Avalanches dynamics in reaction fronts in disordered flows

We report on numerical studies of avalanches of an autocatalytic reaction front in a porous medium. The front propagation is controlled by an adverse flow resulting in upstream, static, or downstream regimes. In an earlier study focusing on front shape, we identified three different universality classes associated with this system by following the front dynamics experimentally and numerically. Here, using numerical simulations in the vicinity of the second-order transition, we identify an avalanche dynamics characterized by power-law distributions of avalanche sizes, durations, and lateral extensions. The related exponents agree well with the quenched-Kardar-Parisi-Zhang theory, which describes the front dynamics. However, the geometry of the propagating front differs slightly from that of the theoretical one. We show that this discrepancy can be understood in terms of the nonquasistatic correction induced by the finite front velocity.

CHEMO-hydrodynamic coupling between forced advection in porous media and self-sustained chemical waves

Autocatalytic reaction fronts between two reacting species in the absence of fluid flow, propagate as solitary waves. The coupling between autocatalytic reaction front and forced simple hydrodynamic flows leads to stationary fronts whose velocity and shape depend on the underlying flow field. We address the issue of the chemico-hydrodynamic coupling between forced advection in porous media and self-sustained chemical waves. Towards that purpose, we perform experiments over a wide range of flow velocities with the well characterized iodate arsenious acid and chlorite-tetrathionate autocatalytic reactions in transparent packed beads porous media. The characteristics of these porous media such as their porosity, tortuosity, and hydrodynamics dispersion are determined. In a pack of beads, the characteristic pore size and the velocity field correlation length are of the order of the bead size. In order to address these two length scales separately, we perform lattice Boltzmann numerical simulations in a stochastic porous medium, which takes into account the log-normal permeability distribution and the spatial correlation of the permeability field. In both experiments and numerical simulations, we observe stationary fronts propagating at a constant velocity with an almost constant front width. Experiments without flow in packed bead porous media with different bead sizes show that the front propagation depends on the tortuous nature of diffusion in the pore space. We observe microscopic effects when the pores are of the size of the chemical front width. We address both supportive co-current and adverse flows with respect to the direction of propagation of the chemical reaction. For supportive flows, experiments and simulations allow observation of two flow regimes. For adverse flow, we observe upstream and downstream front motion as well as static front behaviors over a wide range of flow rates. In order to understand better these observed static state fronts, flow experiments around a single obstacle were used to delineate the range of steady state behavior. A model using the "eikonal thin front limit" explains the observed steady states.

Drying in porous media with gravity-stabilized fronts: experimental results

In a recent paper [Yiotis et al., Phys. Rev. E 85, 046308 (2012)] we developed a model for the drying of porous media in the presence of gravity. It incorporated effects of corner film flow, internal and external mass transfer, and the effect of gravity. Analytical results were derived when gravity opposes drying and hence leads to a stable percolation drying front. In this paper, we test the theory using laboratory experiments. A series of isothermal drying experiments in glass bead packings saturated with volatile hydrocarbons is conducted. The transparent glass cells containing the packing allow for the visual monitoring of the phase distribution patterns below the surface, including the formation of liquid films, as the gaseous phase invades the pore space, and for the control of the thickness of the diffusive mass boundary layer over the packing. The experimental results agree very well with theory, provided that the latter is generalized to account for the effects of corner roundness in the film region (which was neglected in the theoretical part). We demonstrate the existence of an early constant rate period (CRP), which lasts as long as the films saturate the surface of the packing, and of a subsequent falling rate period (FRP), which begins practically after the detachment of the film tips from the external surface. During the CRP, the process is controlled by diffusion within the stagnant gaseous phase in the upper part of the cells, yielding a Stefan tube problem solution. During the FRP, the process is controlled by diffusion within the packing, with a drying rate inversely proportional to the observed position of the film tips in the cell. Theoretical and experimental results compare favorably for a specific value of the roundness of the films, which is found to be constant and equal to 0.2 for various conditions, and verify the theoretical dependence on the capillary Ca(f), Bond Bo, and Sherwood Sh numbers.

