Abstract
The kinetics of swelling and shrinking of gels is studied. A new relation, in addition to the differential equation developed by Tanaka and Fillmore, is formulated to solve the kinetics of gels having arbitrary shape. The gel kinetics is described as a combination of the collective diffusion with finite rate and immediate relaxation of shear deformation. The relation demonstrates the fundamental differences between the gel kinetics and the molecules diffusion process. The difference is a direct result of the existence of the shear modulus of the gel network system. Some interesting details of our theory are further discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Y. Li and T. Tanaka, J. Chem. Phys. (to be published).
T. Tanaka, L. Hocker and G. Benedek, J. Chem. Phys. 59(9), 5151(1973).
T. Tanaka and D. Fillmore, J. Chem. Phys. 70(3), 1214(1979).
T. Tanaka, E. Sato, Y. Hirokawa, S. Hirotsu and J. Peetermans, Phys. Rev. Lett. 55(22), 2455(1985).
E. Sato-Matsuo and T. Tanaka, J. Chem. Phys. 89(3), 1695(1988).
A. Peters and S. J. Candau, Macromolecules 19(7), 1952(1986).
A. Peters and S. J. Candau, Macromolecules 21(7), 2278(1988).
L. D. Landau and E. M. Lifshitz, Theory of Elasticity, 1986 Pergamon Press, Oxford.
The boundary of the ink string can be defined as the density profile of the ink molecules at a certain value. For instance, we can define the radius of the string r as the value at which the relative density p(r)/p (0) = 0.1.
Due to a mistake made in the initial condition, the coefficients A n given by Eq. (6) in [6] are not correct. The correct answer should be display equation The boundary condition of a spherical gel is R = α2 n/(4 − 4αn cot αn).
Akira Onuki, Phys. Rev. A 38(4), 2192(1988).
This does not mean that there is no solution to this problem. Readers can verify easily that for equation x 2 + x = 1, iteration x n+1 = 1 − x 2 n does not converge 54-1.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Li, Y., Tanaka, T. (1990). Swelling of Gels and Diffusion of Molecules. In: Onuki, A., Kawasaki, K. (eds) Dynamics and Patterns in Complex Fluids. Springer Proceedings in Physics, vol 52. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76008-2_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-76008-2_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-76010-5
Online ISBN: 978-3-642-76008-2
eBook Packages: Springer Book Archive