Light scattering and fluid viscosity

Abstract

According to well-known hydrodynamical theory, plane waves of sound propagated through a viscous liquid suffer a diminution of amplitude in the ratio 1/e in traversing a number of wave-lengths given by the quantity 3Cλ/8π²ν, where C is the velocity of sound, λ is the wave-length of sound and ν is the kinematic viscosity. Taking λ = 4358 A., this number for various common liquids which are fairly mobile at room temperature ranges from about 3 in the case of butyl alcohol to about 30 in the case of carbon disulphide. For phenol at 25° C., the number is less than 1, and for glycerine, it is a small fraction of unity. A consideration of these numbers shows that the theories due to Einstein and L. Brillouin, which regard the diffusion of light occurring in liquids as due to the reflection of light by regular and infinitely extended trains of sound-waves present in them, can only possess partial validity for ordinary liquids, and must break down completely in the case of very viscous ones. In an earlier note in Nature, we reported studies of the Fabry-Perot patterns of scattered light with a series of liquids, which showed clearly that the Doppler-shifted components in the spectrum of scattered light fell off in intensity relatively to the undisplaced components, with increasing viscosity of the liquid.