Mathematical modelling of chemical clock reactions

Abstract

A clock reaction is a chemical reaction which gives rise to an initial induction period before a significant concentration of one of the chemical species involved is produced. We study four closely related isothermal model reaction schemes which can exhibit clock reaction behaviour in a well-stirred situation. These reaction schemes represent a combination of quadratic or cubic autocatalysis with linear or quadratic inhibition.

Interfacial Instability of Thixotropic Fluids in Triple-Layered Channel Flow

“…which, fortunately, involves just the velocity gradients at y = 0. It needs to be mentioned that, the boundary conditions on λ are in line with those proposed by Billingham and Ferguson (1993) in their investigating the pipe flow of Moore fluids. We also would like to stress that in the present study we have ignored surface tension effects simply because the working fluids have been assumed to be slightly miscible.…”

Exploding Chemical Gardens: A Phase‐Change Clock Reaction

“…[2] Applications include tubular structure formation in corrosion, [5] cement hydration, [6] polyoxometalates, [7] and the origin of life at submarine hydrothermal vents. [12] Yeto thers have equated clock reactions to oscillations. [9,10] Thep recise definition of ac hemical clock is am atter of debate.S ome have argued for ad efinition that restricts ac lock reaction to an abrupt increase in the concentration of one or more products owing to the total consumption of alimiting reagent, [11] while others argue that it is not the details of the kinetics but the phenomenology that is important.…”

“…[9,10] Thep recise definition of ac hemical clock is am atter of debate.S ome have argued for ad efinition that restricts ac lock reaction to an abrupt increase in the concentration of one or more products owing to the total consumption of alimiting reagent, [11] while others argue that it is not the details of the kinetics but the phenomenology that is important. [12] Yeto thers have equated clock reactions to oscillations. [13,14] But it is inarguable that the classic clock reactions are timers:they have an induction period that may be very long followed by asharp change,often acolor change, at agiven moment, and this induction time can be controlled and predicted by altering the quantities of reagents.Examples in gaseous combustion have shown the dependence of the induction time before explosion on the transport rates of chemicals and heat.…”

Exploding Chemical Gardens: A Phase‐Change Clock Reaction

“…The precise definition of a chemical clock is a matter of debate. Some have argued for a definition that restricts a clock reaction to an abrupt increase in the concentration of one or more products owing to the total consumption of a limiting reagent, while others argue that it is not the details of the kinetics but the phenomenology that is important . Yet others have equated clock reactions to oscillations .…”