SURFACE-WAVE RESONANCE METHOD FOR MEASURING SURFACE TENSION WITH A VERY HIGH PRECISION

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1 SURFAC-WAV RSONANC MTHOD FOR MASURNG SURFAC TNSON WTH A VRY HGH PRCSON M. ino, M. Suzuki, A. kushima To cite this version: M. ino, M. Suzuki, A. kushima. SURFAC-WAV RSONANC MTHOD FOR MA- SURNG SURFAC TNSON WTH A VRY HGH PRCSON. Journal de Physique Colloques, 1985, 46 (C10), pp.c c < /jphyscol: >. <jpa > HAL d: jpa Submitted on 1 Jan 1985 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 JOURNAL D PHYSQU Colloque C10, supplement au n012, Tome 46, decembre 1985 page C SURFAC-WAV RSONANC MTHOD FOR MASURNG SURFAC TNSON WTH A VRY HGH PRCSON M. NO, M. SUZUK AND A.J. KUSHMA The nstitute for Solid State Physics, The University of Tokyo, Roppongi, Minato-ku. Tokyo 106, Japan Abstract - A very precise method for measuring surface tension using the resonance of surface waves on a liquid in a cavity has been developed. The method was then used to measure the surface tension of liquid helium, 3~e and 4~e, giving an absolute accuracy of about 0.5 mdyne/cm and a sensitivity of 10 udyne/cm or better. Further possible applications of this method are discussed.. - NTRODUCTON A new and very precise method for measuring the surface tension of liquids has been developed, in which the resonances of surface waves are measured. The method was developed with the aim of studying the surface of liquid helium at very-low and ultra-low temperatures. The surface of liquid helium is particularly interesting, since it is affected by the strong quantum nature of helium. The difficulty of measuring the surface tension of liquid helium arises not only because the temperature range is low but because the surface tension of liquid helium is quite small. t has its maximum value at absolute zero, but is still about 1/200 of that of water at O C. This therefore means that measurements to determine its variation with temperature, for instance, should be of a very high sensitivity. The present method is very sensitive even at sufficiently small heat input // SURFAC-WAV RSONANC MTHOD The principle of the present method is that the surface tension is deduced by measuring the resonance of surface waves on a liquid contained in a cavity. Figure 1 shows the sample cell, i.e., the resonance cavity, used in the present work. The cell is a simple cylinder. The surface waves are excited by applying an AC voltage to the central generator disc, by which the 1 iquid is pulled up and released cycl i- cally by dielectric force. The surface waves thus excited propagate outward, strike the cell wall, and are reflected. f the waves are excited continuously, standing waves are formed at the resonance frequencies. The restoring force acting on the surface waves are, in general,. surface tension and gravity. The resonant frequency is thus given by the relation where o is the surface tension, p the liquid density, k the wave number of a mode, g the gravitational acceleration, and d the depth of the liquid sample. To determine the resonant frequency w, the frequency of the AC voltage applied to the central generator disc is swept, and the surface standing wave is detected as the change in capacitance of the capacitor formed by the detector ring in Fig. 1 Article published online by DP Sciences and available at

