Nonmonotonic Energy Dissipation in Microfluidic Resonators

Abstract

Nanomechanical resonators enable a range of precision measurements in air or vacuum, but strong viscous damping makes applications in liquid challenging. Recent experiments have shown that fluid damping is greatly reduced in fluidic embedded-channel microcantilevers. Here we report the discovery of nonmonotonic energy dissipation due to the fluid in such devices, which leads to the intriguing prospect of enhancing the quality factor upon miniaturization. These observations elucidate the physical mechanisms of energy dissipation in embedded-channel resonators and thus provide the basis for numerous applications in nanoscience and biology. DOI: 10.1103/PhysRevLett.102.228103 PACS numbers: 87.85.Qr, 81.07.Àb, 85.85.+j Micro-and nanomechanical cantilevers are widely used as sensitive probes for physical measurements in materials science, engineering and biology. In vacuum and air, detecting shifts in the resonance frequency enables exquisitely sensitive measurements of mass and detection of single DNA molecules, single viral particles, and single bacterial cells [1][2][3][4]. However, numerous applications in nanotechnology and the life sciences require samples to be contained in liquid. This is challenging because strong viscous damping severely degrades frequency resolution by lowering the quality factor (inverse scaled energy dissipation, Q) to around unity [5][6][7][8], in stark contrast to Q $ 10 4 -10 6 achieved with resonators in vacuum. In gases, miniaturizing the resonator to dimensions comparable to the mean free path provides substantial improvements [5]. However, liquids do not admit an analogous approach, and uniformly reducing the resonator size, or equivalently, increasing viscosity always lead to a monotonic degradation in Q [6].Recently, measurements have demonstrated that viscous damping is substantially reduced by confining the (liquid) sample to a microfluidic channel embedded inside a cantilever beam surrounded by vacuum; Fig. 1(a) [9]. Such devices enable mass measurements of nanoparticles, single bacterial cells, and submonolayers of adsorbed proteins with femtogram sensitivity in liquid [9]. Applications also include ultralow volume universal detection for liquid chromatography [10], the measurement of fluid density [11][12][13], and the measurement of mass flow [14].A key outstanding question is how energy dissipation, and hence sensitivity, scales with the size of the resonator and the density and viscosity of the fluid. We investigate the effect of the fluid only; variations in the intrinsic quality factor with size have been investigated elsewhere [15]. This is of particular interest since two of the most intriguing size regimes for these devices remain to be explored: (i) where the resonators are small enough to acquire mass spectra of viruses, protein complexes, and ultimately single molecules directly in solution, and (ii) where the channel is large enough to measure the growth of mammalian cells by monitoring their mass with high precision.In this Letter, we address this question ...

Energy dissipation in microfluidic beam resonators: Dependence on mode number

“…These complementary effects lead to rich flow behavior and thus an intricate energy dissipation landscape. 19,20 In this article, we provide the essential extension of these studies to the higher order vibrational modes of microfluidic beam devices. These modes are of critical importance in practice, since they allow for novel flow control of particulates and enhanced mass sensitivity, for example.…”

“…This is in direct contrast to conventional microcantilever devices immersed in fluid, which exhibit a strong decrease in quality factor upon immersion in air and liquid-typically, quality factors in vacuum, air and water are in the range of ϳ15 000, ϳ10-100, and ϳ1 -2, respectively. 9,17,18 This unprecedented and inherent property of microfluidic beam devices was recently examined both experimentally and theoretically, 19,20 and was found to originate from dramatically different flow behavior in comparison to conventional cantilever devices. 9,10,13,14,[21][22][23][24] In short, multiple flow regimes exist in these microfluidic devices, which can result in either an increase or decrease in energy dissipation with increasing fluid viscosity.…”

Toward Attogram Mass Measurements in Solution with Suspended Nanochannel Resonators

“…Importantly, we find that the quality factor remains at approximately 8000 with and without liquid inside the channel, as previously predicted by theory. 15 This device, which we call the suspended nanochannel resonator (SNR), achieves a mass resolution of 2.7 × 10 -20 kg (or 27 ag) in a 1 kHz bandwidth. We demonstrate that particles can either be weighed in a continuous flowthrough format as before or, alternatively, be sequentially trapped at the apex of the resonator by centrifugal force and subsequently removed by increasing the flow rate.…”

“…The nonmonotonic dependence of the quality factor on fluid viscosity is consistent with theory and experiments conducted in SMRs of larger dimensions. 15 Increasing viscosity can increase or decrease the amount of fluid-induced damping due to the complex interplay between different fluid dynamic regimes which govern dissipation in microfluidic cantilever resonators. When these devices are filled with air, dissipation is dominated by the intrinsic energy loss of the solid resonator.…”

“…The nearly symmetric placement of the embedded fluidic channel about the neutral plane of the cantilever improves the quality factor when the resonator is filled with fluid by minimizing the pumping loss. 15 To operate the SNR, the optical-lever detection setup orignally developed for the SMR 14 is modified. The collimated output of a diode laser module (Coherent ULN, 635 nm) is expanded to a waist diameter of ∼5 mm and sent through an iris diaphragm, polarizing beamsplitter, and a quarter wave plate before it is focused onto the cantilever by a 10× microscope objective (10×, NA ) 0.3, WD ) 17.5 mm).…”