Concentration-dependent diffusion instability in reactive miscible fluids

We report on chemoconvective pattern formation phenomena observed in a two-layer system of miscible fluids filling a vertical Hele-Shaw cell. We show both experimentally and theoretically that the concentration-dependent diffusion coupled with frontal acid-base neutralization can give rise to the formation of a local unstable zone low in density, resulting in a perfectly regular cell-type convective pattern. The described effect gives an example of yet another powerful mechanism which allows the reaction-diffusion processes to govern the flow of reacting fluids under gravity conditions.

Figure 1

(a)–(c) Chemoconvective structures arising due to the CDD instability observed 1100 s after as the aqueous solutions of ${\mathrm{HNO}}_3$ (top) and NaOH (bottom) were brought into contact in a vertical Hele-Shaw cell: (a) Velocity field revealed by the tracks of light-scattering particles; (b) interferogram showing a refractive index distribution; (c) $p\mathrm{H}$ distribution obtained in the presence of a color indicator. The initial concentrations of the species are both equal to 1 mol/l. The initial contact line is indicated by the horizontal band. (d), (e) Evolution of the upper [indicated in (a) as $Z_u]$ and lower ($Z_l$) boundaries (d) and wavelength (e) of the CDD pattern in time obtained experimentally (points) and numerically within the theoretical model (lines).

Figure 2

Observed diffusion coefficients for nitric acid, sodium hydroxide, and their salt in aqueous solution at $25{}^{\circ }\mathrm{C}$ as a function of the concentrations of diffusing substances $C=\{A,B,S\}$ are indicated by points. The straight lines represent the least-squares fit to the experimental data set.

Figure 3

(a) Instantaneous base state profiles of the total density (10) for the case of constant diffusion (black circles) and concentration-dependent diffusion (red squares) at $t=5$; (b) neutral curves for DLC and CDD instabilities which arise in two zones low in density, shown in (a).

Figure 4

Stream function (top) and total density (bottom) obtained by numerically solving a full nonlinear set of equations (1, 2, 3, 4, 5, 6, 7, 8) for time $t=3$. The line $z=0$ corresponds to the initial contact line between layers. Nonlinear development of the CDD instability below the contact line is clearly seen.