Light Scattering and Fluid Viscosity

Abstract

ACCORDING to well-known hydrodynamical theory¹, 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/8π²v, where C is the velocity of sound, λ is the wave-length of sound and vis 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 Einstein² and L. Brillouin³, 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 NATURE⁴, 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.