A dimensionless parametric relationship between the velocity and viscous layer thickness of streaming flow caused by an oscillating bubble

Abstract

The dimensionless velocity of steady streaming flow with small oscillation amplitude and low viscous layer thickness was assumed to be a function of one dimensionless parameter (viscous layer thickness). This functional relationship was validated by measuring the streaming velocities for bubbles on the size scale of hundreds of micrometers. The streaming velocities were computed for smaller bubbles to extend the range of viscous layer thickness applicable in the functional relationship. The dimensionless velocities were fitted well to the negative three-fourth power of the dimensionless viscous layer thickness, and a scaling law between the streaming velocity and bubble radius was proposed.