Kinetics of Swelling Gels

We develop a general theory of the swelling kinetics of polymer gels, with the view that a polymer gel is a two-phase fluid. The model we propose is a free boundary problem and can be used to understand both contraction and swelling, including complete dissolving or dehydration of polymeric gels. We show that the equations of motion satisfy a minimum energy dissipation rate principle similar to the Helmholtz minimum dissipation rate principle which holds for a Stokes flow. We also show, using asymptotic analysis and numerical simulation, how the equilibrium swelled state and the swelling rate constant are related to the free energy and rheological properties of the polymer network.

[1]  Tianyu Zhang,et al.  Phase-Field Models for Biofilms II. 2-D Numerical Simulations of Biofilm-Flow Interaction , 2008 .

[2]  A. Onuki,et al.  Theory of pattern formation in gels: Surface folding in highly compressible elastic bodies. , 1989, Physical review. A, General physics.

[3]  Milner.  Hydrodynamics of semidilute polymer solutions. , 1991, Physical review letters.

[4]  P. Flory,et al.  Statistical Mechanics of Cross‐Linked Polymer Networks I. Rubberlike Elasticity , 1943 .

[5]  M. Dembo,et al.  On the mechanics of the first cleavage division of the sea urchin egg. , 1997, Experimental cell research.

[6]  Y Lanir,et al.  Plausibility of structural constitutive equations for swelling tissues--implications of the C-N and S-E conditions. , 1996, Journal of biomechanical engineering.

[7]  G. Batchelor,et al.  An Introduction to Fluid Dynamics , 1968 .

[8]  Jt Johan Padding,et al.  Theory of polymer dynamics , 2007 .

[9]  Toyoichi Tanaka,et al.  Kinetics of swelling of gels , 1979 .

[10]  H. Schott.  Swelling kinetics of polymers , 1992 .

[11]  C. Durning,et al.  Nonlinear swelling of polymer gels , 1993 .

[12]  A. Katchalsky,et al.  Polyelectrolyte gels in salt solutions , 1955 .

[13]  T. Taniguchi,et al.  Shrinking Process of Gels by Stress-Diffusion Coupled Dynamics , 2000 .

[14]  George Oster,et al.  The mechanochemistry of cytogels , 1984 .

[15]  Qi Wang,et al.  Phase Field Models for Biofilms. I. Theory and One-Dimensional Simulations , 2008, SIAM J. Appl. Math..

[16]  E. Hoiczyk,et al.  How Myxobacteria Glide , 2002, Current Biology.

[17]  J. Keener,et al.  The role of the biofilm matrix in structural development. , 2004, Mathematical medicine and biology : a journal of the IMA.

[18]  P. Flory,et al.  STATISTICAL MECHANICS OF CROSS-LINKED POLYMER NETWORKS II. SWELLING , 1943 .

[19]  P. Gennes,et al.  Introduction to polymer dynamics , 1990 .

[20]  Toyoichi Tanaka,et al.  Theory and numerical calculation of pattern formation in shrinking gels , 1999 .

[21]  J. Keener,et al.  Influence of the standard free energy on swelling kinetics of gels. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  George Oster,et al.  The hydration dynamics of polyelectrolyte gels with applications to cell motility and drug delivery , 2004, European Biophysics Journal.

[23]  A. Ravve,et al.  Principles of Polymer Chemistry , 1995 .

[24]  W M Lai,et al.  Boundary conditions at the cartilage-synovial fluid interface for joint lubrication and theoretical verifications. , 1989, Journal of biomechanical engineering.

[25]  Zhibing Hu,et al.  Swelling Kinetics of Polymer Gels , 1997 .

[26]  P. Flory,et al.  Statistical thermodynamics of random networks , 1976, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[27]  W M Lai,et al.  A mixture theory for charged-hydrated soft tissues containing multi-electrolytes: passive transport and swelling behaviors. , 1998, Journal of biomechanical engineering.

[28]  Milner,et al.  Dynamical theory of concentration fluctuations in polymer solutions under shear. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[29]  G. Fredrickson.  The theory of polymer dynamics , 1996 .

[30]  W M Lai,et al.  A triphasic theory for the swelling and deformation behaviors of articular cartilage. , 1991, Journal of biomechanical engineering.

[31]  A. D. Girgidov.  Energy dissipation in the motion of an incompressible fluid , 2009 .