Summary

Conlcusions and the end of a long story

Formation of Liesegang patterns was a mystery of chemistry for more than a century. Probably thousands of scientists reproduced what R. Ed. Liesegang discovered accidentally in the hope that they will understand it more deeply. Although many qualitative and mathematically formulated models have been suggested, none of them was capable to explain every experimental finding.

The IDNB model seems to be the end of this long story.

The most important thing to clarify is why did it take for more than one hundred years to find a proper mechanism for such an apparenty simple chemical process.

It would e failure to think that former scientists simply did not have enough talent or fantasy to formulate a proper set of equations. They just did not have a numerical toolset and the adequate computing power for numerical experiments.

One of the missions of these pages is to demonstrate that in case of reaction-diffusion problems this toolset can be the ReaDiVivus system by that the simulations presented here were performed.

Comparision of the IDNB model and former theories

EXPERIMENTAL FINDING

WHICH MODEL CAN REPRODUCE IT

SCALING LAWS

Spacing law

Essentially all models including IDNB

Time law

All models including IDNB

Matalon-Packter law

Supersaturation theory and all prenucleation models; IDNB

Width law

Probably all postnucleation models can reproduce it but only in its weaker form. According to the IDNB model the stronger form of this law does not exist (see the text).

SPECIAL EFFECTS

Completely revert patterns

IDNB

Partially revert patterning

IDNB

Recurrently revert patterns

IDNB

Spirals

A special form of the competitive particle growth model but only with an initial asymmetry (see Krug et al.) ; IDNB

Helix patterns

IDNB

Revert helix (?)

IDNB (This effect has never been observed in real experiments, but clearly seems to be a possible solution of the RD-equation system.)

Effect of gravity

IDNB

Double banding

IDNB

Chaotic patterning

IDNB and maybe some sol-coagulation models

Formation of ball-like precipitate zones

IDNB

Heterogeneous traveling waves

Supersaturation theory (see Lagzi et al.) ; IDNB

Propagating defects

IDNB

"Bouncing ball" effect

IDNB