Sound Absorption in Liquids in Relation to Their Physical Properties

Viscosity and Specific Heats B y S. P a r t h a s a r a t h y and A . F . C h h a p g a r

With 4figures

Abstract From a study of the physical properties of liquids such as viscosity, sound

absorption and the ratio of specific heats in relation to molecular constitution, a few general rules regarding sound absorption have been derived. It has been found that in all cases, the excess absorption decreases with increasing mole- cular weight in the same manne,r as that of the ratio of specific heats. That t,he ratio of specific heats is as important as viscosity in sound absorption at high frequencies has been brought out clearly in the paper.

1. Introduction It is well known that in liquid media the absorption of sound at ultrasonic

frequencies cannot be completely explained in terms of existing theories like those of shear viscosity, second viscosity, relaxation etc. All the liquids studied so far have been selected a t random and bear no particular relation to one another except by chance. It is also well known from previous work on the velocity of ultrasonic waves in liquids that the velocity is related to the molecular constitution which brings order out of the confusion of a mass of data. This has been done1)2), both empirically and theoretically first by P a r t h a s a r a t h y and later by Lagemann, Rao , Schaaf fs , Bakhshi and others. It was therefore considered interesting to study if similar relations may hold between sound absorption as observed a t high frequencies, above 3 Me., and molecular constitution as well as other physical properties. An exami- nation of a few such physical properties, e. g. specific heats and light scattering has been undertaken in this laboratory and p a p e r ~ 3 ) ~ ) ~ ) ~ ) are under publi-

2, S. P a r t h a s a r a t h y and N. N. B a k h s h i , J. Sci. Ind. Res. 12A-10, 448 (1963). 3) Sound absorption in liquids in relation to their specific heats by S. P a r t h a s a -

r a t h y and D. S. Guruswamy, Ann. Physik (under publication). 4, Sound absorption in liquids in relation to light scattering data by S. P a r t h a -

s a r a t h y and A. P. D e s h m u k h , Ann. Physik (under publication). j) Brillouin components in light scattering in relation to sound absorption by

S. P a r t h a s a r a t h y , D. S. Guruswamy and A. P. D e s h m u k h , Ann. Physik (under publication).

6, Sound absorption in liquids in relation to their specicfic heats - Part 11 by S. P a r t h a s a r a t h y and D. S. G u r u s w a m y , Ann. Physik (under publication).

L. B e r g m a n n , Der Ultraschall (1954).

298 Annalen der Physik. 6 . Folge. Band 16. 1955

cation. These previous papers have suggested that for sound absorption vis- cosity is not the only factor prominent in absorption but the ratio of specific heats y enters in the formula and its influence is as great as that of viscosity. In this paper we have further examined sound absorption at high frequencies in relation to viscosity and specific heats.

2. Data on Physical Properties Data on absorption, viscosity and ratio of specific heats have therefore

been collected from available literature and critically examined. The data are given in Table 1 where liquids have been grouped together according to their molecular constitution. In the following Table values for viscosity have been taken from International Critical Tables while the observed absorption of sound are from the review paper of Markham, Beyer and

Fig. 1. Aliphatic hydrocarbons Lindsay) except in the case of esters where the

values of are from the paper by P a r t h a s a r a t h y , Tipnis and Pancholys) . The ratio of specific heats y are from our previous paper3). The last column gives the ratios of observed to theoretical sound absorption.

Fig. 2. Alcohols Fig. 3. Esters

The data are also given in the form of graphs for a few typical cases in figures 1 to 4. Each graph gives the relation (a) molecular weight and 7, (b) molecular weight and y (c) molecular weight and observed sound absorp-

tion and (d) molecular weight and the ratio ( 4 V 2 ) E X P . (alv2),,.

~ - for a series.

) J. J. Markham, R. T. Beyer and R. B. Lindsay, Rev. mod. Physics23-4, 353 (1951).

8 ) S. Pa r thasa ra thy , C. B. Tipnis and M. Pancholy, Ultrasonic absorption in liquids by an improved optical method and relation between absorption and specific heats Z. Physik (under publication).