3 C JOURNAL D PHYSQU and the cell body as the ground. The resonant frequency is the frequency at which the capacitance change is a maximum. Figure 2 shows such resonances measured with 4 liquid He in the present cell, with the calculated resonant frequencies shown for comparison. The agreement between the two sets of values is excel lent. n practice, the resonant frequency was obtained as the zero-crossing point of the quadrature output or the 90 -out-of-phase output of the resonance curve. Figure 3 shows a resonance and its quadrature. To determine the zero-crossing point, the measuring system in Fig. 4 was used. f the frequency deviates slightly from a resonance under examination, the quadrature output is not zero, and it is then fed back to a vol tage-controlled oscillator (V.C.O. ) so that the output frequency of the V.C.O. becomes exactly the resonant frequency. n other words, the system works as a phaselocked loop (P.L.L.) which always locks the frequency at the zero-crossing value. One difficulty with eq. (1) is to measure the sample depth d in the cryostat to sufficient accuracy. This difficulty was avoided by measuring two resonant frequencies simultaneously, enabling d to be eliminated. To demonstrate the performance of the present method, an experimental result on 4~e near the superfluid transition temperature is shown in Fig. 5 (to be published) COMPARSON OF PRSiT MTHOD WTH CAPLLARY-RS MTHOD The present method has a number of advantages compared with the conventional capillary-rise method, in which the surface tension is determined from the height of a liquid sucked up in a capillary or in a narrow gap between two parallel plates. The advantages are: (1) The method measures the surface tension of bulk 1 iqui ds, while the capi 11 aryrise method measures an "apparent surface tension" due to a liquid film. This is because, in that method, the weight of liquid in the capillary is balanced by the force coming from the "surface tension" of a thin liquid film attached to the inner wall of the capillary, rather than by the bulk surface tension. (2) The time required for the system to reach thermal equilibrium is quite short. On the other hand, it takes a much longer time to reach equilibrium in the capillaryrise method, because thermal diffusion must take place through a narrow geometry. (3) dith the present method, the absolute value of the surface tension can be determined easily, to an accuracy of about 0.5 mdyne/cm. However, with the capillary-rise method, it is extremely difficult to determine the absolute value of the surface tension. (4) The present method is highly sensitive. The sensitivity is about 10 udyne/cm or better, which is roughly 2 orders of magnitude more sensitive than the capillaryrise method. (5) With the present method, measurements are easily carried out automatically, while this is extremely difficult with the capil lary-rise method. As mentioned earlier, the heat input is quite small in the present method, since the surface waves are generated and detected capacitively. The heat input associated with the measurement is thus of the order of pw, which means that the method can be used without difficulty in ultra-low temperature experiments. V. - SOM RSULTS USNG TH PRSNT MTHOD 3 4 Figures 6 and 7 show the surface tension of liquid He and He as a function of temperature. Although several experiments have been carried out on 4~e using the capillary-rise method, the surface-wave resonance method was the first to determine the absolute value of the surface tension. The value at absolute zero was found to be mdyne/cm. The present measurement also gave the temperature dependence in the normal phase, although existing results on 4~e are sufficiently accurate in the superfluid phase because of the shorter equilibrium time in this phase compared with the normal phase. On the other hand, the result with 3~e is the first with sufficient accuracy. See literatures for physical discussions about the results /2,3,41. V. - SUMMARY A new and very precise method for measuring the surface tension of liquids was developed, and the method was used to measure the surface tension of liquid he1 ium, both 3~e and 4~e, giving accurate results. The method can also be used to determine

4 characteristics of the crystallization wave which propagates at the interface between liquid and solid helium. The method also has interesting possibilities in the study of surface activity under various conditions. RFANCS /1/ ino, M., Suzuki, M., kushima, A. J. & Okuda, Y., Jpn. J. Appl. Phys. 23 (1984) 54. /2/ ino, [., Suzuki, iil., kushima, A. J. & Okuda, Y., Proc. LT-17 (Karlsruhe, 13d4) /3/ ino, M., Suzuki, M., kushima, A. J. & Okuda, Y., J. Low Temp. Phys. 59 (1965) /4/ 231. ino, ial., Suzuki, id. d kushima, A. J. ibid. 61, to be published. To Tunnel Diode Oxillator Themometer Fig. 1 The resonant cavity used in the present work i 0, Frequency (Hz) Fig. 2 Observed resonance spectrum with liquid %e, with the calculated Fig. 3 Resonance curve of a mode resonance frequencies which are and its quadrature. marked by arrows.

5 ( JOURNAL D PHYSQU frequency Counter Micro- Computer k L VCO PD Lock-in \ u Amp T r t - Power C/F F/V D Amp. Converter Converter a ;, b ) Resonator Cryostat --,,--. L,-,,,- C #- XO-~ - -. i '* 'L - -% -~-*.Pv".,. - A t T-Th(mK) Fig. 4 Block diagram of the present Fig. 5 Singular part of the surface tenmeasuring system. sion of liquid 4~e near the superfluid transition temperature (Suzuki, ino & kusnima, to be published). Present Results,. Allen & Misener * U \ v 5 roo... b 50 - % '\ - % e0 '. -9 '?? - *P 'P, Present Results Zinov'eva, OD. Fig. 6 Temperature dependence of the Fig. 7 Temperature dependence of the surface tension of liquid 4He surface tension of liquid 3He 141. /2,3/.