Energy dissipation in microfluidic beam resonators: Dependence on mode number

Energy dissipation experienced by vibrating microcantilever beams immersed in fluid is strongly dependent on the mode of vibration, with quality factors typically increasing with mode number. Recently, we examined energy dissipation in a new class of cantilever device that embeds a microfluidic channel in its interior—the fundamental mode of vibration only was considered. Due to its importance in practice, we examine the effect of mode number on energy dissipation in these microfluidic beam resonators. Interestingly, and in contrast to other cantilever devices, we find that the quality factor typically decreases with increasing mode number. We explore the underlying physical mechanisms leading to this counterintuitive behavior, and provide a detailed comparison to experimental measurements for which good agreement is found.