Quantitative measurement of solid fraction in a silo using SPRITE

Solid fraction is a critical parameter in granular rheology, yet its direct measurement during flow remains difficult. Prior research has shown that granular behavior is significantly influenced by the packing density of particles. However, no prior work had resolved how to capture this parameter in real-time with high accuracy. Existing techniques often fail to account for spatial and temporal variations in the material. This gap motivated the development of new imaging strategies that can overcome these limitations. The challenge lies in distinguishing between solid and void spaces in a moving granular system. Conventional methods lack the resolution and sensitivity needed for such measurements. Therefore, a novel approach was required to quantify solid fraction in dynamic conditions. This paper introduces a method using MRI to address these issues.

The aim of this research is to develop a reliable MRI-based technique for measuring solid fraction in granular flows. The study focuses on mustard seeds discharging from a 3D-printed hopper. The motivation stems from the need to understand how packing density affects granular flow behavior. The researchers propose that SPRITE imaging can provide the necessary spatial resolution and sensitivity. By correcting for imaging artifacts, the method can yield accurate solid fraction maps. The study also seeks to validate the technique against known standards. The ultimate goal is to create a tool for real-time, quantitative analysis of granular systems. This approach could improve the design and operation of industrial systems involving granular materials.

Centric sectoral-SPRITE imaging was used to capture images of mustard seeds in a hopper. The researchers accounted for artifacts caused by flow and relaxation effects. They corrected for spatial variations in the B1 field using static images of the seeds. Different sample geometries were tested to assess B1 field sensitivity. An internal standard was introduced to scale signal intensity across measurements. The method involved comparing image intensities with known solid fractions. Linear regression was used to establish a calibration curve. The technique was validated using gravimetric mass flow measurements. These steps ensured the accuracy of the solid fraction maps.

A strong linear correlation (R² = 0.999) was found between image intensities and solid fractions. The calibration was based on samples with solid fractions between 0.55 and 0.64. The method successfully corrected for B1 field variations and spectrometer differences. Time-averaged solid fraction maps were generated during steady flow. The mass flow rate calculated from these maps matched gravimetric measurements. The internal standard improved consistency across multiple experiments. The technique demonstrated high spatial resolution and accuracy. These results confirm the method's potential for real-time granular flow analysis.

The authors propose that the developed MRI method can accurately measure solid fraction in granular flows. The technique accounts for B1 field variations and spectrometer differences. The linear correlation supports the method's reliability. The mass flow rate validation confirms its accuracy. The use of an internal standard enhances reproducibility. The method is suitable for time-averaged spatial analysis. The results suggest it can be applied to other granular systems. The study highlights the importance of correcting for imaging artifacts.