Viscosities 2.2.3



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2.2.3 Viscosities

Viscosities of liquids

The dynamic viscosity, η of a (Newtonian) fluid is given by η = τ ÷ dv/dr; τ = shearing stress between two planes parallel with the direction of flow, dv/dr = velocity gradient at right angles to the direction of flow. The dimensions of dynamic viscosity are ML⁻¹T⁻¹, and the SI unit is Pa s.

Kinematic viscosity, ν, is the ratio of the dynamic viscosity to the density, ρ. The dimensions of kinematic viscosity are L²T⁻¹ and the SI unit is m² s⁻¹.

Fluidity, is the reciprocal of the dynamic viscosity, η. The dynamic viscosity of liquids decreases with the temperature approximately according to the equation log η = A + B/T, where A and B are characteristic constants and T is the absolute temperature. Values of A and B for a large number of liquids are given by Barrer (1943).

(i) Viscosity of water. Data from Kestin, Sokolov and Wakeham (1978).

Temp.

°C

mPa s

Temp.

°C

mPa s

Temp.

°C

mPa s

Temp.

°C

mPa s

1.792

1.0020

0.5471

0.3150

1.519

0.8902

0.4670

100

0.2821

1.307

0.7973

0.4046

125

0.2217

1.138

0.6526

0.3551

150

0.1818

(ii) Viscosities of various liquids. η in mPa s

Liquid	−100 °C	− 50 °C	0 °C	25 °C	30 °C	50 °C	75 °C	100 °C

Acetic acid . .	—	—	—	1.116	1.037	0.792	0.591	0.457
Acetone . .	—	—	0.402	0.310	0.295	0.247	0.200	0.165
Aniline . .	—	—	9.450	3.822	3.298	1.982	1.201	0.808
Benzene . .	—	—	—	0.603	0.562	0.436	0.332	0.263
Bromobenzene .	—	—	1.592	1.065	0.995	0.780	0.605	0.488
n-Butane . . .	0.747	0.339	0.197	0.157	0.150	—	—	—
Carbon disulphide	2.132	0.796	0.445	0.357	0.343	—	—	—
Carbon dioxide .	—	0.227	0.098	0.057	—	—	—	—
Carbon tetrachloride	—	—	1.341	0.912	0.851	0.662	0.503	0.395
Chloroform . .	—	1.514	0.709	0.536	0.510	0.422	0.341	0.281
Di-ethyl ether .	1.545	0.544	0.288	0.224	0.214	0.179	0.146	0.119
Ethanol . . .	98.96	8.318	1.873	1.084	0.983	0.684	0.459	0.323
Ethyl acetate .	—	1.284	0.575	0.428	0.406	0.332	0.264	0.215
Ethyl formate .	—	1.060	0.504	0.381	0.362	0.299	0.240	0.196
n-Hexane . .	—	0.782	0.387	0.296	0.282	0.235	0.190	0.155
n-Hexadecane .	—	—	—	3.044	2.729	1.852	1.245	0.896
Mercury . .	—	—	1.616	1.528	1.497	1.401	1.322	1.255
Methane . .	0.0357	—	—	—	—	—	—	—
Methanol . .	—	2.258	0.797	0.543	0.507	0.392	0.294	0.227
Nitrobenzene .	—	—	—	1.842	1.688	1.244	0.915	0.710
n-Octane . .	—	1.837	0.719	0.516	0.486	0.390	0.306	0.247
Oil, castor . .	—	—	—	700	451	125	42.0	16.9
Oil, olive . . .	—	—	—	67.0	54.0	25.8	9.4	7.0
n-Pentane . .	1.300	0.498	0.273	0.214	0.205	0.173	0.140	0.115
n-Propane . .	0.421	0.215	0.127	0.099	0.094	—	—	—
Sulphuric acid .	—	—	—	23.8	20.1	11.7	6.6	4.1
Toluene . . .	—	2.124	0.768	0.551	0.520	0.420	0.334	0.272

For more data see: ESDU (1966–83), Landolt-Börstein (1969).

