Diffusion and Supersaturation in Gelatine

Self-organization in precipitation reactions far from the equilibrium

“…In addition to these general observations for interband spacing, a simple power law describes the width ( w ) of the precipitation bands, which typically increases at distances farther from the gel-solution interface according to . Finally, the fourth empirical law, which was discovered by Morse and Pierce, captures the temporal dynamics of Liesegang band formation as , where t n is the time at which the n th band begins to precipitate ( 132 ). Notice that the scaling coefficient δ is analogous to a diffusion constant, which is not a surprising result in the limit of fast reaction kinetics and slow diffusive transport.…”

Intermediate colloidal formation and the varying width of periodic precipitation bands in reaction–diffusion systems

“…Hence ξ n is a better choice of distance than x n and hence the modified width relation [10] seems to be more meaningful. The width of the (n + 1)th band is given by…”

“…Earlier investigators have framed three quantitative relations, characterizing the banding. The first one called time law was given by Morse and Pierce [10] and has a simple form (1) x n = αt 1/2 n + β, where x n is the distance up to the lower end of the nth precipitation band measured from the gel solution interface, t n is the time elapsed since the diffusion started, and α and β are constants. This result is analogous to the solution of the well-known Einstein-Smoluchowski relation for Brownian motion interpreted in terms of random walk in a homogeneous space [11].…”

Regular Liesegang patterns and precipitation waves in an open system

“…In several cases, modification of the dynamics (including the presence of external electric field, advection field, curvature effect) results in some deviations compared to the time law. 20 Fig. 3a presents the evolution of the pattern for various values of k. Relatively high coupling hampers the depletion of B, therefore, the more intensive precipitate formation reduces the concentration of A in the reactive medium, which leads to the slower evolution of the pattern.…”

“…The distribution of the precipitate is usually non-uniform behind this front. Appearing precipitation zones (Liesegang bands or rings, depending on the geometry of the experimental setup) [11][12][13][14][15][16][17][18][19] have several empirical regularities (time, 20,21 spacing, 22 and width law [23][24][25] ), in which some well-measurable quantities are connected with each other. These are X n , the position of the nth band, measured from the junction point of the electrolytes, t n the appearance time, and w n , the width of the nth band, respectively.…”