SOLITONS, SOLITARY WAVES, AND VOIDAGE DISTURBANCES IN GAS-FLUIDIZED BEDS

In this paper, we consider the evolution of an initially small voidage disturbance in a gas-fluidized bed. Using a one-dimensional model pro posed by Needham & Merkin (1983), Crighton (1991) has shown that weakl y nonlinear waves of voidage propagate according to the Korteweg-de Vr ies equation with perturbation terms which can be either amplifying or dissipative, depending on the sign of a coefficient. Here, we investi gate the unstable side of the threshold and examine the growth of a si ngle KdV voidage soliton, following its development through several di fferent regimes. As the size of the soliton increases, KdV remains the leading-order equation for some time, but the perturbation terms chan ge, thereby altering the dependence of the amplitude on time. Eventual ly the disturbance attains a finite amplitude and corresponds to a ful ly nonlinear solitary wave solution. This matches back directly onto t he KdV soliton and tends exponentially to a limiting size. We interpre t the series of large-amplitude localized pulses of voidage formed in this way from initial disturbances as corresponding to the 'voidage sl ugs' observed in gas fluidization in narrow tubes.