Abstract
Rotational dynamics often challenge physical intuition while enabling unique realizations, from the rotor of a gyroscope that maintains its orientation regardless of the outer gimbals, to a tennis racket that rotates around its handle when tossed face-up in the air. In the context of inertial sensing, which can measure mass with atomic precision, rotational dynamics are normally considered a complication hindering measurement interpretation. Here, we exploit the rotational dynamics of a microfluidic device to develop a modality in inertial sensing. Combining theory with experiments, we show that this modality measures the volume of a rigid particle while normally being insensitive to its density. Paradoxically, particle density only emerges when fluid viscosity becomes dominant over inertia. We explain this paradox via a viscosity-driven, hydrodynamic coupling between the fluid and the particle that activates the rotational inertia of the particle, converting it into a ‘viscous flywheel’. This modality now enables the simultaneous measurement of particle volume and mass in fluid, using a single, high-throughput measurement.
Highlights
Rotational dynamics often challenge physical intuition while enabling unique realizations, from the rotor of a gyroscope that maintains its orientation regardless of the outer gimbals, to a tennis racket that rotates around its handle when tossed face-up in the air
The fluid has shear viscosity, μ, and mass density, ρ; ω 1⁄4 2πf is the angular frequency of the wall motion, which here is a resonant frequency of the cantilever
Our findings enable a direct measurement of particle density
Summary
Rotational dynamics often challenge physical intuition while enabling unique realizations, from the rotor of a gyroscope that maintains its orientation regardless of the outer gimbals, to a tennis racket that rotates around its handle when tossed face-up in the air. We explain this paradox via a viscosity-driven, hydrodynamic coupling between the fluid and the particle that activates the rotational inertia of the particle, converting it into a ‘viscous flywheel’ This modality enables the simultaneous measurement of particle volume and mass in fluid, using a single, high-throughput measurement. When a particle traverses inside or lands upon the surface of the sensor[8,9,10,11,12], provided a local displacement exists, the particle changes the resonant frequency of the sensor in proportion to its mass[7,13] Within this standard framework, rotational dynamics of the sensor are either ignored, or considered to be an erroneous or complicating factor in the measurement[14]. The cantilevers vibrate in their second resonant flexural mode, where local rotation, without displacement, occurs at the vibrational nodes
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