Isothermal flame balls

The heads and tails of buoyant autocatalytic balls

Buoyancy produced by autocatalytic reaction fronts can produce fluid flows that advect the front position, giving rise to interesting feedback between chemical and hydrodynamic effects. In this paper, we numerically investigate the evolution of autocatalytic iodate-arsenous acid reaction fronts initialized in spherical configurations. Deformation of these "autocatalytic balls" is driven by buoyancy produced by the reaction. In our simulations, we have found that depending on the initial ball radius, the reaction front will develop in one of three different ways. In an intermediate range of ball size, the flow can evolve much like an autocatalytic plume: the ball develops a reacting head and tail that is akin to the head and conduit of an autocatalytic plume. In the limit of large autocatalytic balls, however, growth of a reacting tail is suppressed and the resemblance to plumes disappears. Conversely, very small balls of product solution fail to initiate sustained fronts and eventually disappear.

Lateral instability of stationary spherical reaction balls

Three-dimensional stability of stationary reaction balls is investigated in a system consisting of an autocatalysis accompanied by a slow decay of the autocatalyst. Radially stable stationary spherical structures become unstable to three-dimensional perturbations at small decay rate when the radius of the reaction ball is sufficiently large and the reactant diffuses faster than the autocatalyst. A thorough linear stability analysis and simulations in three spatial dimensions are carried out in the simplest system sustaining stationary reaction balls.

Buoyant plumes and vortex rings in an autocatalytic chemical reaction

Buoyant plumes, evolving free of boundary constraints, may develop well-defined mushroom-shaped heads. In conventional plumes, overturning flow in the head entrains less buoyant fluid from the surroundings as the head rises, robbing the plume of its driving force. We consider here a new type of plume in which the source of buoyancy is an autocatalytic chemical reaction. The reaction occurs at a sharp front which separates reactants from less dense products. In this type of autocatalytic plume, entrainment assists the reaction, producing new buoyancy which fuels an accelerating plume head. When the head has grown to a critical size, it detaches from the upwelling conduit, forming an accelerating, buoyant vortex ring. A second-generation head then develops at the point of detachment. Multiple generations of autocatalytic vortex rings can detach from a single triggering event.

Isothermal flame balls: effect of autocatalyst decay

The steady, spherically symmetric solutions to the reaction-diffusion equations based on a simple autocatalytic reaction followed by the decay of the autocatalyst are considered. Three parameters-the orders with respect to the autocatalyst in the autocatalysis p and in the decay q and the rate of decay of the autocatalyst relative to its autocatalytic production K-determine the steady concentration profiles. Numerical integrations for a fixed value of the order of the autocatalyst show that the concentration profiles have different forms depending on whether q<p or q>/=p. In the former case, there is a critical decay rate K(crit) for solutions to exist, with multiple solutions for K<K(crit). In the latter case, there is a single solution for each value of K. This difference in the nature of the solution is confirmed by an analysis for p large. The temporal stability of the isothermal flame balls is examined, with temporally stable solutions being possible, provided that the ratio of the diffusion coefficient of the autocatalyst to that of the reactant is sufficiently small. The change in stability appears only when there are multiple solutions and is through a subcritical Hopf bifurcation.