S. Parthasarathy and A . F . Chhapgar: Viscosity and Specific Heats 299

3. Observations Briefly the relation between the different physical entities can be summari-

sed thus: (a) with increase in molecular weight, the viscosity always in- creases for anyseries, as observed by earlier workers, notably Gar tenme is t e r ; (b) y decreases with molecular weight whatever the series ; ( c ) the observed sound absorption decreases in the case of aromatic compounds, while it in- creases for aliphatics ; and finally (d) the excess sound absorption over the classical value continues to diminish as one ascends in the series. These results are significant and will be discussed further.

Considering the classical S t okes theory of absorption, absorption is directly proportional to viscosity. Now it is well known that viscosity and sound velocity v are related to molecular weight for members of a homologous series 9, and hence sound absorption as given by Stokes theory will also be related to molecular weight as determined by 5 . A plot of viscosity q against molecular weight M shows that q increases with M . The observed absorption however does not follow this relation. A plot of absorption against molecular weight 1M shows that for a few series like alcohols the absorption does increase with the molecular weight but that it is always higher than expected from Stokes relation. For most other series however like aromatic hydrocarbons, alkyl halides etc., the absorption decreases with increasing molecular weight and the absorption is very much higher than that given by Stokes relation. In the case of fatty acids and esters, it is found that the absorption is dependent on the frequency v of sound. This relation may be expected in accordance with the relaxation theory put forward by H e r z - feldlO), Kneser l l ) and others; yet the agreement is not complete. Even so, if a plot is made of the absorption at the same frequency against the molecular weight the same relation is found to hold good as with other series, namely the absorption decreases with molecular weight a t each frequency and is higher than that given by theory. In general, it can be stated that for aliphatic compounds, total abserved absorption increases with M (the exceptions to this are esters, bromides, etc.) but the excess ratio decreases. For aromatic compounds on the other hand total observed absorption decreases as M in- creases and the excess ratio also decreases.

In all the above cases it is found that it is always the first member of the series which has an excessively high absorption and that the observed excess absorption decreases with increasing molecular weight ; for very high values of M , it approaches the theoretical value. In other words, the excess absorp-

Fig. 4. Aromatic hydrocarbons

9, R. Gartcnmeister, Z . physik. Chem. 6, 624 (1890). l o ) K. F. Herzfeld and F. 0. Rice, Physic. Rev. 31, 691 (1928). 11) H. 0. Kneser, Ergcb. exakt. Naturwiss. 22, 121 (1949).

300 Annalen der Physik. 6 . Folge. Band 16. 1955

Table 1

Liquids

I Observed I Excess absorp- Molecular Viscosity Ratio of 'Sound abSorP- tion

(a/v*)Ex,. weights 20" C specific tion

n-pentane . . . . . . n-hexane . . . . . . n-heptane n-octane . . . . . . . n-decane . . . . . . n-undecane . . . . . n-dodecane . . . . . Methyl alcohol . . . . Ethyl alcohol . . . . n-butyl alcohol. . . .

n-nonanc . . . . . . .

n-propyl alcohol . . . n-amyl alcohol . . . . n-hexyl alcohol . . . n-heptyl alcohol . . . n-octyl alcohol . . . .

, M centipoise I

Methyl acetate . . . Propyl acetate . . . . Ethyl acetate . . . . Butyl acetate . . . . Amy1 acetate. . . . .

heatsy 1(a/v2)Exp:1017 _ _ ~ I cm-1 sec2 (a/v2),h. (i) Aliphatic Hydrocarbo

0.24 I 1.37

128,25 142,28 156,30 170,33

0,59 1,72 2,lO 2,80 4,65 4,37

32,04 46,07 60,09 74J2 88,15

102,17 116,20 130,23

1,214 1,204 1,173 1,180 1,298 1,218

74,08 I 88,lO i

102,13 116,16 130,18

3Mc.SMc.7Mc. - 296 219 156

1,436 1252 157 110 - 276 145 114

262 131 - lT81 1241 145 106

3 Mc. 5 Mc. 7 Mc 44,5 32,2 22,9 30,3 18,9 13,2 26,5 14,O 11,O 26,2 13,l - 15,8 9,5 6,9

\ ,

0,37 0,44 0,58 0,73 0,81

Ethyl bromide . . . .

n-amyl bromide . . . n-propyl bromide. . . n-butyl bromide . . .

