Hopf bifurcation in mass transfer with Sievert's solubility law

Abstract

A numerical study of isothermal gas absorption by underpressurized, axisymmetric, thin, inviscid, incompressible, annular liquid jets which form enclosed volumes where toxic wastes may be burned is presented. It is shown that, once combution is terminated, there exist two critical solubility ratios. For a solubility ratio less than the first critical one, the mass of the gases enclosed by the jet increases until a new, fixed, equilibrium steady state is reached. For solubility ratios larger than the first, but smaller than the second critical solubility ratio, the mass of the gases enclosed by the jet decreases either monotonically or in a damped oscillatory manner until a new, fixed, equilibrium steady state is reached. The time required to reach this equilibrium state increases as the solubility ratio is increased. At the second critical solubility ratio, a supercritical Hopf bifurcation exists. This bifurcation is characterized by oscillating, periodic pressure coefficients and mass transfer rates, and the amplitude of these oscillations increases, whereas their frequency decreases, as the solubility ratio is increased beyond its second critical value.