Bubble size effect on electrical signal fluctuations in flow of sub-millimeter bubbles at low void fractions: A simulation study

Bubbly flow is widely encountered in industrial applications and in human physiology during Decompression Sickness, so the interest for non-intrusive measuring techniques is still great. Karapantsios et al. (2016, 2022) have developed an EU patented, ultra-sensitive electrical impedance spectroscopy method, called I-VED, for in-vitro and in-vivo detection of sub-mm bubbles in liquids at low void fractions (< 10⁻¹). Previous experiments in a flow loop led to an empirical correlation that estimates the arithmetic average bubbles diameter from the intensity of I-VED signal fluctuations. In an effort to provide physical insight to the above-mentioned correlation, this work applies a unique mathematical model that simulates bubbly flow electrical conductance signals under prescribed conditions. Simulations are performed for different bubble populations, void fractions and Bubble Size Distribution (BSD) types (mono-disperse and uniform/non-uniform bi-disperse). Both the average value and the intensity of fluctuations of simulated signals increase with bubbles size and population of a mono-disperse BSD. Despite the two-dimensional simplified character of the model, the exponent relating signal fluctuations to bubbles average size appears to be comparable to the experimental one. Signal fluctuations increase also with the width of a uniform bi-disperse BSD as well as with the population and size of the larger bubbles in the case of a non-uniform bi-disperse BSD. Interestingly, analysis of simulated signals suggests that a correction factor for BSD width should be incorporated in the empirical equation, while an average bubble diameter of higher order than the arithmetic one may be directly proportional to the intensity of signal fluctuations.