Microfluidic QCM enables ultrahigh Q-factor: a new paradigm for in-liquid gravimetric sensing

Biosensing plays a crucial role in detecting and quantifying biological signals¹ or molecules⁵⁻⁷. Its applications range from improving healthcare⁸⁻¹⁰ to monitoring environmental pollutants¹¹⁻¹³. As an essential tool in biology, medicine, and environmental science, biosensing remains an area of continuous research and development¹⁴⁻¹⁸.

Biosensors employ various transduction principles, including electrical¹⁹⁻²¹, optical⁹,²²,²³ and acoustic methods²⁴⁻²⁶. Among these, acoustic gravimetric biosensors stand out for their simplicity, robustness, and low cost, making them attractive for a wide range of applications, particularly in point-of-care (POC) settings²⁷,²⁸.

Despite their advantages, acoustic biosensors often face a common drawback—a low-quality factor (Q-factor)²⁵ in liquid measurements. The Q-factor (Q), which measures energy loss (or dissipation, D = 1/Q) in an acoustic system, significantly impacts the sensitivity and accuracy of acoustic biosensors²⁹,³⁰. For out-of-plane mode acoustic biosensors, low Q-factors mainly result from acoustic radiation energy loss. Hence, in-plane mode operation is preferred as it avoids direct acoustic energy emission into the surrounding environment. Nevertheless, even in-plane acoustic biosensors encounter energy dissipation due to friction within the shear evanescent boundary layer²⁵.

Over the years, researchers have explored several methods to enhance the Q-factors of acoustic biosensors. These methods include using wave interference³¹, isolating sensors from their surroundings³², and implementing meta structures to trap acoustic energy³². However, these efforts have only partially addressed the issue of low Q-factors, without fully resolving the underlying challenge. In this context, we demonstrate an innovative acoustic bio-sensor design that effectively eliminates dissipation in the liquid phase, leading to a significant improvement in the Q-factor. By tackling this fundamental issue, our design opens new possibilities for advancing the performance and capabilities of acoustic biosensors for diverse applications.

We implemented our paradigm using a quartz crystal microbalance (QCM) as the model system. QCMs are thickness shear mode (TSM) resonators capable of detecting surface-bound mass and the associated energy loss by measuring resonance frequency shifts (Δf) and dissipation shifts (ΔD), respectively25,33-36. The selection of a QCM as a model system is justified by its simplicity and widespread application37,38, low production cost, and the relevance of its operating principles to other acoustic gravimetric biosensors, including surface acoustic wave (SAW) sensors, film bulk acoustic resonator (FBAR) sensors26, and other bulk acoustic wave (BAW) sensors.

Our approach incorporates rigid microfluidic channels on conventional QCM crystals, leading to the creation of a new device we termed microfluidic QCM (µ-QCM). Through a comprehensive combination of simulations, theoretical studies, and experiments, we demonstrate a 10-fold decrease in dissipation shift (ΔD) induced by liquid loading. In addition to the significant decrease in dissipation, the µ-QCM offers several other advantages. These include direct data interpretation, significantly reduced sample volume requirements, and less stringent temperature control, all of which render the µ-QCM potentially attractive for POC sensing applications.

Our research also aimed at gaining a deeper understanding of the physics underlying µ-QCM operation. For the µ-QCM to exhibit low dissipation (i.e., high Q-factor) in liquid, we found that the width of the microfluidic channels has to be significantly smaller than the pressure wavelength across the channel width, while the channel height does not necessarily need to be smaller than the penetration length of the evanescent shear wave. Our findings provide valuable insights into the design and performance of other acoustic biosensors and thus contribute more broadly to advancing acoustic gravimetric biosensor technologies and their practical implementations.

Prior work to improve the Q-factors of acoustic biosensors has included wave interference, isolation of sensors from their surroundings, and meta structures to trap acoustic energy. Despite these approaches, conventional in-liquid acoustic biosensors still suffer from low Q-factors due to energy dissipation via acoustic radiation (in out-of-plane modes) and friction in the shear evanescent boundary layer even for in-plane modes. Conventional QCM behavior in liquids is described by the extended Sauerbrey relation linking frequency shift to the square root of liquid viscosity–density, reflecting viscosity-driven dissipation limits.

Device design: The approach confines sample liquid in many parallel, rigid microfluidic channels placed atop a QCM crystal. Channels have 2 µm × 10 µm cross-sections and are oriented perpendicular to the QCM shearing direction to generate pressure waves across the channel width. To minimize dissipation, channel width W was kept below one-quarter of the pressure wavelength λp in the sample liquid. The device targets operation up to the 7th overtone (≈35 MHz for a ~330 µm thick AT-cut crystal), corresponding to λp ≈ 42 µm in water; channel width was limited to 10 µm. Channel height was 2 µm to avoid mass overloading yet remains larger than the shear evanescent wavelength (~250 nm). About 100 parallel channels spaced 20 µm apart were placed centrally over a ~3 mm width of the active sensor region.

Fluid handling: Liquid is entrained through capillary action; complete filling is critical. A diverging approach flow channel network connects the inlet to the 100 channels, and micro-pillows are distributed between the outlet and channel termini to enable steady, bubble-free flow and merging, inspired by tree-line capillary pumping designs.

Materials and fabrication: Channels were fabricated from aluminum to maximize stiffness-to-mass ratio. A thin (~40 nm), conformal gold coating was added to enable surface modification of inner channel surfaces.

