Toward rational design of drug delivery substrates: II. Mixture theory for three-scale biocompatible polymers and a computational example

Multiscale Modeling and Simulation

Volumn 2, Issue 2, 2004, Pages 335-357

  Cushman, John H ^a   Singh, Pawan P ^b   Bennethum, Lynn S ^c  

^a PURDUE UNIVERSITY   (United States)

^b UNIVERSITY OF IDAHO   (United States)

^c UNIVERSITY OF COLORADO   (United States)

Author keywords

Biocompatible polymer; Constitutive theory; Drug delivery systems; Multiple scales; Swelling tissue

Indexed keywords

BIOCOMPATIBILITY; COMPUTATION THEORY; CONSTITUTIVE EQUATIONS; LIQUIDS;

BIOCOMPATIBLE POLYMER; CONSTITUTIVE THEORY; DRUG DELIVERY SYSTEM; ENTROPY INEQUALITY; FIELD EQUATION; MULTIPLE SCALE; RATIONAL DESIGN; TWO LIQUID PHASIS;

POLYMERS;

EID: 84983748075     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/030600369     Document Type: Article

References (41)

1. S. Achanta, J. H. Cushman, and M. R. Okos, On multicomponent, multiphase thermomechanics with interfaces, Internat. J. Engrg. Sci., 32 (1994), pp. 1717-1738.
2. S. Achanta, M. Okos, J. Cushman, and D. Kessler, Moisture transport in shrinking gels during saturated drying, AIChE J., 43 (1997), pp. 2112-2122.
3. G. Astarita and G. Sarti, A class of mathematical models for sorption of swelling solvents in glassy polymers, Polymer Engrg. Sci., 18 (1978), pp. 388-395.
4. L. Bennethum and J. Cushman, Coupled solvent and heat transport of a mixture of swelling porous particles and fluids: Single time-scale problem, Transp. Porous Media, 36 (1999), pp. 211-244.
5. L. Bennethum, M. A. Murad, and J. Cushman, Macroscale thermodynamics and the chemical potential for swelling porous media, Transp. Porous Media, 39 (2000), pp. 187-225.
6. L. S. Bennethum and J. H. Cushman, Multiscale, hybrid mixture theory for swelling systems. 1. Balance laws, Internat. J. Engrg. Sci., 34 (1996), pp. 125-145.
7. L. S. Bennethum and J. H. Cushman, Multiscale, hybrid mixture theory for swelling systems. 2. Constitutive theory, Internat. J. Engrg. Sci., 34 (1996), pp. 147-169.
8. L. S. Bennethum and T. Giorgi, Generalized Forchheimer equation for two-phase flow based on hybrid mixture theory, Transp. Porous Media, 26 (1997), pp. 261-275.
9. L. S. Bennethum, M. A. Murad, and J. H. Cushman, Modified Darcy's law, Terzaghi's effective stress principle and Fick's law for swelling clay soils, Computers and Geotechnics, 20 (1997), pp. 245-266.
10. R. M. Bowen, Compressible porous-media models by use of the theory of mixtures, Internat. J. Engrg. Sci., 20 (1982), pp. 697-735.
11. R. Christensen, Theory of Viscoelasticity, Academic Press, New York, 1982.
12. A. Eringen, Mechanics of Continua, 2nd ed., R. E. Krieger, Huntington, NY, 1980.
13. M. Fukuoka, H. Watanabe, T. Mihori, and S. Shimada, Moisture diffusion in a dry soybean seed measured using pulsed-field-gradient NMR, Journal of Food Engineering, 23 (1994), pp. 533-541.
14. G. Hartley, Diffusion and swelling of high polymers, Transactions of the Faraday Society, 45 (1949), pp. 820-832.
15. S. Hassanizadeh, High velocity flow in porous media, Transp. Porous Media, 2 (1987), pp. 521-531.
16. D. J. Kim, J. M. Caruthers, and N. A. Peppas, Experimental verification of a predictive model of penetrant transport in glassy polymers, Chemical Engineering Science, 51 (1996), pp. 4827-4841.
17. M. Liu, K. Haghighi, R. L. Stroshine, and E. C. Ting, Mechanical-properties of the soybean cotyledon and failure strength of soybean kernels, Transactions of the ASAE, 33 (1990), pp. 559-566.
