Cross-Diffusion in a Water-in-Oil Microemulsion Loaded with Malonic Acid or Ferroin. Taylor Dispersion Method for Four-Component Systems

Abstract

We describe an improved Taylor dispersion method for four-component systems, which we apply to measure the main- and cross-diffusion coefficients in an Aerosol OT water-in-oil microemulsion loaded with one of the reactants of the Belousov-Zhabotinsky (BZ) reaction, water(1)/AOT(2)/R(3)/octane(4) system, where R is malonic acid or ferroin. With [H(2)O]/[AOT] = 11.8 and volume droplet fraction phi d = 0.18, when the microemulsion is below the percolation transition, the cross-diffusion coefficients D(13) and D(23) are large and positive ( D(13)/ D(33) congruent with 14, D(23)/ D(33) congruent with 3) for malonic acid and large and negative for ferroin ( D(13)/ D(33) congruent with -112, D(23)/ D(33) congruent with -30) while coefficients D(31) and D(32) are small and negative for malonic acid ( D(31)/ D(33) congruent with -0.01, D(32)/ D(33) congruent with -0.14) and small and positive for ferroin ( D(31)/ D(33) congruent with 5 x 10(-4), D(32)/ D(33) congruent with 8 x 10(-3)). These data represent the first direct determination of cross-diffusion effects in a pattern-forming system and of the full matrix of diffusion coefficients for a four-component system. The results should provide a basis for modeling pattern formation in the BZ-AOT system.

Cross-diffusion and pattern formation in reaction–diffusion systems

“…The eluted peak, sometimes called the Taylor peak, is monitored by a suitable detector such as a flow-through spectrophotometer, refractive index detector (RID) or Raman spectrometer. 93,94 The diffusion coefficients are calculated from the parameters of the Gaussian functions that fit the eluted peak. A typical peak is shown in Fig.…”

“…[170][171][172] We recently found that cross-diffusion in BZ-AOT microemulsions is quite significant and may therefore be responsible for many of the wealth of patterns observed in this system. 93 A sampling of BZ-AOT patterns is shown in Fig. 4, where we have grouped the most important classes of patterns: wave patterns (upper row and right column), Turing patterns (three left snapshots in the second row), patterns originating from a wave instability (third row), and localized patterns (three left snapshots in the last row).…”

“…Very large positive and negative crossdiffusion coefficients have been found in three-component water-in-oil AOT microemulsions consisting of water(l)-AOT(2)-heptane 28,116,117 and water(l)-AOT(2)-octane, and in the analogous four-component systems water(l)-AOT(2)-ferroin(3)-octane and water(l)-AOT(2)-malonic acid(3)-octane. 93 The large positive D 12 grows almost linearly with the radius of the water nanodroplets, which is proportional to the ratio o = c 1 /c 2 , and can be approximately expressed as 28,116 …”

Cross-diffusion-induced convective patterns in microemulsion systems

“…2 shows the appearance of convective fingers, which grow upwards and downwards around the interface, in a system where [NaBrO 3 ] B = 0.1 M and [NaBrO 3 ] T = 0 M. Here we assume that the addition of the fourth component in the bottom layer does not change the structural parameters of the microemulsions. 11 The typical growth dynamics of a single finger can be followed and characterized from the space-time (ST) plot depicted in Fig. 2f that is built along the vertical line in Fig.…”

“…7 Typical systems in which cross-diffusion-driven reactive patterns can be studied include AOT (sodium bis(2-ethylhexyl)sulfosuccinate aerosol OT) micelles, for which a large number of RD patterns have been characterized 8 and the diffusion matrix often contains large off-diagonal terms. [9][10][11][12] Cross-diffusion effects are also known to be able to trigger convective motions around liquid interfaces in the absence of chemical reactions. Experimental studies of a ternary system, polyvinylpyrrolidone(PVP)-dextran-H 2 O, 13 have indeed demonstrated hydrodynamic instabilities at the miscible interface between non-reactive solutions exhibiting large cross-diffusion properties.…”