Analytical solutions of drying in porous media for gravity-stabilized fronts

We develop a mathematical model for the drying of porous media in the presence of gravity. The model incorporates effects of corner flow through macroscopic liquid films that form in the cavities of pore walls, mass transfer by diffusion in the dry regions of the medium, external mass transfer over the surface, and the effect of gravity. We consider two different cases: when gravity opposes liquid flow in the corner films and leads to a stable percolation drying front, and when it acts in the opposite direction. In this part, we develop analytical results when the problem can be cast as an equivalent continuum and described as a one-dimensional (1D) problem. This is always the case when gravity acts against drying by opposing corner flow, or when it enhances drying by increasing corner film flow but it is sufficiently small. We obtain results for all relevant variables, including drying rates, extent of the macroscopic film region, and the demarkation of the two different regimes of constant rate period and falling rate period, respectively. The effects of dimensionless variables, such as the bond number, the capillary number, and the Sherwood number for external mass transfer are investigated. When gravity acts to enhance drying, a 1D solution is still possible if an appropriately defined Rayleigh number is above a critical threshold. We derive a linear stability analysis of a model problem under this condition that verifies front stability. Further analysis of this problem, when the Rayleigh number is below critical, requires a pore-network simulator which will be the focus of future work.

Numerical simulations of a buoyant autocatalytic reaction front in tilted Hele-Shaw cells

We present a numerical analysis of solutal buoyancy effects on the shape and the velocity of autocatalytic reaction fronts, propagating in thin tilted rectangular channels. We use two-dimensional (2D) lattice Bathnagar-Gross-Krook (BGK) numerical simulations of gap-averaged equations for the flow and the concentration, namely a Stokes-Darcy equation coupled with an advection-diffusion-reaction equation. We do observe stationary-shaped fronts, spanning the width of the cell and propagating along the cell axis. We show that the model accounts rather well for experiments we performed using an Iodate Arsenous Acid reaction propagating in tilted Hele-Shaw cells, hence validating our 2D modelization of a three-dimensional problem. This modelization is also able to account for results found for another chemical reaction (chlorite tetrathionate) in a horizontal cell. In particular, we show that the shape and the traveling velocity of such fronts are linked with an eikonal equation. Moreover, we show that the front velocity varies nonmonotonically with the tilt of the cell, and nonlinearly with the width of the cell.

Measurement of the temperature profile of an exothermic autocatalytic reaction front

Autocatalytic reactions 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. When the reaction is exothermic, a thermal wave is linked to the chemical front. As the thermal diffusivity is nearly two orders of magnitude larger than the molecular one, the temperature profile spreads over length scales (mm) two orders of magnitude larger than the concentration one. Using an infrared camera, we measure the temperature profiles for a chlorite-tetrathionate autocatalytic reaction. The profiles are compared quantitatively to lattice Bhatnagar-Gross-Krook (BGK) numerical simulations. Our analysis also accounts for the lack of observation of the thermal wave for the iodate arsenous acid reaction.

Crossing the elliptic region in a hyperbolic system with change-of-type behavior arisingin flow between two parallel plates

Change-of-type behavior from hyperbolic to elliptic is common to quasilinear hyperbolic systems. This issue is addressed here for the particular case of miscible flow of three fluids between two parallel plates. Change of type occurs at the leading edge of the displacement front and reflects the failing of the equilibrium assumption, necessary for the quasilinear hyperbolic formalism, at the front. To cross the elliptic region requires the solution of the full, higher-dimensionality problem, obtained here using lattice gas simulations. For the specific example, it is found that the system self-selects a front structure independent of injection conditions.

Mixing and reaction fronts in laminar flows

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.

Pattern of reaction diffusion fronts in laminar flows

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 Bhatnagar-Gross-Krook 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.

Buoyancy-driven instability of an autocatalytic reaction front in a Hele-Shaw cell

An autocatalytic reaction-diffusion front between two reacting species may propagate as a solitary wave, namely, at constant velocity and with a stationary concentration profile. Recent experiments on such reactions have been reported to be buoyancy unstable, under certain conditions. We calculate the linear dispersion relation of the resulting instability, by applying our recent analysis of the Rayleigh-Taylor instability of two miscible fluids in a Hele-Shaw cell. The computed dispersion relation as well as our three-dimensional lattice Bhatnagar-Gross-Krook (BGK) simulations fit reasonably well experimental growth rates reported previously.

[Strength training with superimposed vibrations]

To examine the effects of strength training with superimposed vibrations ten subjects trained over a period of six weeks (three sessions per week) one leg with back squats and superimposed vibrations and the other leg with traditional squats. In each training session participants performed 4 sets with 8-12 repetitions. Before and after the training period maximum strength and rate of force development were measured. The results show that both training modes induced comparable and statistical significant increases in maximum strength (vibration training +6.5%, traditional training +6.2%. The slight increases in rate of force development in both groups didn't reach statistical significance. As a consequence it seems that strength training with superimposed vibrations for the leg extensor chain is not superior to a traditional training mode.