Structural Stability of the Coalescence/Breakup Equation

Abstract

An analysis of the structural stability of the coalescence/breakup equation is performed to determine the degree to which changes in the equation's formulation can affect the solution. The work was motivated by speculation in various quarters that the currently used coalescence/breakup formulation should be adjusted to achieve better agreement between solutions and field observations. Both analytical procedures and numerical experiments, in which hypothetical changes in the rate coefficients are assumed, show the coalescence/breakup equation in its current formulation to be structurally stable. Not only do small changes in the rate coefficients produce negligible change in the solutions, but even large changes in the rate coefficients fail to destroy the fundamental behavior of the system in that all solutions continue to approach a unique equilibrium. Moderate-sized perturbations of the coefficients are found to have only minor influence on the solutions unless the coalescence and breakup efficiencies, constituents of the rate coefficients, are perturbed in an opposite sense to reinforce the individual effects. Only with such changes in the formulation is the equilibrium solution found to be altered to a significant degree.