(iii) Viscosity of aqueous glycerol solutions. Data from Segur and Oberstar (1951), corrected to value for water at 20 °C of 1.002 mPa s.

Density 20° kg/l	% weight glycerol	η/Pa s
		20°C	30°C	40°C


1.2611	100	1.408	0.610	0.283
1.2588	99	1.146	0.498	0.234
1.2562	98	0.936	0.408	0.195
1.2534	97	0.763	0.339	0.165
1.2508	96	0.622	0.280	0.142
1.2482	95	0.521	0.236	0.121
1.2085	80	0.059 9	0.033 8	0.020 7
1.1254	50	0.005 98	0.004 20	0.003 09
1.0459	20	0.001 75	0.001 35	0.001 07
1.0215	10	0.001 31	0.001 03	0.000 823

(iv) Viscosity of aqueous sucrose solutions. Data from Bingham and Jackson (1918), corrected to a more recent value for the viscosity of water.

Relative density
20°/4 °C

% weight
sucrose

η/Pa s

15 °C

20 °C

25 °C

1.3790	75	4.039	2.328	1.405
1.3472	70	0.746 9	0.481 6	0.321 6
1.3163	65	0.211 3	0.147 2	0.105 4
1.2865	60	0.079 49	0.058 49	0.040 03
1.2296	50	0.019 53	0.015 43	0.012 40
1.1764	40	0.007 463	0.006 167	0.005 164
1.1270	30	0.003 757	0.003 187	0.002 735

(v) Relative viscosities of some aqueous solutions at 1 N concentration. For a complete list see International Critical Tables (1928) and Stokes and Mills (1965). (The latter covers 1929–63.)

Substance	Temp./°C	Relative viscosity	Substance	Temp./°C	Relative viscosity
Ammonia . . . . .	25	1.02	Potassium chloride . .	17.6	0.98
Ammonium chloride . .	17.6	0.98	Potassium iodide . .	17.6	0.91
Calcium chloride . . .	20	1.31	Sodium hydroxide . .	25	1.24
Hydrochloric acid . . .	15	1.07	Sulphuric acid . . .	25	1.09

(vi) Viscosity of liquid metals and molten salts. η in mPa s

Liquid	100 °C	400 °C	600 °C	700 °C	800 °C	1100 °C	1200 °C
Aluminium . . . . . .	—	—	—	2.96	2.66	—	—
Gold . . . . . . .	—	—	—	—	—	5.13	4.64
Lead . . . . . . .	—	2.32	1.55	1.37	1.24	—	—
Potassium . . . . .	0.458	0.224	0.172	0.155	0.141	—	—
Sodium . . . . . .	0.680	0.286	0.215	0.192	0.174	—	—
Tin . . . . . . . .	—	1.33	1.04	0.95	0.89	0.78	0.77
Potassium chloride . . .	—	—	—	—	1.096	–	–
Potassium nitrate . . . .	—	2.09	1.07	—	—	—	—
Sodium chloride . . . .	—	—	—	—	1.500^†	—	—
Sodium nitrate . . . .	—	1.91	–	—	—	—	—

^†816°C.

For more data on molten salts see G. J. Janz (1968). For liquid metal see Smithell (1983, p. 14.2).

Viscosities of glasses and minerals. log₁₀(η/Pa s)

Material	900 °C	1000 °C	1100 °C	1200 °C	1300 °C	1400 °C	1600 °C	1800 °C	2000 °C

Plate glass . .	4.00	3.03	2.41	1.87	1.46	1.07	—	—	—
Medium flint glass	3.9	2.8	1.9	1.4	0.9	0.7	—	—	—
Silica . . .	—	—	14.6	12.7	11.8	9.7	8.2	4.7	3.4
Olivine . .	—	—	—	2.5	1.5	1.2	—	—	—
Diorite . .	—	—	—	3.1	2.3	1.8	—	—	—
Diopside . .	—	—	—	—	0.52	0.43	—	—	—