18. P. F. Low, The swelling of clay. 2. Montmorillonites, Soil Science Society of America Journal, 44 (1980), pp. 667-676.
19. P. F. Low, The swelling of clay. 3. Dissociation of exchangeable cations, Soil Science Society of America Journal, 45 (1981), pp. 1074-1078.
20. P. F. Low, Structural component of the swelling pressure of clays, Langmuir, 3 (1987), pp. 18-25.
21. P. F. Low and J. F. Margheim, The swelling of clay. 1. Basic concepts and empirical equations, Soil Science Society of America Journal, 43 (1979), pp. 473-481.
22. S. Lustig and N. Peppas, Solute and penetrant diffusion in swellable polymers. VII. A free volume-based model with mechanical relaxation, Journal of Applied Polymer Science, 33 (1987), pp. 533-549.
23. S. R. Lustig, J. M. Caruthers, and N. A. Peppas, Continuum thermodynamics and transport theory for polymer-fluid mixtures, Chemical Engineering Science, 47 (1992), pp. 3037-3057.
24. L. Mandelkern and F. Long, Rate of sorption of organic vapors by films of cellulose acetate, J. Polymer Science, 6 (1951), pp. 457-469.
25. R. Misra and J. Young, Numerical solution of simultaneous moisture diffusion and shrinkage during soybean drying, Transactions of the ASAE, 23 (1980), pp. 1277-1282.
26. M. A. Murad, L. S. Bennethum, and J. H. Cushman, A multi-scale theory of swelling porous media: I. Application to one-dimensional consolidation, Transp. Porous Media, 19 (1995), pp. 93-122.
27. M. A. Murad and J. H. Cushman, Multiscale flow and deformation in hydrophilic swelling porous media, Internat. J. Engrg. Sci., 34 (1996), pp. 313-338.
28. M. A. Murad and J. H. Cushman, Multiscale theory of swelling porous media: II. Dual porosity models for consolidation of clays incorporating physicochemical effects, Transp. Porous Media, 28 (1997), pp. 69-108.
29. G. Park, The diffusion of some halo-methanes in polystrene, Transactions of the Faraday Society, 46 (1950), pp. 684-690.
30. I. Patlashenko, D. Givoli, and P. Barbone, Time-stepping schemes for systems of Volterra integro-differential equations, Comput. Methods Appl. Mech. Engrg., 190 (2001), pp. 5691- 5718.
31. L. A. Segel and G. H. Handelman, Mathematics Applied to Continuum Mechanics, Macmillan, New York, 1977.
32. R. Showalter, Diffusion models with microstructure, Transp. Porous Media, 6 (1991), pp. 567-580.
33. P. Singh, Effect of Viscoelastic Relaxation on Fluid and Species Transport in Biopolymeric Materials, Ph.D. thesis, Purdue University, West Lafayette, IN, 2002.
34. P. Singh, J. Cushman, and D. Maier, Multiscale fluid transport theory for swelling biopolymers, Chemical Engineering Science, 58 (2003), pp. 2409-2419.
35. P. Singh, J. H. Cushman, and L. S. Bennethum, Thermomechanics of swelling biopolymeric systems, Transp. Porous Media, 53 (2003), pp. 1-24.
36. P. Singh, J. H. Cushman, and D. Maier, Three-scale thermomechanical theory for swelling biopolymeric systems, Chemical Engineering Science, 58 (2003), pp. 4017-4035.
37. N. L. Thomas and A. H. Windle, A deformation model for case-II diffusion, Polymer, 21 (1980), pp. 613-619.
38. N. L. Thomas and A. H. Windle, A theory of case-II diffusion, Polymer, 23 (1982), pp. 529-542.
39. V. B. Tolstoguzov, The importance of glassy biopolymer components in food, Nahrung-Food, 44 (2000), pp. 76-84.
40. B. Webster and C. Leopold, The ultrastructure of dry and imbibed cotyledons of soybean, American Journal of Botany, 64 (1977), pp. 1286-1293.
41. J. Wolfe, Lateral stresses in membranes at low water potential, Australian Journal of Plant Physiology, 14 (1987), pp. 311-318.