The two coefficients of viscosity for an incompressible fluid containing air bubbles

Abstract

Incompressible fluids possess only one coefficient of viscosity because, by definition, no changes in volume can occur. If such a fluid contains air bubbles it becomes compressible, and any changes in volume involves a contraction or expansion of the bubbles which is resisted by the ordinary viscosity of the surrounding fluid. The resulting second coefficient of viscosity is found to be 4μ/3v, where μ is the viscosity of the incompressible fluid and v the (small) proportion of the total volume which is occupied by the bubbles. The effect of compressibility in the fluid is discussed in Notes by Sir Geoffrey Taylor and Dr R. O. Davies. In the second of these it is shown that a relaxation time must exist and in the first the volume viscosity of water containing air bubbles is calculated. This is found to reach a maximum value of 6700 times the viscosity of water when v = 5 x 10 -5 .