Initial motion of a bubble in a fluidized bed Part 1. Theory

Abstract

This is a theoretical study of the experimental work in the succeeding paper by Partridge & Lyall (1967). This paper shows that the characteristic shape of typical bubbles in fluidized beds, with a large solids to fluid density ratio, will be reached after a time of order (r₀/g)^½ from the introduction, naturally or artificially, into the bed of a circular or spherical bubble, where r₀ is the initial bubble radius and g the gravitation constant. The initial acceleration is g in two dimensions and 2g in three dimensions. A measure of the growth rate of the distortion from a circular or spherical shape is given as a tentative guide to wake formation and growth rate. It is shown that the wake growth rate in the three-dimensional case is faster than in the two-dimensional case, and, further, that bubbles formed naturally at the bottom of a fluidized bed will distort faster than bubbles starting from rest.

The method used is based on a convective term linearization process on equations of motion for a fluidized system given by Murray (1965a, b) and an extension of a method given by Walters & Davidson (1962, 1963) in the case of the initial motion of a gas bubble formed in an inviscid liquid and starting from rest.

Comparison with experiment is difficult since the bubble conditions discussed in the theory are very difficult to reproduce artificially in the laboratory. The results obtained by Partridge & Lyall (1967) are shown to be not inconsistent with those predicted here.