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

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

HIGH PRECISION

M. Iino, M. Suzuki, A. Ikushima

To cite this version:

M. Iino, M. Suzuki, A. Ikushima. SURFACE-WAVE RESONANCE METHOD FOR MEASURING

SURFACE TENSION WITH A VERY HIGH PRECISION. Journal de Physique Colloques, 1985, 46

(C10), pp.C10-813-C10-816. �10.1051/jphyscol:198510178�. �jpa-00225391�

JOURNAL DE PHYSIQUE

Colloque C10, supplement au n012, Tome 46, decembre 1985 page C10-813

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

M . I I N O , M. SUZUKI AND A.J. IKUSHIMA

The Institute for Solid State Physics, The University of Tokyo, Roppongi, Minato-ku. Tokyo 106, Japan

Abstract

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A very precise method for measuring surface tension using the reso- nance o f 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 s e n s i t i v i t y of 10 udyne/cm or better. Further possible applications of t h i s method are discus- sed.

I.

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INTRODUCTION

A new and very precise method f o r measuring the surface tension of liquids has been developed, in which the resonances of surface waves a r e measured. The method was developed with the aim of studying the surface of liquid helium a t very-low and ultra-low temperatures. The surface of liquid helium i s particularly interesting, since i t i s affected by the strong quantum nature of helium.

The d i f f i c u l t y of measuring the surface tension of liquid helium a r i s e s not only because t h e temperature range i s low but because the surface tension of l i q u i d helium i s quite small. I t has i t s maximum value a t absolute zero, but i s s t i l l about 1/200 of t h a t of water a t O°C. This therefore means t h a t measurements t o determine i t s variation with temperature, f o r instance, should be of a very high s e n s i t i v i t y . The present method is very sensitive even a t sufficiently small heat input /I/.

11.

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SURFACE-WAVE RESONANCE METHOD

The principle of the present method i s t h a t the surface tension i s deduced by measuring the resonance of surface waves on a l i q u i d contained i n a cavity. Figure

1 shows the sample c e l l , i . e . , the resonance cavity, used i n the present work. The c e l l i s a simple cylinder. The surface waves a r e excited by applying an AC voltage t o the central generator d i s c , by which the 1 iquid i s pulled up and released cycl i - c a l l y by d i e l e c t r i c force. The surface waves thus excited propagate outward, s t r i k e the cell wall, and a r e reflected. I f the waves a r e excited continuously, standing waves a r e formed a t the resonance frequencies.

The restoring force acting on the surface waves are, i n general

,.

surface ten- sion and gravity. The resonant frequency i s thus given by the r e l a t i o n

where o i s 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 t o the central generator d i s c i s swept, and the surface standing wave i s detected as the change in capacitance of the capacitor formed by the d e t e c t o r ring in Fig. 1

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:198510178

C10-814 JOURNAL DE PHYSIQUE

and the cell body a s the ground. The resonant frequency i s the frequency a t which the capacitance change i s a maximum. Figure 2 shows such resonances measured with liquid He in the present c e l l , with the calculated resonant frequencies shown f o r 4 comparison. The agreement between the two s e t s of values i s excel lent.

In practice, the resonant frequency was obtained a s 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 i t s quadrature. To determine the zero-crossing point, the measuring system i n Fig. 4 was used. I f the frequency deviates s l i g h t l y from a reso- nance under examination, the quadrature output i s not zero, and i t i s then fed back t o a vol tage-controlled o s c i l l a t o r (V.C.O. ) so t h a t the output frequency of the V.C.O.

becomes exactly the resonant frequency. In other words, the system works as a phase- locked loop (P.L.L.) which always locks the frequency a t the zero-crossing value.

One d i f f i c u l t y with eq. (1) is t o measure the sample depth d i n the cryostat t o s u f f i c i e n t accuracy. This d i f f i c u l t y was avoided by measuring two resonant fre- quencies simultaneously, enabling d t o be eliminated.

