Influence of Young's modulus and geometrical shapes on the 2D simulation of pH-sensitive hydrogels by the meshless random differential quadrature method

Modelling and Simulation in Materials Science and Engineering

Volumn 19, Issue 6, 2011, Pages

  Mulay, Shantanu S ^a   Li, Hua ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

2D SIMULATIONS; ANALYTICAL EXPRESSIONS; DIFFERENTIAL QUADRATURE; DIFFERENTIAL QUADRATURE METHODS; FIELD VARIABLES; GEOMETRICAL SHAPES; HYDROGEL SWELLING; IONIC SPECIES; MECHANICAL EQUILIBRIUM; MESH-LESS METHODS; MESHLESS; MESHLESS TECHNIQUES; MULTIPLE DOMAINS; NUMERICAL VALUES; PH-RESPONSIVE HYDROGELS; PH-SENSITIVE HYDROGEL; POISSON-NERNST-PLANCK EQUATIONS; REPRODUCING KERNEL PARTICLE METHOD; SIMULATION RESULT; YOUNG'S MODULUS;

DIFFERENTIATION (CALCULUS); ELASTIC MODULI; ELASTICITY;

HYDROGELS;

EID: 80052082086     PISSN: 09650393     EISSN: 1361651X     Source Type: Journal    
DOI: 10.1088/0965-0393/19/6/065009     Document Type: Article

References (68)