Viscosities of liquids at high pressures

(i) Relative viscosity of water

Pressure/MPa

2.2 °C

10 °C

20 °C

30 °C

50 °C

75 °C

100 °C


0.1	1.000	1.000	1.000	1.000	1.000	1.000	1.000
49	0.946	0.969	0.990	0.998	1.021	1.029	1.043
98	0.926	0.957	0.990	1.008	1.046	1.063	1.085
196	0.940	0.982	1.023	1.053	1.104	1.137	1.170
294	0.993	1.037	1.081	1.116	1.174	1.217	1.256
392	1.072	1.185	1.163	1.195	1.253	1.302	1.349
588	1.296	1.330	1.367	1.386	1.439	1.492	1.546
784	—	—	1.629	1.642	1.664	1.708	1.757
981	—	—	—	1.950	1.936	1.948	1.986

(ii) Relative viscosities of various liquids. Ratio = η_p/η₀ at same temperature.

Liquid	Temp./°C	Pressure/MPa
Liquid	Temp./°C	98	100	392	400	784	1177

Acetone . . . .	30	1.68	—	4.03	—	9.70	—
	75	1.65	—	3.55	—	7.36	13.7
Benzene . . . .	30	2.22	—	—	—	—	—
	50	—	2.06	—	—	—	—
	75	2.07	2.00	—	—	—	—
	100	—	1.98	—	7.40	—	—
Carbon disulphide .	30	1.45	—	3.23	—	6.92	15.5
	75	1.50	—	3.14	—	6.25	11.8
Di-ethyl ether . .	30	2.11	—	6.20	—	18.2	46.8
	75	1.87	—	5.28	—	12.8	27.1
Ethanol . . . .	30	1.59	—	4.14	—	10.5	24.5
	75	1.64	—	4.28	—	9.48	18.3
n-Hexane . . . .	25	—	2.10	—	—	—	—
	30	2.15	—	8.20	—	32.7	—
	75	2.33	2.21	7.91	7.41	24.8	69.7
	100	–	2.26	—	7.22	—	—
n-Hexadecane . .	50	—	2.89	—	—	—	—
	75	—	2.69	—	—	—	—
	100	—	2.61	—	15.0	—	—
Methanol . . . .	30	1.47	—	2.96	—	5.62	9.95
	75	1.46	2.74	—	—	4.77	7.69
n-Octane . . . .	25	–	2.31	—	12.9	—	—
	30	2.12	—	12.3	—	—	–
	75	2.20	2.24	8.97	9.19	35.7	—
	100	—	2.25	—	8.56	—	—
n-Pentane . . . .	30	2.07	—	7.03	—	22.9	70.2
	75	2.25	—	7.33	—	20.3	48.1
Toluene . . . .	30	1.87	7.89	—	—	50.0	—
	75	1.86	—	6.33	—	24.6	109

Data from Bridgman (1926), except at 100 and 400 MPa which comes from K. J. Young, PhD Thesis, University of Glasgow, Nov. 1980, and Dymond, Robertson and Isdale (1981).

Viscosities of gases and vapours

(i) Viscosities at normal pressure. Units: μPa s.

