Taylor’s regime of an autocatalytic reaction front in a pulsative periodic flow

Abstract

Autocatalytic reaction fronts between reacted and unreacted species may propagate as solitary waves, that is, at a constant front velocity and with a stationary concentration profile, which result from a balance between molecular diffusion and chemical reaction. A velocity field in the supporting medium may affect the propagation of such fronts through different phenomena: advection, diffusion enhancement, front shape changes, etc. Here, we report on an experimental study and lattice Bhatnagar-Gross-Krook numerical simulations of the effect of an oscillating flow on the autocatalytic reaction between iodate and arsenous acid in a Hele-Shaw cell. In the low frequency range covered by the experiments, the front behavior is controlled by the flow across the gap and is reproduced with two-dimensional numerical simulations. It is shown that the front velocity oscillates at the frequency of the flow, whereas the front width oscillates at twice that frequency. Moreover, the Taylor regime in the presence of a Poiseuille flow is fully investigated: The description obtained in the case of a stationary flow provides an analytical prediction for the sinusoidal flow. The range of parameters, for which the prediction applies, is delineated and discussed.

Frozen fronts selection in flow against self-sustained chemical waves

“…These fronts are analogous to flames in combustion [4] and autocatalytic reactions are a kind of "cold combustion model" especially in the thin flame limit. In contrast to flame propagation in combustion [4], where it has been analyzed thoroughly theoretically and experimentally, the effect of fluid flow (laminar or turbulent) on reaction fronts has not been explored in detail until recently [5][6][7][8][9][10][11][12][13][14][15][16][17][18]. In the presence of an hydrodynamic flow, it has already been observed and understood that such fronts while propagating at a new constant velocity, adapt their shape in order to achieve a balance between reaction diffusion and flow advection.…”

Laminar dispersion at high Péclet numbers in finite-length channels: Effects of the near-wall velocity profile and connection with the generalized Leveque problem

“…5,28,29 Zhao and Bau 29 analyze the influence of cross flows, whereas Dutta and Leighton 28 consider the coupling of a pressure-driven flow in an electrokinetically driven microchannel for reducing dispersion in polymerase chain reaction and DNA-hybridization is considered in Refs. 32 and 33, while Leconte et al 34 study the occurrence of Taylor regimes in the evolution of autocatalytic reaction fronts.…”

Thin front propagation in random shear flows

“…[13]. Another interesting example is represented by the theoretical studies on time periodic shear flows [6,10] and the recent experimental work [12] which study aqueous reactions in periodically modulated Hele-Shaw flows.…”

“…Front propagation in fluid flows is a problem relevant to many areas of science and technology ranging from combustion technology [1] to chemistry [2] and marine ecology [3]. In the last years several theoretical [4,5,6,7,8,9,10] and experimental [11,12,13,14] works studied chemically reactive substances stirred by laminar flows. This problem, though considerably simpler than the case of turbulent flows [1], is non trivial and displays a very rich and interesting phenomenology.…”

“…In particular this could be performed in experimental studies in settings similar to those of Refs. [12] where flows of the form u(r, t) = U (t)v(r) can be easily generated with a good control of the time dependence of the amplitude.…”