To demonstrate the performance of the present method, an experimental r e s u l t on 4 ~ e near the superfluid t r a n s i t i o n temperature i s shown i n Fig. 5 ( t o be published).

111.

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COMPARISON OF PRESEiIT METHOD WITH CAPILLARY-RISE METHOD

The present method has a number of advantages compared with the conventional capillary-rise method, i n which the surface tension i s determined from the height of a liquid sucked up in a capillary or i n 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 ary- r i s e method measures an "apparent surface tension" due t o a liquid film. T h i s is because, in t h a t method, the weight of liquid in the c a p i l l a r y i s balanced by the force coming from the "surface tension" of a thin liquid film attached t o the inner wall of the capillary, rather than by the bulk surface tension.

( 2 ) The time required f o r the system to reach thermal equilibrium i s q u i t e short. On the other hand, i t takes a much longer time t o reach equilibrium in the capillary- r i s e method, because thermal diffusion must take place through a narrow geometry.

( 3 ) d i t h the present method, the absolute value of the surface tension can be deter- mined e a s i l y , t o an accuracy of about 0.5 mdyne/cm. However, with the capillary-rise method, i t i s extremely d i f f i c u l t t o determine the absolute value of the surface tension.

(4) The present method i s highly sensitive. The s e n s i t i v i t y i s about 10 udyne/cm or b e t t e r , which i s roughly 2 orders of magnitude more sensitive than the capillary- r i s e method.

(5) With the present method, measurements a r e e a s i l y carried out automatically, while t h i s i s extremely d i f f i c u l t with the capil l a r y - r i s e method.

As mentioned e a r l i e r , the heat input is q u i t e small i n the present method, since the surface waves a r e generated and detected capacitively. The heat input associated with the measurement i s thus of the order of pW, which means t h a t the method can be used without d i f f i c u l t y i n ultra-low temperature experiments.

IV.

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SOME RESULTS USING THE PRESENT METHOD

3 4

Figures 6 and 7 show the surface tension of liquid He and He a s a function of temperature. Although several experiments have been carried out on 4 ~ e using the capillary-rise method, t h e surface-wave resonance method was the f i r s t t o determine the absolute value of the surface tension. The value a t absolute zero was found t o be 354.4 2 0.5 mdyne/cm. The present measurement also gave the temperature dependen- ce in the normal phase, although existing r e s u l t s on 4 ~ e are s u f f i c i e n t l y accurate i n the superfluid phase because of the shorter equilibrium time in t h i s phase compared w i t h the normal phase. On the other hand, the r e s u l t with 3 ~ e i s the f i r s t with suf- f i c i e n t accuracy. See l i t e r a t u r e s f o r physical discussions about the r e s u l t s /2,3,41.

V.

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^SUMMARY

A new and very precise method f o r measuring the surface tension of liquids was developed, and the method was used t o measure the surface tension of liquid he1 ium, both 3 ~ e and 4 ~ e , giving accurate results. The method can also be used t o determine

c h a r a c t e r i s t i c s o f the c r y s t a l l i z a t i o n wave which propagates a t the i n t e r f a c e between l i q u i d and s o l i d helium. The method a l s o has i n t e r e s t i n g p o s s i b i l i t i e s i n t h e study o f surface a c t i v i t y under various conditions.

REFEAENCES

/1/ I i n o , M., Suzuki, M., Ikushima, A. J. & Okuda, Y., Jpn. J. Appl. Phys.

23

(1984) 54.

/2/ I i n o , [ I . , Suzuki, iil., Ikushima, A. J. & Okuda, Y., Proc. LT-17 (Karlsruhe, 13d4) /3/ I i n o , M., Suzuki, M., Ikushima, A. J. & Okuda, Y., J. Low Temp. Phys.

59

(1965)

231.

/4/ I i n o , ial., Suzuki, id. d Ikushima, A. J. i b i d .

61,

t o be published.

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