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

TL;DR

This work addresses the challenge of measuring velocity distributions in dense granular matter where optical particle tracking fails due to opacity. It introduces a fiber Bragg grating (FBG) in situ sensing technique that converts collision-induced fiber deflections into a wavelength shift, enabling extraction of particle velocities and the ensemble distribution. Calibration with controlled single-particle drops validates the $\Delta\lambda$–$v$ relationship, and shaker experiments at 3% volume fraction show that FBG-derived distributions align with traditional particle tracking and exhibit a non-Maxwellian high-velocity tail with exponent $\alpha \approx 1.05\pm0.3$, consistent with freely cooling granular gas behavior. The method demonstrates potential to probe denser granular systems beyond imaging limits and may be enhanced by microgravity experiments to eliminate confounding fiber motion and anisotropies.

Abstract

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.

Figures (10)

• Figure 1: Schematic illustration of the employed experimental set-up, with a side-view in top and a top-view in bottom panel of the figure. The vibration shaker sinusoidally excites a spherical sample cell filled with 3% MuMetal particles. A camera, positioned perpendicular to the fiber, records the particles in the vicinity of the fiber (green) and the FBGs (red). Collision-induced wavelengths shifts in the FBG sensors are monitored using an interrogator.
• Figure 2: Schematic illustration of the incident, transmitted and reflected light's spectrum in a FBG sensor. The left panel shows the normalized incident spectrum before passing the grating (blue) and the light transmitted through the grating (orange). The reflected light, which is the one detected by the interrogator, is shown in the right panel. The reflected signal shows a wavelength shift $\Delta\lambda$ once the FBG is strained (dashed green).
• Figure 3: (a) Illustration of the fiber-deflection during particle-fiber collision, defining the parameters for the derivation of the $v(\Delta\lambda)$ relation. (b) Definition of the polar angle $\varphi$ and (c) the contact angle $\vartheta$ of particle-fiber collision.
• Figure 4: Velocity distribution functions for a Maxwell-Boltzmann distribution ($P_V(v_p)$) and the angle-dependent skewed versions.
• Figure 5: Wavelength shift versus time for two gratings in a 5 ms time interval. The red line is the fit by Eq. (\ref{['equ:temporal']}) while the blue and orange dots represent grating 1 and 2, respectively.