Gas

0 °C

20 °C

50 °C

100 °C

200 °C

300 °C

400 °C

500 °C

600 °C


Air . . . . .	17.3	18.2	19.6	22.0	26.1	29.8	33.2	36.4	39.4
Ammonia . . .	9.2	9.9	11.0	13.0	16.8	20.6	24.4	28.2	31.9
Argon . . . .	21.0	22.3	24.2	27.3	32.8	37.7	42.2	46.4	50.4
Benzene . . .	7.0	7.5	8.1	9.4	12.0	—	—	—	—
Carbon dioxide .	13.7	14.7	16.1	18.5	23.0	27.1	30.8	34.2	37.4
Carbon monoxide	16.6	17.4	18.8	21.0	25.2	29.0	32.5	35.6	38.6
Chlorine . . .	12.3	13.2	14.5	16.9	21.0	25.0	—	—	—
Chloroform . .	9.4	10.1	11.1	12.8	16.2	19.5	—	—	—
Ethylene . . .	9.7	10.3	11.2	12.8	15.4	17.9	—	—	—
Helium	18.7	19.6	21.0	23.2	27.3	31.2	34.8	38.4	41.8
Hydrogen . . .	8.4	8.8	9.4	10.4	12.1	13.7	15.3	16.9	18.4
Krypton . . .	23.4	25.0	27.4	31.2	38.0	44.2	49.9	55.2	60.2
Methane . . .	10.3	11.0	11.9	13.5	16.3	18.8	21.1	23.3	25.3
Neon . . .	29.8	31.3	33.6	37.0	43.2	48.9	54.3	59.4	64.4
Nitrogen . . .	16.6	17.6	18.9	21.2	25.1	28.6	31.9	34.9	37.8
Nitrous oxide . .	13.7	14.7	16.1	18.4	22.9	27.0	30.7	34.0	37.0
Oxygen . . .	19.5	20.4	21.8	24.4	29.3	33.7	37.6	41.3	44.7
Steam . . .	9.2	9.7	10.6	12.4	16.2	20.3	24.5	28.6	32.6
Sulphur dioxide .	11.6	12.6	14.0	16.4	20.9	25.1	29.0	32.6	36.1
Xenon . . .	21.2	22.8	25.1	28.8	35.7	42.0	47.9	53.4	58.6

For viscosity of gases μPa s is a convenient size of unit. From the kinetic theory the viscosity is expected to be independent of pressure and to vary as the square root of the absolute temperature. The first is true except at very low and at high pressures; the second requires correction. Dividing the kinetic theory expression by a correction factor which is a linear function of the reciprocal of the absolute temperature leads to Sutherland’s formula η = KT^3/2/(T + C), where K and C are constants characteristic of the gas. For higher accuracy a polynomial can be used instead of a linear factor.

(ii) Viscosities of some gases at high pressure. η/μPa s (all at 300 K)

Gas

Pressure/MPa

Air . . . . . .	18.7	19.3	20.5	23.7	27.5
Argon . . . . .	23.3	24.0	25.7	30.5	36.4
Helium . . . . .	19.9	19.9	20.0	20.1	20.3
Hydrogen . . . .	8.98	9.01	9.09	9.31	9.59
Methane . . . .	11.6	12.3	14.0	19.2	24.7
Nitrogen. . . . .	18.3	18.9	20.1	23.2	26.8
Oxygen . . . .	20.9	21.5	22.9	27.1	32.2

(iii) Viscosity of nitrogen at high pressure. η/μPa s.

Temperature/K	Pressure/MPa
Temperature/K	5	10	20	30	50

200	14.6	17.6	26.4	34.9	48.9
250	16.7	18.5	23.1	28.4	38.8
300	18.9	20.1	23.2	26.8	34.4
350	20.9	21.9	24.2	26.9	32.7
400	22.9	23.7	25.5	27.6	32.3
500	26.5	27.1	28.4	29.9	33.2

References

Barrer (1943) Trans. Farad., 39, 48.
Bingham and Jackson (1918) National Bureau of Standards, Bulletin, 14, 59.
P. W. Bridgman (1926) Proc. Am. Acad. Arts Sci., 61, 57–99.
J. H. Dymond, J. Robertson and J. D. Isdale (1981) Int. J. Thermophysics, 2(2), 133–154; ibid., 2(3), 223–236.
Engineering Science Data (ESDU) Physical Data (1966–83) Chemical Engineering, vol. 3, Viscosity, London.
International Critical Tables (1928).
G. J. Janz (1968) NSRDS-NBS 15, report, Natl. Bur. Standards, Washington.
Kestin, Sokolov and Wakeham (1978) J. Phys. Chem. Ref. Data, 7(3), 941.
Landolt-Börnstein (1969) Vol. II, Properties of Matter in its Aggregated States, Part 5a, Viscosity and Diffusion, 6th edn, Springer-Verlag, Berlin.
Segur and Oberstar (1951) Ind. Eng. Chem., 43, 2117.
Smithell (1983) Metal Reference Book, 6th edn, Butterworth, London, p. 14.2.
R. H. Stokes and R. Mills (1965) Viscosity of Electrolytes and Related Properties, Pergamon Press, London.
K. J. Young (1980) PhD Thesis, University of Glasgow.

J.T.R.Watson

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