On stability of a bubble column

The goal of this contribution is to formulate the simplest possible model for the bubble column hydrodynamics and analyse it for steady states, stability, and unsteady behaviour. The governing equations are based on the mass balance of the gas phase. Two closures for the gas velocity are used and reflect two typical operational regimes, homogeneous (HoR) and heterogeneous (HeR). The model has five parameters: column height H, terminal bubble speed u0, hindrance exponent n, enhance exponent m, gas flow rate q. Three branches of steady solutions were found for HoR, one stable, one unstable, one neutrally stable. The first two are physically relevant, are of the node-type, and merge in the turning point bifurcation at large enough gas input. Two branches of steady solutions were found for HeR, one stable and one neutrally stable. The first one is physically relevant, is of the node-type, and persists for all plausible parameter values. In both regimes, the neutrally stable solution was classified as unphysical. The transition regime (TrR) was obtained by matching the stable solutions of HoR and HeR, with help of a sigmoidal bridging function. The system stability was related to the model topology. The linear approximation of the bubble column dynamics was studied and the relaxation time estimated. The full nonlinear dynamics was demonstrated too. Both the steady and unsteady behaviour of the bubble column was compared with available experimental data.

► Multiplicity of steady solutions exists in the homogeneous flow regime of bubble column.
► Only single solution exists in the heterogeneous flow regime of bubble column.
► Transition behaviour of bubble column involves combination of the both flow regimes.
► Besides the steady states and their stability, the model also describes the unsteady behaviour of bubble column.