Towards probing velocity distributions in dense granular matter: Utilizing Fiber Bragg Gratings

Granular gases are commonly characterized through their velocity distribution, which provides access to the granular temperature. In experiments, velocity distributions are typically obtained by particle tracking, which however becomes limited at moderate and high particle densities. As a way forward, we propose a new technique for measuring particle velocities in situ by using a Fiber Bragg Grating (FBG) sensor, which remains applicable at significantly higher particle densities.The FBG sensor detects strain pulses induced by particle-fiber collisions, from which the velocity of the impacting particle can be derived. Applying this method to an ensemble of granular particles allows to extract its velocity distributions as we present for a granular system excited by a vibrational shaker. We validate the extracted velocity distribution against conventional particle-tracking measurements, confirming the reliability of the FBG-based technique.

💡 Research Summary

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This paper introduces a novel method for measuring particle velocity distributions in dense granular media using Fiber Bragg Grating (FBG) sensors, addressing the limitations of conventional optical particle tracking at moderate to high volume fractions. Granular gases are typically characterized by their velocity distribution, which yields the granular temperature, but optical tracking becomes unreliable once the particle volume fraction exceeds roughly 5 % because particles obscure each other. Tomographic techniques such as CT or MRI lack the temporal resolution required to capture the fast dynamics of granular collisions. The authors therefore propose an in‑situ, non‑intrusive technique based on the strain pulses generated when particles collide with an optical fiber that contains embedded Bragg gratings.

The principle of an FBG sensor is first explained: a periodic modulation of the refractive index in the fiber core reflects a narrow band of light at the Bragg wavelength λB0. Mechanical strain ε changes the effective grating period, shifting the reflected wavelength by Δλ = λB0(1 − cPhoto)ε, where cPhoto is the photo‑elastic constant. By connecting the fiber to an interrogator that monitors Δλ with picometer precision, the sensor can detect minute deformations caused by particle impacts.

A theoretical framework links the particle’s kinetic energy to the work required to deflect the fiber. Assuming a central impact on a tensioned fiber of length L, axial spring constant k, and pre‑tension T, the work W(h) needed to achieve a maximum deflection h is derived, leading to an energy balance ½ mv² = W(h). Using the geometric relation between deflection and strain, the authors obtain a direct expression for the particle velocity in terms of the measured wavelength shift:

v² = (2 L / m κ)