Spatial Bistability and Related Chemomechanical Instabilities

Consider an inert gel immersed in a CSTR and a reaction with an autocatalytic path driven by species X. The result of the autocatalysis is that the reaction rate considerably increases when the amount of X becomes sufficient, so that the state of the reaction is essentially either an almost unreacted state F before this amount has been reached or a state T where the chemical conversion is almost complete after it has been reached. The CSTR contents are maintained in the unreacted state by imposing a short residence time r. This fixes the gel state at the CSTR/gel boundary. The distribution of concentrations in the depth of the gel is controlled 

When the inert gel is replaced by a chemoresponsive gel that swells in state F and shrinks in state FT, it is possible to find an appropriate CSTR composition and an initial gel size L so that the two hmits linf and Isup are crossed alternatively. Every time the system reaches one of these hmits, the system jumps to the other state and reverses the direction of swelhng/shrinking, giving rise both to mechanical (volume) oscillations and to chemical oscillations between F and FT. The process is made possible by the hysteresis loop and by the slow diffusion of the polymeric network that rules the swelling process. 

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