Viscosity, Second

Viscosity, Second


(also second viscosity coefficient, bulk coefficient of friction, or dilatational coefficient of friction), a property of a liquid or gaseous medium that characterizes the irreversible transformation of mechanical energy into heat within the medium when this transformation is due to dilatational strains. Second viscosity is manifested, for example, during the propagation of sound waves and especially ultrasonic waves in liquids and gases. The value of the second viscosity coefficient η’, like that of the shear viscosity coefficient η, determines the magnitude of sound absorption.

If the equilibrium state of a medium is practically undisturbed when sound propagates through the medium, which is the case when the characteristic time required for the establishment of equilibrium (the relaxation time) is very small in comparison with the period of the sound wave, then the second viscosity coefficient η’ is independent of the frequency. If, however, thermodynamic equilibrium is disrupted when sound propagates through the medium, then η’ assumes anomalously large values and becomes a function of the sound frequency. In this case, processes that tend to restore equilibrium—relaxation processes—arise. These processes are accompanied by the irreversible transformation of mechanical strain energy into heat.

Data on the absorption and dispersion of sound usually are used to determine the second viscosity coefficient. The value of η’ depends on the temperature and pressure: it usually decreases with increasing temperature and increases with increasing pressure. The value of the second viscosity usually is greater in liquids than in gases, on the average, by one to three orders of magnitude.


Landau, L. D., and E. M. Lifshits. Mekhanika sploshnykh sred, 2nd ed. Moscow, 1954. Section 78.
Fizicheskaia akustika, vol. 2, part A. Edited by W. P. Mason. Svoistva gazov. zhidkostei i rastvorov. Moscow, 1968. (Translated from English.)