Steady Streaming and Pumping Driven by Two Frequency Oscillations

Recent experiments showed net transport of an object sliding on a surface undergoing two mode vibrations for certain frequency pairs. Inspired by these experiments, we revisit the classical problem of steady streaming in fluids (i.e. nonzero mean flow produced from periodic forcing) driven by multifrequency oscillations. Using numerical simulations, we examine the flow generated by two-frequency oscillations of a rigid object immersed in fluid. Our results show that net pumping occurs when these two-frequency pairs produce a non-antiperiodic driving force. Furthermore, we use small amplitude analysis and extend the past results of steady streaming to the double frequency case. While steady streaming occurs at second-order in amplitude, pumping is a third-order effect which is analytically challenging to compute. Therefore, we use a hybrid numerical and analytical method to explain the mechanism behind pumping of two-frequency oscillations.