Pumping and Streaming with Two-Frequency Oscillations

The classical problem of steady streaming induced by an oscillating object has been studied extensively, but prior work has focused almost exclusively on single-frequency oscillations, which result in symmetric, quadrupole-like flow. Here we demonstrate that dual-frequency oscillations induce asymmetric steady streaming with a non-zero net flux in a direction determined by the polarity of the oscillation – the oscillator serves as a pump. For certain frequency pairs, the computational experiments show asymmetrical streaming and pumping, i.e., net flux downstream. It is well known from asymptotic analysis that steady streaming is second order in amplitude, but pumping is a higher order effect. Specifically, pumping is third order in amplitude for frequency ratio 2; however, an analytical solution up to third order is intractable. Therefore, we solve the solutions using a combination of analytical and numerical methods. From the solution structure, we simplify the problem to a PDE of single variable, and then, we numerically compute the solutions. Finally, we apply a parameter study on the net force and discuss its implications for using dual-mode vibrations to pump fluids in lab-on-a-chip and other applications.