Time-resolved photon-counting densitometry for particle-laden liquid flows

Abstract

Particle-laden liquid flows, such as sand-water flows encountered in turbidity currents, are difficult to measure due to optical-opacity. Radiation-based methods, such as X-ray densitometry, are a useful tool to measure the local volume fraction regardless of opacity; however, applying the method to flows with comparable density of phases is challenging due to poor signal-to-noise ratios (SNR). In this study, time-resolved X-ray densitometry using a medical-style X-ray source and a hybrid photon-counting (HPC) detector is applied to perform line-of-sight-integrated volume fraction measurements in a turbid flow of simulated sand (glass particles) and water. Measurements were performed over a range of simulated particle volume fractions using known thicknesses of glass matching the composition of the particles. As each pixel counts incident photons in a given exposure time, spatial and temporal summation is indistinguishable from collecting data with larger pixels or longer exposures. Leveraging this, an a posteriori approach to significantly improve measurement SNR is presented. Using this method with expected values between 0 and 0.113, the maximum measured volume fraction error is improved from \(\pm 0.015\) at 18.1 pixel/mm and 500  frame/s to \(\pm 0.005\) at 2.6 pixel/mm and 100  frame/s. The methodology is demonstrated on a lock-exchange turbidity current in a laboratory setting, showing the viability of photon-counting densitometry to the study of sand-water flows. This approach can enable detailed study of the internal dynamics particle-laden liquid flows, thus providing crucial data.