Conversion of pierced lengths measured at a probe to bubble size measures: An assessment of the geometrical probability approach and bubble shape models

Abstract

Submersible probes are often used to study the local bubble properties in gas-fluidized beds. Since the axes of the intercepted bubbles need not be aligned with the probe axis of the probe, simple probes measure only the pierced length of the bubbles; and the deduction of the diameters of the bubbles is not simple. Geometrical probability offers an elegant solution to the conversion of the distribution of pierced lengths to that of bubble size measures. However, the theory has not been verified experimentally so far. In this investigation, digital image analysis techniques were used to obtain the pierced length and several size measures (maximum horizontal and vertical dimensions, circumference and area equivalent diameter) of bubbles intercepted at an ‘imaginary’ probe in a thin two-dimensional fluidized bed. The measured pierced lengths, along with assumed bubble shapes, were used to obtain theoretical predictions of the bubble size measures using geometrical probability. The comparison of the predictions with experimental data, for the first time, enables assessment of the geometrical probability approach and bubble shape assumptions in the prediction of bubble size from measurements on bubble pierced lengths. The results indicate that the use of spherical and ellipsoidal (aspect ratio = 0.77) bubble shapes with geometrical probability leads to good agreement between theory and experiment.