The development of microfluidics has revolutionized the capability to analyze a variety of substances, including cells and microparticles, in physiological conditions with minimal reagents¹. This technique relies on precise hydrodynamic forces exerted on particles within microfluidic channels to evaluate their mechanical, optical, or chemical properties. The mechanical properties are of particular importance, as they are closely linked to the chemical composition of the analytes and can be used to differentiate between different types of particles. In the field of microbiology, it has been demonstrated that cell mechanics play a critical role in various biological processes, such as the development of diseases like cancer².

Conventional microfluidic devices lack the ability to directly measure the hydrodynamic forces acting on a particle and must rely on other parameters to infer these forces. However, the suspended microchannel resonator (SMR) approach has shown great potential in measuring these forces by combining the benefits of nanomechanical resonators and microfluidics. SMR devices consist of a suspended structure with an integrated microfluidic channel that allows for the precise introduction of particles into the suspended region³. The device can oscillate in flexural modes, and changes in the mechanical properties of the resonator caused by the presence of particles can be measured by monitoring variations in its resonance frequency. Previous studies on SMR devices have demonstrated their usefulness as mass sensors⁴ and their ability to measure particle optical absorption⁵, hydrodynamic characteristics⁶, and hydrostatic forces⁷.

Figure 1. Schematics of the suspended microchannel resonator (SMR) device

Our study proposes the use of SMRs as sensors to measure the hydrodynamic force acting on flowing particles⁸. Through analytical investigation, we demonstrate that the resonance frequency shift of SMRs caused by a passing particle can be understood as a linear combination of two distinct phenomena: the added mass from the particle's buoyant mass (mass effect) and the stiffness change caused by the hydrodynamic force transmitted (force effect) to the microchannel walls. Furthermore, we show that different experimental conditions can be adjusted to minimize either effect, with flow rate being the most crucial parameter. We identify the maximum/minimum flow rate required to disregard the force or mass effect.

Figure 2. Decoupling the force and mass effects on the resonance frequency of the suspended microfluidic channel

Lastly, we discuss the optimal fabrication conditions for SMRs to measure this hydrodynamic force effect, suggesting the use of soft materials like PDMS and thick walls for the devices. By utilizing soft materials, we can reduce the stiffness of the device, which increases the sensitivity of the measurement to the hydrodynamic force effect. Thick walls, on the other hand, reduce the effect of the mass effect and increase the sensitivity to the force effect. We also discuss the importance of accurate device fabrication to ensure consistent results, as variations in device dimensions can significantly affect the measurement results.

Figure 3. Hydrodynamic force and mass sensitivity as a function of the flow rate and the mechanical properties of the supporting material

Overall, the use of SMRs as sensors to measure the hydrodynamic force acting on flowing particles represents a promising new direction in microfluidic analysis. This technique has the potential to provide valuable insights into various biological processes, including the development of diseases such as cancer. However, further research is needed to fully explore the capabilities of this approach and to optimize the fabrication and measurement techniques for SMR devices.

References

1          Bhatia, S. N. & Ingber, D. E. Microfluidic organs-on-chips. Nature Biotechnology 32, 760-772 (2014). https://doi.org:10.1038/nbt.2989

2          Shaw Bagnall, J. et al. Deformability of Tumor Cells versus Blood Cells. Scientific Reports 5, 18542 (2015). https://doi.org:10.1038/srep18542

3          Burg, T. P. et al. Weighing of biomolecules, single cells and single nanoparticles in fluid. Nature 446, 1066 (2007). https://doi.org:10.1038/nature05741

https://www.nature.com/articles/nature05741#supplementary-information

4          Bryan, A. K. et al. Measuring single cell mass, volume, and density with dual suspended microchannel resonators. Lab on a Chip 14, 569-576 (2014). https://doi.org:10.1039/C3LC51022K

5          Martín-Pérez, A. et al. Mechano-Optical Analysis of Single Cells with Transparent Microcapillary Resonators. ACS Sensors 4, 3325-3332 (2019). https://doi.org:10.1021/acssensors.9b02038

6          Martín-Pérez, A. et al. Hydrodynamic assisted multiparametric particle spectrometry. Scientific Reports11, 3535 (2021). https://doi.org:10.1038/s41598-021-82708-0

7          Khan, M. F., Knowles, B., Dennison, C. R., Ghoraishi, M. S. & Thundat, T. Pressure modulated changes in resonance frequency of microchannel string resonators. Applied Physics Letters 105 (2014). https://doi.org:10.1063/1.4889744