- 77 80 - - - - -

34 54 75

104 106 132 - -

39 0,63 49

151,06 1 - c301 I - I

- 10 8 - - - - -

2,35 2,45 2,08 2,02 1,83 1,80 - -

Benzene . . . . . . . Toluene . . . . . . . o-xylene . . . . . . . p-xylene . . . . . . .

(viii) Benzene . . . . . . . Fluorobenzene Chlorobenzene Bromobenezene . . .

m-xylene. . . . . . .

. . . .

. . . .

' 78,11 900 92,13 I 8::: ~ t::2: 1

106,16 ' 0,81 - 106,16 0,60 1,319 106,16 1 0,64 I - 1 78 1

Aromatic Halogen Substitution Compounds 78,11 1 0,65 I 1,447 900 ' 96,lO 0,68 ' - l -

112,56 1 0,80 157,02 I 1,17

167 40 25

-

6 J 3,5 3 8 -

593

3,5 399

103

-

10,3 -

993 -

103 - 15,5 24 -

S. Parthasarathy and A . F. Ghhapgar: Viscosity and Specific Heats 301

tion becomes negligibly small or nil. This can be clearly shown by plotting the excess absorption (expressed as a ratio of observed to theoretical absorp- tions) against molecular weight. It is seen that the excess ratio diminishes with increasing AT in all cases. Thus it can be stated in general that there are two factors which influence absorption, both of them being some physical properties of the liquid, (a) one which predominates a t high molecular weights and (b) the other which predominates a t low molecular weights. The former factor is evidently the shear viscosity of the medium and it can be expected that for very high molecular weights, the observed absorption will reach the limiting value given by theory. The question now to be answered is - what is the other property of a liquid which fits in with all the above changes of absorption as observed and whose trend is similar to them. That the ratio of specific heats answers well this question appears to be clear.

4. Discussion Most of the postulates put forward to explain the excess observed absorp-

tion do not succed entirely when applied to all the liquids. As was noted above, viscosity by itself was not sufficient for the purpose. Therefore it was proposed that there existed a ,,second viscosity" which was responsible for the excess absorption at high frequencies. However sufficient experimental evidence is not available to support this theory. It has been contended that the streaming motion observed in a sound field is caused by this second vis- cosity factor12), but it has been pointed out by others that this streaming effect is due to other factors and not to second viscosity13). The theory of thermal relaxation is very successful in explaining the excess absorption in gases for which it was originally proposed. Rut it does not succeed in the case of liquids except for a few cases like fatty acids and esters ; even for these exceptions, the predicted dispersion of sound velocity is not found in spite of careful observation, except for the case of acetic acid1'). The theory of struc- tural relaxation 15) put forward for the case of water succeeds in the case of this particular liquid but it is not applicable as a general rule to other cascs. The absorption due to thermal conductivity as given by Kirchhoff 16) can also be neglected in the case of all liquids, this factor being negligibly small. Very recently another empirical relatian ha++ been put forward by one of us (S. P.) and G u r ~ m w i t r n y ~ ) relating the ratio of specific heats to the excess absorption from data collected for over 40 liquids. The complete sound ab- sorption can be expressed by

which has been found to be satisfactory not only in indicating and stating by how much the excess absorption varies but also the variation of sound absorp-

12) L. N. Liebermann, Physic. Rev. 76, 1415 (1949). l 3 ) J. J. Markham, J. Acoust. Soc. Amer. 23, 144 (1951). la) J. Lamb and J. M. M. P inker ton , Proc. Roy. Soc. A 199, 114 (1949). 15) L. Hall, Physic. Rev. 73, 775 (1948). 16) G. Kirchhoff, I'ogg. Ann. 134, 177 (1868).

