Autocatalytic reaction between reacted and unreacted species may propagate as solitary waves, namely at a constant front velocity and with a stationary concentration profile, resulting from a balance between molecular diffusion and chemical reaction. The effect of advective flow on the autocatalytic reaction between iodate and arsenous acid in cylindrical tubes and Hele-Shaw cells is analyzed experimentally and numerically using lattice BGK simulations. We do observe the existence of solitary waves with concentration profiles exhibiting a cusp and we delineate the eikonal and mixing regimes recently predicted.The motion of interfaces and the propagation of fronts resulting from chemical reactions occur in a number of different areas [1], including population dynamics [2,3] and flame propagation [4]. It is known that autocatalytic reaction fronts between two reacting species propagate as solitary waves, namely at a constant front velocity and with a stationary concentration profile [5,6]. The important issue of the selection of the front velocity was addressed earlier on, but only a few cases are well understood, such as the pioneering works of Fisher [2] and Kolmogorov-Petrovskii-Piskunov [3] on a reactiondiffusion equation with second-order kinetics [1,4,7]. The effect of advective flow (inviscid and/or turbulent) on reacting systems was analyzed extensively in the propagation of flames in the context of combustion [4,8]. On the other hand, advective effects on the behavior of autocatalytic fronts have been only recently addressed [9,10,11]. B. F. Edwards [11] studied theoretically the effect of a 2D laminar flow on an autocatalytic reaction front between two infinite planes separated by a gap b. In this geometry, the velocity profile is unidirectional in the direction z of the flow and is given by Poiseuille's equation,5 U is the maximum velocity, U is the mean velocity, ζ = 2x/b is the transverse normalized coordinate and − → z is the unit vector parallel to the flow, chosen as the direction of the front propagation in the absence of flow (see below). Consider the iodate-arsenous acid reaction described by a thirdorder autocatalytic reaction kinetics [1,5,6]:where C is the concentration of the (autocatalytic) reactant iodide, normalized by the initial concentration of iodate, D m is the molecular diffusion coefficient, and α is the reaction rate kinetic coefficient. In the absence of hydrodynamics ( − → U = − → 0 ), Eq.1 admits a well-known solitary wave solution with front velocity V 0 = αD m /2 and front width L 0 = D m /V 0 [5,6]. The use of these two quantities to normalize velocities and lengths in Eq.1, leads to two independent parameters η = b/2L 0 and ε = U /V 0 . Reference [11] investigated numerically the solitary wave solution of Eq.1, and particularly its normalized front velocity, v = V F /V 0 , as a function of ε, for different values of η. Of interest are the following asymptotic predictions:In the narrow-gap regime (η → 0 or ε → 0), it was found that v = 1 + ε. Namely, when L 0 >> b, mixing ac...

Autocatalytic reaction fronts between unreacted and reacted mixtures in the absence of fluid flow propagate as solitary waves. In the presence of imposed flow, the interplay between diffusion and advection enhances the mixing, leading to Taylor hydrodynamic dispersion. We present asymptotic theories in the two limits of small and large Thiele modulus (slow and fast reaction kinetics, respectively) that incorporate flow, diffusion, and reaction. For the first case, we show that the problem can be handled to leading order by the introduction of the Taylor dispersion replacing the molecular diffusion coefficient by its Taylor counterpart. In the second case, the leading-order behavior satisfies the eikonal equation. Numerical simulations using a lattice gas model show good agreement with the theory. The Taylor model is relevant to microfluidics applications, whereas the eikonal model applies at larger length scales.

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.

The authors describe a setup to measure accurately the normal restitution coefficient between a quasiresonant ball and a plane. It uses the fact that the trajectory of a single ball in a cylindrical box with a vibrating wall reduces rapidly to a merely periodic one dimensional dynamics, with little rotation. The ball speed is measured accurately from the time series of impacts. It is also used to study and calibrate a sphere-plane impact sensor. This sensor allows to determine the collision time at a microsecond accuracy and the maximum force applied. The collision is found to obey the Hertz law.