Influence of Marangoni flows on the dynamics of isothermal A + B → C reaction fronts

Abstract

The nonlinear dynamics of A + B → C fronts is analyzed both numerically and theoretically in the presence of Marangoni flows, i.e., convective motions driven by surface tension gradients. We consider horizontal aqueous solutions where the three species A, B, and C can affect the surface tension of the solution, thereby driving Marangoni flows. The resulting dynamics is studied by numerically integrating the incompressible Navier-Stokes equations coupled to reaction-diffusion-convection (RDC) equations for the three chemical species. We show that the dynamics of the front cannot be predicted solely on the basis of the one-dimensional reaction-diffusion profiles as is the case for buoyancy-driven convection around such fronts. We relate this observation to the structure of Marangoni flows which lead to more complex and exotic dynamics. We find in particular the surprising possibility of a reversal of the front propagation direction in time for some sets of Marangoni numbers, quantifying the influence of each chemical species concentration on the solution surface tension. We explain this reversal analytically and propose a new classification of the convective effects on A + B → C reaction fronts as a function of the Marangoni numbers. The influence of the layer thickness on the RDC dynamics is also presented. Those results emphasize the importance of flow symmetry properties when studying convective front dynamics in a given geometry.

Making a Simple A+B→C Reaction Oscillate by Coupling to Hydrodynamic Effect

“…For simplicity, we choose A 0 ¼ B 0 and consider the same surface tension, γ R , and density, ρ R , for the reactant solutions. Chemical species are also taken with the same diffusivity to ensure a symmetrical development of the reactive zone [15,16,38,39]. The formation of the product C occurs upon diffusive mixing of the two reactants A and B across the initial contact line localized at x 0 .…”

Interaction of Pure Marangoni Convection with a Propagating Reactive Interface under Microgravity

“…The Marangoni shear stress, which can also arise upon contact of the reaction front propagating in the bulk liquid phase with the open liquid surface, can couple to the buoyant forces leading to intricate flow patterns [31]. The dynamics depends on the relative magnitude of surface tension versus buoyancy effects generally quantified by the Marangoni and Rayleigh numbers, respectively [31][32][33][34][35]. For a positive Marangoni number, defined as…”

Spatial and Temporal Oscillations of Surface Tension Induced by an A + B → C Traveling Front

“…or, in dimensionless form, where δ b,c = D b,c /D a are the two diffusion coefficient ratios, D c is the diffusion coefficient of species C, and S c = (]/D a ) is the Schmidt number (fixed to 10 3 as typical for small species at room temperature in water), with ] = (μ/ρ 0 ) the kinematic viscosity, μ the dynamic viscosity and ρ 0 the solution density. To nondimensionalize the problem, as in Tiani and Rongy [26], we have used the characteristic scales of the reaction-diffusion system: for time,…”

“…As described in Section 3, the mechanism of oscillating surface tension profiles requires the front to be (mainly) located at the free surface and to be in motion along the surface. As a result, such oscillations are prevented in the symmetric case (i.e., when β = 1 and δ b = 1, ∀ M), where two convective rolls of identical intensity leads to a stationary front with surface tension profiles that admit either a global maximum or a global minimum (the symmetric case is described in reference Tiani and Rongy [26]). Hence, oscillations as in Figure 2 can only be triggered in an asymmetric scheme (i.e., when β ≠ 1 and/or δ b ≠ 1).…”