A theory of adsorption kinetics of solutes onto a solid surface from the solution phase is proposed in which a time delay is introduced into the solute concentration on the surface. Equations governing the adsorption kinetics are similar to those for membrane transport with time delay (Ohshima and Kondo, Biophys. Chem. (1989) 33: 303). It is found that introduction of time delay τ causes, under certain conditions, overshoot or oscillation in the solute concentrations, both in the solution phase and on the surface. The criterion for oscillation depends on the scaled delay time ατ, the ratio of the possible maximum amount of solutes adsorbed on the surface to the total solute amountR, and the scaled binding constantK. When the number of the binding sites is small, the criterion for oscillation is expressed as γ>exp(−1), where γ=(ατ/K) exp(ατ).
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Milsum JB (1967) Biological control systems analysis. McGraw-Hill, New York
May RM (1976) Nature 261:459
Frisch R, Holme H (1935) Economics 3:225
Allen RGD (1956) Mathematical economics. Macmillan, London
Ohshima H, Kondo T (1989) Biophys Chem 33:303
Ohshima H, Kamei M, Kondo T (1991) Biophys Chem 41:301
Neihof R, Soliner K (1957) J Phys Chem 61:159
Takeguchi N, Horikoshi I, Tanaka S (1957) Bull Chem Soc Japan 48:3044
Ohara Y, Arakawa M, Kondo T, Lee KB (1985) J Membrane Sci 23:1
About this article
Cite this article
Ohshima, H., Fujita, N. & Kondo, T. Adsorption kinetics with time delay. Colloid Polym Sci 270, 707–710 (1992). https://doi.org/10.1007/BF00654047