Concentration waves and the instability of bubbly flows

This paper examines whether G. K. Batchelor's (1988) theory of the propagation of planar concentration disturbances and the occurrence of instabilities in uniform fluidized beds can be applied to bubbly flows. According to this theory the propagation of long weakly nonlinear gas volume concentration waves is governed by the Burgers equation. Experiments on the propagation of weak concentration shock waves and small, but finite, amplitude periodic waves are presented; good agreement is found with classic solutions of Burgers' equation. For example, the phenomenon of amplitude saturation, familiar from nonlinear acoustics, is established here for concentration waves. Batchelor's instability conditions are given for bubbly flows, and his model for the bulk modulus of elasticity of the dispersed phase is used to obtain estimates of the critical volume concentration at which a uniform bubbly flow becomes unstable to planar disturbances. Observations of the onset of instabilities of bubbly flow in a pipe are described, and compared with what would be expected from Batchelor's theory.