302 Annaltn der Ph ysik. C. Fclse. Band 16. 1955

I

111 IV

tion as observed with temperature, pressure and at critical solution tem- peratures. It may be mentioned that though specific heats and their ratio occur in the Kirchhoff factor of thermal conduction, the contribution of this term itself to total sound absorption is negligible. It is the purpose of this paper to show that y plays an important part in sound absorption. Un- fortunately the values of y are not available for more series of liquids. For cases where these values are known it is found that in a homologous series y decreases with M , being highest for the lowest menber. This is very similar

to the variation of excess absorption with M and a plot of ~- against M shows that this variation is in all cases similar to that of excess absorption. This would seem to indicate that y can successfully explain the observed absorption in liquids.

5. Classification of Liquids From the above discussion it can be seen that y , an important property

of the liquid state, and q together can explain the observed absorption in liquids, y being usually predominant a t the low molecular weights and q at a t the higher end. A study of the various liquids shows that they can be divided into four groups as follows, according as y or q is the predominant factor.

This classification is similar to that proposed by Pin kertonl7) who classified them according to their absorptions and to their temperature varia- tions. In fact, it is seen that the same liquids form a group in both types of classifications. In view of the fact that the excess absorption can now be completely explained in terms of q and y , Pinke r ton ' s empirical classifi- cation in terms of absorption takes on a physical significance in the classifica- tion proposed above. We may indeed go further and state that since observed absorption can be satisfactorily accounted for by q and y and therefore presents no anomaly, the above classification, though useful, is no longer necessary for grouping the liquids.

( d V 2 ) E , , .

(@/V')T,,

Liquids showing anomalous absorption like benzene, carbon disulphide etc. Water, alcohols, etc. 1 No liquids known in this class

1 High 1 High ~ Viscous liquids like glycerine, castor oil etc. High Low

High 1 High Low

-

Class Examples

As was stated above,it is unfortunate that the liquids which have been studied so far for their sound absorbing properties have been mostly selected a t random. The foregoing discussion shows that a great deal of information can be obtained if the liquids can bestudied in terms of their molecular con- stitution. The liquids do not show any absorption in it random manner but follow a regular order. There are very few data available for different homo-

l7) J. M. M. P i n k e r t o n , Proc. physic. Soo. 62B, 129 (1949).

X. Parthasarathy and A . P. Chhupgar: Viscosity and Specific Heats 303

logous series as regards y and z/vz and hence more data would fill in the gaps. Experiments are on hand in this laboratory in this connection and results will be published when completed.

6. Sound Absorption and Chemical Constitution From the above observations and discussion, some general rules relating

sound absorption at high frequencies to chemical constitution may be derived. This is possible since sound absorption shows definite regularity with molecular constitution.

(1) Both y and 7 are operative in sound absorption. ( 2 ) High y or high 7 alone is enough to give high ultrasonic absorption. (3) Liquids having both 7 and high are unknown. (4) y is highest for the first member of a series (lowest C atom) and then

it decreases regularly. ( 5 ) In all cases, the excess sound absorption over the classical value also

follows the same trend as y, the noticeably excess absorption being found only in the first few members of the series.

(6) In aliphatic compounds, which have low y, ultrasonic absorption increases with molecular weight but the excess absorption over the classical decreases.

( 7 ) In aromatic compounds however, both ultrbsonic and the excess absorption decrease as molecular weight increases.

(8) The observed value of absorption for liquids of high molecular weight approaches the limiting value given by S tokes s theory.

From these observations we may infer that what has been considered so far as anomalous absorption does not exist, this anomaly being due to the neglect of the part y plays in sound absorption a t high frequencies. Sound absorption is normal for any liquid if both y and 7 are considered as effective in the process.

NewDelhi 12, National Physical Laboratory of India.

Bei der Redaktion eingegangen am 8.Marz 1955.