A mathematical formulation is presented of Wilhelm Ostwald’s supersaturation theory of Liesegang ring formation. The theory involves diffusion of two reactants toward one another, their chemical reaction to form a product, the reverse reaction, and diffusion of the product. When the product concentration reaches a certain supersaturation value, it begins to precipitate. It is shown that this theory can lead to recurrent precipitation, resulting in rings or bands of precipitate. Conditions under which this occurs are determined. In addition, the locations and times of formation of the bands are calculated and shown to agree with experimental results.

1.
R. E.
Liesegang
,
Photgr. Archiv.
21
,
221
(
1896
).
2.
W. Ostwald, Lehrburch der Allgemeinen Chemie (Engelman, Leipzig, 1897), p. 778.
3.
C.
Wagner
,
J. Colloid Sci.
5
,
85
(
1950
).
4.
S.
Prager
,
J. Chem. Phys.
25
,
279
(
1956
).
5.
Ya. B.
Zeldovitch
,
G. I.
Barenblatt
, and
R. L.
Salganik
,
Sov. Phys. Dokl.
6
,
869
(
1962
).
6.
K. H.
Stern
,
Chem. Rev.
54
,
79
(
1954
).
7.
J. B. Keller, in Dynamics and Modelling of Reactive Systems, edited by W. Stewart (Academic, New York, 1980), pp. 257–274.
8.
J. B. Keller and P. S. Hagan, Fast reaction and slow diffusion (unpublished).
9.
S.
Shinohara
,
J. Phys. Soc. Jpn.
29
,
1073
(
1970
).
10.
C. A.
Schleussner
,
Kolloid Z.
34
,
338
(
1924
).
11.
H. W.
Morse
and
G. W.
Pierce
,
Z. Phys. Chem.
45
,
489
(
1903
).
12.
Lord
Rayleigh
,
Philos. Mag.
38
,
738
(
1919
).
13.
H.
Flicker
and
J.
Ross
,
J. Chem. Phys.
60
,
3458
(
1974
).
14.
D. N.
Ghosh
,
J. Ind. Chem. Soc.
7
,
509
(
1930
).
15.
P. B.
Mathur
and
S.
Ghosh
,
Kolloid Z.
159
,
143
(
1958
).
16.
A.
Packter
,
Kolloid Z.
142
,
109
(
1955
).
17.
K. S.
Ramaiah
,
Proc. Indian Acad. Sci., Sect. A
,
9
,
467
(
1939
).
18.
W.
Moeller
,
Kolloid Z.
20
,
242
(
1917
).
19.
C. A.
Schleussner
,
Kolloid Z.
31
,
347
(
1922
).
20.
M. H. Protter and H. Weinberger, Maximum Principles in Differential Equations (Prentice‐Hall, Englewood Cliffs, 1967), p. 168.
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