1. Flory P J and Rehner J Jr 1943 Statistical mechanics of cross-linked polymer networks: II. Swelling J. Chem. Phys. 11 521-6
2. Flory P J and Rehner J Jr 1943 Statistical mechanics of cross-linked polymer networks: I. Rubberlike elasticity J. Chem. Phys. 11 512-20
3. Lai W M, Hou J S and Mow V C 1991 A triphasic theory for the swelling and deformation behaviors of articular cartilage J. Biomech. Eng. 113 245-58
4. Hon Y C, Lu M W, Xue W M and Zhou X 1999 New formulation and computation of the triphasic model for mechano-electrochemical mixtures Comput. Mech. 24 155-65 (Pubitemid 30505441)
5. De S K and Aluru N R 2004 A chemo-electro-mechanical mathematical model for simulation of pH sensitive hydrogels Mech. Mater. 36 395-410
6. Li H, Ng T Y, Yew Y K and Lam K Y 2005 Modeling and simulation of the swelling behavior of pH-stimulus-responsive hydrogels Biomacromolecules 6 109-20 (Pubitemid 40277006)
7. Li H et al 2005 A novel multiphysic model for simulation of swelling equilibrium of ionized thermal-stimulus responsive hydrogels Chem. Phys. 309 201-8
8. Hong W, Zhao X, Zhou J and Suo Z 2008 A theory of coupled diffusion and large deformation in polymeric gels J. Mech. Phys. Solids 56 1779-93
9. Zhang J, Zhao X, Suo Z and Jiang H 2009 A finite element method for transient analysis of concurrent large deformation and mass transport in gels J. Appl. Phys. 105 093522
10. Wallmersperger T and Ballhause D 2008 Coupled chemo-electro-mechanical finite element simulation of hydrogels: II. Electrical stimulation Smart Mater. Struct. 17 045012
11. Wallmersperger T, Ballhause D, Kraplin B, Nther M and Gerlach G 2009 Coupled multi-field formulation in space and time for the simulation of intelligent hydrogels J. Intell. Mater. Syst. Struct. 20 1483-92
12. Wallmersperger T, Ballhause D, Kröplin B, Günther M, Shi Z and Gerlach G 2008 Coupled chemo-electro-mechanical simulation of polyelectrolyte gels as actuators and sensors Proc. SPIE 6927 69270Y
13. Wallmersperger T, Kröplin B, Holdenried J and Gülch R W 2001 A coupled multi-field-formulation for ionic polymer gels in electric fields Proc. SPIE 4329 264-75 (Pubitemid 32934359)
14. Samson E, Marchand J, Robert J L and Bournazel J P 1999 Modelling ion diffusion mechanisms in porous media Int. J. Numer. Methods Eng. 46 2043-60 (Pubitemid 30516830)
15. Li H 2009 Kinetics of smart hydrogels responding to electric field: a transient deformation analysis Int. J. Solids Struct. 46 1326-33
16. Li H, Chen J and Lam K Y 2004 Multiphysical modeling and meshless simulation of electric-sensitive hydrogels J. Polym. Sci. B 42 1514-31
17. Li H and Luo R 2009 Modeling and characterization of glucose-sensitive hydrogel: effect of Young's modulus Biosensors Bioelectron. 24 3630-6
18. Li H, Luo R, Birgersson E and Lam K Y 2009 A chemo-electro-mechanical model for simulation of responsive deformation of glucose-sensitive hydrogels with the effect of enzyme catalysis J. Mech. Phys. Solids 57 369-82
19. Li H, Luo R and Lam K Y 2007 Modeling of ionic transport in electric-stimulus-responsive hydrogels J. Membr. Sci. 289 284-96 (Pubitemid 46223471)
20. Li H, Ng T Y, Yew Y K and Lam K Y 2007 Meshless modeling of pH-sensitive hydrogels subjected to coupled pH and electric field stimuli: Young modulus effects and case studies Macromol. Chem. Phys. 208 1137-46 (Pubitemid 47234199)
21. Li H and Yew Y K 2009 Simulation of soft smart hydrogels responsive to pH stimulus: ionic strength effect and case studies Mater. Sci. Eng. C 29 2261-9
22. Li H, Yew Y K, Lam K Y and Ng T Y 2004 Numerical simulation of pH-stimuli responsive hydrogel in buffer solutions Colloids Surf. A 249 149-54 (Pubitemid 39531608)
23. Li H, Yew Y K, Ng T Y and Lam K Y 2005 Meshless steady-state analysis of chemo-electro-mechanical coupling behavior of pH-sensitive hydrogel in buffered solution J. Electroanal. Chem. 580 161-72 (Pubitemid 40643725)
24. Li H et al 2004 Model development and numerical simulation of electric-stimulus-responsive hydrogels subject to an externally applied electric field Biosensors Bioelectron. 19 1097-107
25. Ballhause D and Wallmersperger T 2008 Coupled chemo-electro-mechanical finite element simulation of hydrogels: I. Chemical stimulation Smart Mater. Struct. 17 045011
26. Birgersson E, Li H and Wu S 2008 Transient analysis of temperature-sensitive neutral hydrogels J. Mech. Phys. Solids 56 444-66 (Pubitemid 351187940)
27. Brock D and Lee W 1994 Dynamic model of a linear actuator based on polymer hydrogel J. Intell. Mater. Syst. Struct. 5 764-71
28. Chatterjee A N, Yu Q, Moore J S and Aluru N R 2003 Mathematical modeling and simulation of dissolvable hydrogels J. Aerospace Eng. 16 55-64 (Pubitemid 40265227)
29. Chen J, Li H and Lam K Y 2005 Transient simulation for kinetic responsive behaviors of electric-sensitive hydrogels subject to applied electric field Mater. Sci. Eng. C 25 710-2 (Pubitemid 41627455)
30. Luo R and Li H 2009 Simulation analysis of effect of ionic strength on physiochemical and mechanical characteristics of glucose-sensitive hydrogels J. Electroanal. Chem. 635 83-92
31. Luo R, Li H, Birgersson E and Khin Y L 2008 Modeling of electric-stimulus-responsive hydrogels immersed in different bathing solutions J. Biomed. Mater. Res. A 85 248-57 (Pubitemid 351355375)
32. Luo R, Li H and Lam K Y 2007 Modeling and simulation of chemo-electro-mechanical behavior of pH-electric-sensitive hydrogel Anal. Bioanal. Chem. 389 863-73 (Pubitemid 47462456)
33. Mann B A, Kremer K and Holm C 2006 The swelling behavior of charged hydrogels Macromol. Symp. 237 90-107 (Pubitemid 43841431)
