Deformations and Splittings of a Bubble in a Two-Dimensional Fluidized Bed

Abstract

To explain experimental results of bubble deformations and splittings, a model assuming that these phenomenacome from the growing of a disturbance generated at the bubble surface near the stagnation point is proposed. The motion of particles is expressed by the velocity potential around a steadily rising bubble. Under the condition of constant pressure within a bubble, the differential equations for the bubble deformation were derived from the velocity potential and were solved with the initial condition that the disturbance was generated at time t=0. It was assumed that the disturbance is presented as the centripetal velocity of particles superposed on the normal velocity at the bubble surface. The bubble splitting was also calculated by the same model for the case of stronger intensity of disturbance. Calculated results agree qualitatively with experimental values of bubble deformations and splittings. Intro ductionThe course of bubble deformations and splittings in a two-dimensional fluidized bed were previously studied experimentally by the authors2\ and the following results were found. 1) Small downward cusps were generated at a bubble surface near the stagnation point, running along the edge to be lost near the wake. Consequently the bubble became vertically elongated.The authors called these cusps "disturbances".2) In some cases, a disturbance grew so fast relative to its lateral movement that it divided the bubble in two. 3) Most splittings were caused by disturbances generated very close to the stagnation point.There have been few papers1)3) which dealt theoretically with the bubble deformation caused by the wake formation from a cylindrical one. A theoretical study of bubble deformation and splitting by a disturbance is nowhere to be found. In the present paper, a numerical model is proposed. Using a procedure similar to that of Walters et al?\ the basic equations were derived from the velocity potential of particles at the bubble surface. The bubble deformation and splitting were calculated by solving these equations with the initial condition that the disturbance was generated at t=0. Calculated results were compared *