Operating conditions and measurements: Conventional QCM fundamental frequency is ~5 MHz with operation at higher overtones; µ-QCM measurements and comparisons were performed across modes 1–7. Upon admitting DI water, normalized resonance frequency shifts (Δf/n) and dissipation shifts (ΔD) were recorded for both conventional and µ-QCM. Channel orientation dependence was tested by rotating channels parallel vs. perpendicular to the shearing direction. Ethanol–water mixtures (up to 30 wt% ethanol) with well-known density and viscosity were used to assess sensitivity to density vs. viscosity.

Finite element analysis (FEA): FEA modeled both conventional and µ-QCM responses in DI water. For the µ-QCM, a single repeating unit located in the center region was used to achieve computational efficiency (rigid channel walls with no-slip boundary conditions). Simulations predicted normalized frequency and dissipation shifts across modes 1–7 and enabled parametric studies of key nondimensional ratios, notably W/λp and H/λs, to identify regimes of low dissipation. Model predictions were compared with experimental data for validation.

• Dissipation reduction: The µ-QCM exhibited about a 10-fold reduction in dissipation shift (ΔD) upon liquid loading compared to conventional QCM.
• Mass coupling and sensitivity: Despite lower dissipation, the µ-QCM showed a normalized resonance frequency shift at the 7th mode that was ~5× larger than that of a conventional QCM, indicating greater liquid mass coupling.
• Frequency–mode behavior: Conventional QCM Δf/n decreases with increasing overtone due to reduced shear evanescent penetration; in contrast, µ-QCM Δf/n increases with mode number (observed experimentally and in FEA), potentially enabling higher sensitivity at higher modes.
• Orientation dependence: Channels perpendicular to shearing direction yield low dissipation; channels parallel to shearing produce high dissipation akin to conventional QCM due to persistence of shear boundary layer behavior.
• Figure of merit (FOM): The µ-QCM significantly surpasses the theoretical FOM limit for AT-cut QCMs in water and outperforms literature data for conventional QCMs across a range of fundamental frequencies.
• Density-only response: Conventional QCM follows Δf ∝ −√(μη) dependence; µ-QCM responds only to density (mass), being insensitive to viscosity-driven losses. Experiments with ethanol–water mixtures showed frequency shifts consistent with density decrease (frequency increase) for µ-QCM, while conventional QCM frequency decreased with increasing mixture viscosity.
• FEA validation: Conventional QCM FEA matched experiments within ~5% across modes 1–7. For µ-QCM, normalized frequency predictions matched experiments; dissipation agreement was best at higher modes (5 and 7), with discrepancies at lower modes attributed to peripheral mass loading from inlet droplets not captured in the unit-cell model.
• Design rules for low dissipation: Parametric FEA identified W/λp as the dominant factor; keeping W/λp ≲ 0.2 maintained ΔD < 20 × 10⁻⁶. Rigid channel coupling and no-slip boundaries result in near-uniform liquid velocity across the channel, minimizing frictional dissipation. Channel height H need not be below the shear evanescent penetration length to achieve low dissipation.
• Operating parameters: Target frequency 35 MHz (7th overtone) in water gives λp ~42 µm; channel width 10 µm and height 2 µm met low-dissipation criteria while limiting mass loading.

The study addresses the central challenge of high dissipation (low Q) in in-liquid acoustic gravimetric sensing by confining the liquid within rigid, narrow microchannels oriented perpendicular to the QCM shear motion. This configuration induces pressure waves across the channel width and homogenizes liquid velocity profiles when W/λp is small, thereby suppressing shear-driven frictional losses. Experimental and FEA results collectively support the hypothesis that geometric acoustic confinement (primarily W/λp, with a secondary role for H/λs) governs dissipation. The µ-QCM’s higher normalized frequency shifts alongside much lower ΔD indicate improved mass coupling without the penalty of viscous losses, directly improving Q and thus the FOM beyond conventional theoretical limits. Orientation tests confirm the mechanism: only the perpendicular orientation generates the pressure-wave field needed to avoid boundary layer dissipation. The demonstrated viscosity insensitivity and density-only response simplify interpretation to direct mass sensing, while microfluidic integration affords reduced sample volumes and relaxed temperature control. These outcomes enhance applicability for point-of-care biosensing and suggest broader relevance for other acoustic gravimetric platforms (SAW, FBAR, BAW) adopting similar microfluidic-acoustic confinement principles.

By integrating rigid microfluidic channels with a QCM, the µ-QCM paradigm substantially suppresses in-liquid dissipation, yielding an approximate 10-fold improvement in ΔD, enhanced mass coupling, and a FOM surpassing the theoretical limit for conventional QCMs in water. Finite element analyses and experiments identify W/λp < ~0.2 as a key design criterion for low dissipation, with channel orientation perpendicular to shear being critical. The device exhibits direct mass (density) sensing with minimal viscosity influence and offers practical advantages in sample volume and temperature control. Future improvements include relocating inlet/outlet further from the active region to eliminate peripheral mass-loading effects and deeper investigation into the increasing Δf/n with mode number to optimize high-overtone performance.

• Modeling and edge effects: The FEA used a central repeating unit and did not capture edge/peripheral effects; discrepancies in µ-QCM dissipation at lower modes are attributed to inlet droplet mass loading outside the active area, not represented in the model.
• Experimental artifact: Peripheral liquid at the inlet/outlet contributes to added mass and dissipation at low modes; design adjustments are needed to further isolate the sensing region.
• Open question: While the increase of normalized frequency shift with overtone in µ-QCM is consistently observed, a complete quantitative explanation remains unresolved within the current study.