Nonlinear reactive processes in constrained media

The first system we study is a reversible trimolecular chemical reaction which is taking place in closed one-dimensional lattices. We show that the low dimensionality may or may not prevent the reaction from reaching its equilibrium state, depending on the microscopic properties of the molecular reactive mechanism.

The second reactive process we consider is a network of biological interactions between pigment cells on the skin of zebrafish. We show that the combination of short-range and long-range contact-mediated feedbacks can promote a Turing instability which gives rise to stationary patterns in space with intrinsic wavelength, without the need of any kind of motion.

Then we investigate the behavior of a typical chemical oscillator (the Brusselator) when it is constrained in a finite space. We show that molecular crowding can in such cases promote new nonlinear dynamical behaviors, affect the usual ones or even destroy them.

Finally we look at the situation where the constraint is given by the presence of a solid porous matrix that can react with a perfect gas in an exothermic way. We show on one hand that the interplay between reaction, heat flux and mass transport can give rise to the propagation of adsorption waves, and on the other hand that the coupling between the chemical reaction and the changes in the structural properties of the matrix can produce sustained chemomechanical oscillations.

These results show that spatial constraints can affect the kinetics of reactions, and are able to produce otherwise absent nonlinear dynamical behaviors. As a consequence of this, the usual understanding of the nonlinear dynamics of reactive systems can be put into question or even disproved. In order to have a better understanding of these systems we must acknowledge that mechanical and structural feedbacks can be important components of many reactive systems, and that they can be the very source of complex and fascinating phenomena.