in figure 1 , peak heights of the sigaal received by. the microphone depend linearly on 3 ~ e concentration of Xiqbid phase X,, while peak heights of the bolometer signal divided by that of the microphone signal de-
Fig. 1 : a) Peak height of microphone signal AP nor- malized by the value for pure 4 ~ e depends linearly on liquid concentration X and its proportional constant is 1.58 ? 0.25. 'b) Ratio of bolometer sig- nal AT to micropohone signal AP normalized by the value for pure 4 ~ e depends linearly on gas concen- tration Xg and its proportional constant is
-
0.69 C 0.06 pend linearly on 3 ~ e concentration of gas phase Xin equilibrium. by emitting bulk excitation. Assuming that the atoms
order to quantitatively these evaporating from the liquid have a Maxwellian velo- experimental results in connection to the ratio of city distribution of liquid temperature, and the gas concentration tq liquid in equili- drift velocity v of the distribution of gas is equal brium, we assume a following semi-microscopic weak to zero near the surface, this model leads to the coupling model for the mechanism of evaporation and following expressions for the number of evaporating condensation. ~h~ atoms evapQrate from the ground and condensing atoms per unit area and unit time.
state of the 9urface.eigenstate excited to the con- N . = N .a.n. (TI)
~ e v a p s l i 1 tinuum by absorbing bulk excitation which has ener-
and gies greater than a threshold value
Ai
(i=3.4). Theatoms condensed from the continuum fall to the Ni con = N s a ! ~ 1 sl .I ( ~ m n ~ k ~ ~ ) ' / ~
,
i = 3,4 (2)Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1978686
where n.(T1) is the number of bulk excitations arri- ving at the surface of unit area per unit time ef- fective for evaporating a 3 ~ e or 'He atom from the surface at liquid temperature T1, and we assume ni(T1) = f (Tl)exp(-Ai/kTl) where f (TI) is slowly varying function. Nsi is the number of surface 3 ~ e or '~e atoms per unit area. For the low concentra- tion of 3 ~ e we write as ; NS3 = aXINS,
Ns r = (I-aXI)Ns, where a is the enhancement factor of 3 ~ e concentration at the surface and N is the total number of atoms at the surface.
a.
and o! are the average cross sections for the evaporation and condensation, and we assume from detailed balance a. is equal to a!. Psi and T are the partial pres- sure and the temperature of gas phase just above the surface. m. is the mass of 3 ~ e or 'He atoms.For non-equilibrium conditions when a heat pulse W(t) is put into the liquid film from the hea- ter or when the pressure variation 6P (t) arrives
in
at the surface of liquid film, we write following expressions for the conservation of energy in the liquid film and for the continuity of mass, energy and momentum flux in the gas phase between far field and.interfacia1 boundary /I/.
-N. ) = 1m.n
i i a 1 con 1 giV
,
(4)and
where C 1 is the specific heat of the liquid film.
n is the number of 3 ~ e or 'He atoms in gas phase gi
of unit volume. To and P o are the temperature and pressure in equilibrium. &Pout is the pressure va- riation of gas phase produced by the net evapora- ting atoms. We firstaolve 6Ts, 6Ps and Spout from eq.(1,2,4-6) in terms of &TI and 6Pi, (6 denotes de- viation from thermal equilibrium) by setting v=v .
out
of the temperature variation 6T1 and the maximum peak height 6Pm of the pressure variation 6P out' and we obtain the expressions normalized by their values at XI =O of 6Pm/ (SP,) and (STm/SPm) / (6Tm/SPm) L,
.
Byequating these two expressions with our experimen- tal data and by using a relation X /X =a(n3/nb)
g 1
(m31m1,)~' which is obtained for small XI from the conditions of Ni evap = Ni con at equilibrium state, we obtain :
A = 4.5k0.7 K a = 5.5 1- 2.1, a3/a4 = 0.31 i 0.02;
where we assume A is equal to the latent heat of pure liquid 4 ~ e at 0 K.
The analysis of the data based on this model gives a fairly good agreement for the surface state with the measurement of surface tension for the 3 ~ e -
'He mixture. The condensation coefficient for 4 ~ e and 3He atoms has been known by reflection measure- ment /2,3/ to be close to unity. Our results toge-
ther with this model seems to indicate that the cross section of surface 3 ~ e atoms to capture the bulk excitation is smaller than that of 4 ~ e atoms by the factor 0.3. It is not understood at present moment whether this discrepancy should be attributed to the difference of the experimental conditions (temperature range, concentration range, etc
...
) orif the model used here requires further improvements.
References
/ I / Hunter, G.H. and Osborne, D.V., J. Phys. C
(Solid St. Phys.)
2
(1969) 2414/2/ Edwards, D.O., Fatouros, P., IHAS, G.G., Mrozinski, P., Shen, S.Y., Gasparini, F.M. and Tam, C.P., Phys. Rev. Lett.
2
(1975) 1153 /3/ Edwards, D.O., Fatouros, P.P. and Ihas, G.G.,Phys. Lett. (1976) 131
-vin
and. e.xpressing V andvin
in terms of &Pout outand 6Pin(t) from the relation of sound wave. From equation (3) we can gel! the maximum peak height STm
