Kinetics of swelling gels

SIAM Journal on Applied Mathematics

Volumn 71, Issue 3, 2011, Pages 854-875

  Keener, James P ^a   Sircar, Sarthok ^a   Fogelson, Aaron L ^a  

^a UNIVERSITY OF UTAH   (United States)

Author keywords

Free energy; Gel diffusivity; Moving boundary; Swelling kinetics

Indexed keywords

FREE-BOUNDARY PROBLEMS; GENERAL THEORY; HELMHOLTZ; MINIMUM DISSIPATION RATES; MINIMUM ENERGY; MOVING BOUNDARIES; POLYMER GELS; POLYMER NETWORKS; POLYMERIC GELS; RHEOLOGICAL PROPERTY; STOKES FLOWS; SWELLING GELS; SWELLING KINETICS; SWELLING RATE CONSTANT; TWO PHASE FLUID;

ASYMPTOTIC ANALYSIS; COMPUTER SIMULATION; ENERGY DISSIPATION; EQUATIONS OF MOTION; FREE ENERGY; GELS; KINETICS; POLYMERS; RATE CONSTANTS; RHEOLOGY;

SWELLING;

EID: 79960352413     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/100796984     Document Type: Article

References (33)

1. G. K. BATCHELOR, An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, UK, 1967.
2. N. COGAN AND J. P. KEENER, The role of the biofilm matrix in structural development, Math. Medicine Biol., 21(2004), pp. 147-166. (Pubitemid 38867857)
3. M. DOI, Introduction to Polymer Dynamics, Oxford University Press, Oxford, England, 1996.
4. M. DOI AND S. F. EDWARDS, Theory of Polymer Dynamics, Clarendon Press, Oxford, England, 1986.
5. C. J. DURNING AND K. N. MORMAN, Nonlinear swelling of polymer gels, J. Chem. Phys., 98(1993), pp. 4275-4293.
6. P. J. FLORY, Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY, 1953.
7. P. J. FLORY, Statistical thermodynamics of random networks, Proc. R. Soc. Lond. Ser. A, 351(1976), pp. 351-380.
8. P. J. FLORY AND J. REHNER, JR., Statistical mechanics of cross-linked polymer networks I. Rubberlike elasticity, J. Chem. Phys., 11(1943), pp. 512-520.
9. P. J. FLORY AND J. REHNER, JR., Statistical mechanics of cross-linked polymer networks II. Swelling, J. Chem. Phys., 11(1943), pp. 521-526.
10. A. GIRGIDOV, Energy dissipation in the motion of an incompressible fluid, Dokl. Phys., 54(2009), pp. 306-308.
11. W. Y. GU, W. M. LAI, AND V. C. MOW, A mixture theory for charged-hydrated soft tissues containing multi-electrolytes: Passive transport and swelling behaviors, Trans ASME J. Biomech. Eng., 120(1998), pp. 169-180. (Pubitemid 28194393)
12. X. HE AND M. DEMBO, On the mechanics of the first cleavage division of the sea urchin egg, Exp. Cell Res., 233(1997), pp. 252-273. (Pubitemid 27252006)
13. J. S. HOU, M. H. HOLMES, W. M. LAI, AND V. C. MOW, Boundary conditions at the cartilagesynovial fluid interface for joint lubrication and theoretical verifications, J. Biomech. Eng., 111(1989), pp. 78-87.
14. A. KATCHALSKY AND I. MICHAELI, Polyelectrolyte gels in salt solutions, J. Polymer Sci., 15(1955), pp. 69-86.
15. J. P. KEENER, S. SIRCAR, AND A. L. FOGELSON, The influence of the standard free energy on swelling kinetics of gels, Phys. Rev. E, 83(2011), 041802.
16. W. M. LAI, J. S. HOU, AND V. C. MOW, A triphasic theory for the swelling and deformation behaviors of articular cartilage, J. Biomech. Eng., 113(1991), pp. 245-258.
17. Y. LANIR, Plausibility of structural constitutive equations for swelling tissues-Implications of the c-n and s-e conditions, Trans ASME J. Biomech. Eng., 118(1996), pp. 10-16. (Pubitemid 26087277)
18. V. LYUL'KA, On the principle of minimum kinetic energy dissipation in the nonlinear dynamics of viscous fluid, Tech. Phys., 46(2001), pp. 1501-1503.
19. J. MASKAWA, T. TAKEUCHI, K. MAKI, K. TSUIJII, AND T. TANAKA, Theory and numerical calculation of pattern formation in shrinking gels, J. Chem. Phys., 110(1999), pp. 10993-10999.
20. S. T. MILNER, Hydrodynamics of semidilute polymer solutions, Phys. Rev. Lett., 66(1991), pp. 1477-1480.
21. S. T. MILNER, Dynamical theory of concentration fluctuations in polymer-solutions under shear, Phys. Rev. E, 48(1993), pp. 3674-3691.
22. A. ONUKI, Theory of pattern formation in gels: Surface folding in highly compressible elastic bodies, Phys. Rev. A, 39(1989), pp. 5932-5948.
23. G. F. OSTER AND G. M. ODELL, The mechanochemistry of cytogels, Phys. D, 12(1984), pp. 333-350.
24. K. SEKIMOTO, N. SUEMATSU, AND K. KAWASAKI, Spongelike domain structure in a twodimensional model gel undergoing volume-phase transition, Phys. Rev. A, 39(1989), pp. 4912-4914.
25. T. TANAKA AND D. J. FILLMORE, Kinetics of swelling in gels, J. Chem. Phys., 70(1979), pp. 1214-1218.
26. T. TANAKA, D. FILLMORE, S. T. SUN, I. NISHIO, G. SWISLOW, AND A. SAHA, Phase transition in ionic gels, Phys. Rev. Lett., 45(1980), pp. 1636-1639.
27. C. WANG, Y. LI, AND Z. HU, Swelling kinetics of polymer gels, Macromolecules, 30(1997), pp. 4727-4732. (Pubitemid 127569604)
28. C. WOLGEMUTH, E. HOICZYK, D. KAISER, AND G. OSTER, How myxobacteria glide, Current Biol., 12(2002), pp. 369-377. (Pubitemid 34209283)
29. C. WOLGEMUTH, A. MOGILNER, AND G. OSTER, The hydration dynamics of polyelectrolyte gels with applications to cell motility and drug delivery, Eur. Biophys. J., 33(2004), pp. 146-158. (Pubitemid 38987101)
30. C. W. WOLGEMUTH, E. HOICZYK, AND G. OSTER, How gliding bacteria glide, Biophys. J., 82(2002), pp. 1956 ff.
31. T. YAMAUE, T. TANIGUCHI, AND M. DOI, Shrinking process of gels by stress-diffusion coupled dynamics, Prog. Theor. Phys. Supp., 138(2000), pp. 416-417.
32. T. ZHANG, N. G. COGAN, AND Q. WANG, Phase field models for biofilms. I. Theory and onedimensional simulations, SIAM J. Appl. Math., 69(2008), pp. 641-669.
33. T. ZHANG, N. COGAN, AND Q. WANG, Phase field models for biofilms. II. 2-D numerical simulations of biofilm-flow interaction, Comm. Comp. Phys., 4(2008), pp. 72-101.