MR relaxometry of micro-bubbles in the vertical bubbly flow at a low magnetic field (0.2T)

Measurements of the vertical bubbly flow were performed at a low magnetic field of 0.2T. The void fraction data were acquired. The susceptibility-induced changes in T₂ relaxation time were analyzed using the previously introduced approaches by Sukstanskii et al. and Ziener et al., originally developed for the Magnetic Resonance analysis of randomly distributed and isolated spherical inclusions, and a simple model of a spherical particle, respectively. The CPMG signal decay due to the presence of spherical inclusions was approximated as linear vs. CPMG inter-echo times to extract the average inclusion's size information. Two equations were derived for a simplified analysis of gas-liquid systems with basic T₂ measurements, and without prior knowledge on the gas-liquid susceptibility or a need for the magnetic gradient setup. They can provide estimates for the void fraction and the average inclusion size, provided the CPMG inter-echo time requirements are met. For the control samples, there was a good agreement with the theory. For the bubbly flows, a good agreement was observed between the Magnetic Resonance and optics-based estimates for the slowest airflow rate. The deviation, however, increased for higher airflow rates. The introduced approach lends itself to the characterization of multi-phase systems such as cavitating media and well-separated bubbly flows.