The classical theory of the dynamics of viscous fluids is based on the assumption that there is only one fundamental coefficient of viscosity, $\mu$, the coefficient of shear viscosity. The other quantity, ${\mu }^{\prime }$, the second coefficient of viscosity, is assumed to be equal to $-\frac{2\mu }{3}$ in order that $\kappa (=\frac{(2\mathrm{}\mu +3\mathrm{}{\mu }^{\prime })}{3})$, the coefficient of bulk viscosity, should be zero. In making this assumption classical hydrodynamics parts company from classical elasticity, in which two fundamental quantities, the Lamé constants $\lambda$ and $\mu$, are introduced.

The above assumption seems to have some basis in theory only in the case of ideal monatomic gases; it has, however, been carried over implicitly to both liquids and gases of all degrees of complexity. One might therefore expect some differences to exist between theoretical predictions and experimental results due to this oversimplification. The present review has been undertaken with a view to exploring the existence and the magnitude of any such differences.

Up to the present, discrepancies have been noticed in the field of investigation which deals with the transmission of sound energy through liquid and gases.

As far as liquids are concerned no work has been done on the absorption of energy associated with vibrations in the sonic range (20 to 20,000 vibrations per second). In the ultrasonic range experimental values of absorption differ from the theoretical ones by factors ranging from 3 to 1000. In gases, both in the sonic and supersonic ranges, the values differ by a factor whose magnitude lies in the range of 4 to 100.

Most of the work which has been done in this field has been concerned with the passage through liquids of sound energy in the ultrasonic range of frequencies. Here it is clear that the value of $\frac{{\mu }^{\prime }}{\mu }$ deduced from experiment is in good agreement with the value of the ratio deduced from information on excess absorption of energy. The viscosity ratio is never negative; its value ranges from about 1 to about 120 in the cases so far investigated.

DOI:https://doi.org/10.1103/RevModPhys.24.108