Pumping of granular materials via horizontal multimodal vibrations

Recent experimental work demonstrated that dual-frequency, horizontal vibrations cause dry granular materials to pump in a desired direction within a lab-on-a-chip device. Here we present numerical predictions of the pumping velocity by applying Coulomb’s friction law with a shooting method over one period of the vibrational motion. At sufficiently fast vibrations, the steady velocity is predicted to be a unique function of the vibratory amplitude ratio, frequency modes, and phase lag between the two modes. At sufficiently slow vibrations and for certain ranges of frictional coefficients, however, multiple solutions are obtained. Furthermore, for some frequency mode ratios and relatively low amplitudes, granules with slightly different friction coefficients are predicted to move in opposite directions. We present experimental tests of these predictions, and we discuss the implications for manipulate granular materials on the millimeter to micrometer scale for lab-on-a-chip applications.