34. Ostroha J, Pong M, Lowman A and Dan N 2004 Controlling the collapse/swelling transition in charged hydrogels Biomaterials 25 4345-53 (Pubitemid 38388596)
35. nita D, Paes M, Lindner J, Kosek J and Marek M 2001 Nonlinear behaviour of simple ionic systems in hydrogel in an electric field Faraday Discuss. 120 53-66
36. Suthar K J, Ghantasala M K and Mancini D C 2008 Simulation of hydrogel micro-actuation Canberra, ACT
37. Traitel T, Kost J and Lapidot S A 2003 Modeling ionic hydrogels swelling: characterization of the non-steady state Biotechnol. Bioeng. 84 20-8 (Pubitemid 37080574)
38. Wang Q X, Li H and Lam K Y 2006 Meshless simulation of equilibrium swelling/deswelling of PH-sensitive hydrogels J. Polym. Sci. B 44 326-37 (Pubitemid 43143826)
39. Wu S, Li H, Chen J P and Lam K Y 2004 Modeling investigation of hydrogel volume transition Macromol. Theory Simul. 13 13-29
40. Wu Y, Joseph S and Aluru N R 2009 Effect of cross-linking on the diffusion of water, ions, and small molecules in hydrogels J. Phys. Chem. B 113 3512-20
41. Yew Y K, Ng T Y, Li H and Lam K Y 2007 Analysis of pH and electrically controlled swelling of hydrogel-based micro-sensors/actuators Biomed. Microdevices 9 487-99
42. Yu Y G, Xu Y, Ning H and Zhang S S 2008 Swelling behaviors of thermoresponsive hydrogels cross-linked with acryloyloxyethylaminopolysuccinimide Colloid Polym. Sci. 286 1165-71
43. Yu Y Q, Li Z Z, Tian H J, Zhang S S and Ouyang P K 2007 Synthesis and characterization of thermoresponsive hydrogels cross-linked with acryloyloxyethylaminopolysuccinimide Colloid Polym. Sci. 285 1553-60
44. Yuan Z, Yin L and Jiang H 2007 Numerical simulation of transient nonlinear behaviors of electric-sensitive hydrogel membrane under an external electric field Proc. SPIE 6465 64650W
45. Zhao X and Suo Z 2009 Electromechanical instability in semicrystalline polymers Appl. Phys. Lett. 95 031904
46. Zhou J, Hong W, Zhao X, Zhang Z and Suo Z 2008 Propagation of instability in dielectric elastomers Int. J. Solids Struct. 45 3739-50 (Pubitemid 351601774)
47. Zhou X, Hon Y C, Sun S and Mak A F T 2002 Numerical simulation of the steady-state deformation of a smart hydrogel under an external electric field Smart Mater. Struct. 11 459-67 (Pubitemid 34758955)
48. Lucy L B 1977 A numerical approach to testing the fission hypothesis Astron. J. 82 1013-24
49. Gingold R A and Monaghan J J 1977 Smoothed particle hydrodynamics - theory and application to non-spherical stars Mon. Not. R. Astron. Soc. 181 375-89
50. Liu W K, Chen Y, Uras R A and Chang C T 1996 Generalized multiple scale reproducing kernel particle methods Comput. Methods Appl. Mech. Eng. 139 91-157 (Pubitemid 126382695)
51. Liu W K and Jun S 1998 Multiple-scale reproducing kernel particle methods for large deformation problems Int. J. Numer. Methods Eng. 41 1339-62 (Pubitemid 128570852)
52. Liu W K, Jun S and Zhang Y F 1995 Reproducing kernel particle methods Int. J. Numer. Methods Fluids 20 1081-106
53. Aluru N R 1999 Reproducing kernel particle method for meshless analysis of microelectromechanical systems Comput. Mech. 23 324-38
54. Aluru N R and Li G 2001 Finite cloud method: a true meshless technique based on fixed reproducing kernel approximation Int. J. Numer. Methods Eng. 50 2373-410 (Pubitemid 32214752)
55. Jin X, Li G and Aluru N R 2004 Positivity conditions in meshless collocation methods Comput. Methods Appl. Mech. Eng. 193 1171-202 (Pubitemid 38439210)
56. Jin X, Li G and Aluru N R 2005 New approximations and collocation schemes in the finite cloud method Comput. Struct. 83 1366-85 (Pubitemid 40574501)
57. Li G, Paulino G H and Aluru N R 2003 Coupling of the mesh-free finite cloud method with the boundary element method: a collocation approach Comput. Methods Appl. Mech. Eng. 192 2355-75 (Pubitemid 36715384)
58. Bellman R, Kashef B G and Casti J 1972 Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations J. Comput. Phys. 10 40-52
59. Quan J R and Chang C T 1989 New insights in solving distributed system equations by the quadrature method: II. Numerical experiments Comput. Chem. Eng. 13 1017-24 (Pubitemid 20632558)
60. Quan J R and Chang C T 1989 New insights in solving distributed system equations by the quadrature method: I. Analysis Comput. Chem. Eng. 13 779-88 (Pubitemid 20620969)
61. Shu C, Khoo B C and Yeo K S 1994 Numerical solutions of incompressible Navier-Stokes equations by generalized differential quadrature Finite Elements Anal. Des. 18 83-97 (Pubitemid 288868)
62. Mulay S S, Li H and See S 2009 On the random differential quadrature (RDQ) method: consistency analysis and application in elasticity problems Comput. Mech. 44 563-90
63. Li H, Mulay S S and See S 2009 On the convergence of random differential quadrature (RDQ) method and its application in solving nonlinear differential equations in mechanics Comput. Modeling Eng. Sci. 48 43-82
64. Li H, Mulay S S and See S 2009 On the location of zeroes of polynomials from the stability analysis of novel strong-form meshless random differential quadrature method Comput. Modeling Eng. Sci. 54 147-99
65. Mulay S S, Li H and See S 2010 On the development of adaptive random differential quadrature method with an error recovery technique and its application in the locally high gradient problems Comput. Mech. 46 1-27
66. Timoshenko S P and Goodier J N 1970 Theory of Elasticity (New York: McGraw-Hill)
67. Hong W, Zhao X and Suo Z 2010 Large deformation and electrochemistry of polyelectrolyte gels J. Mech. Phys. Solids 58 558-77
68. Shu C 2000 Differential Quadrature and its Application in Engineering (London: Springer)