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SCIENCE CHINA Technological Sciences, Volume 62 , Issue 8 : 1375-1384(2019) https://doi.org/10.1007/s11431-018-9472-2

The inhomogeneous diffusion of chemically crosslinked polyacrylamide hydrogel based on poroviscosity theory

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  • ReceivedDec 28, 2018
  • AcceptedFeb 25, 2019
  • PublishedJul 11, 2019

Abstract

The diffusion of hydrogels is a phenomenon not only profound in novel applications of mechanical engineering but also very common in nature. Comprehensive studies of the swelling properties under stable states have been carried out in the past several years; however, ambiguities in the understanding of the kinetic behaviour of the diffusion phenomenon of hydrogels still remain. The potential applications of hydrogels are confined due to the lack of perceptiveness of the kinetic behaviour of diffusion in hydrogels. Based on our previous work, in this study, we initiate the theoretical kinetic study of the inhomogeneous diffusion of hydrogels. With poroviscosity introduced, we develop a theory for the inhomogeneous diffusion of hydrogels. After implementing this theory into the finite element solution, we could predict the water content in the hydrogel as a function of time and location. The quantitative prediction of the inhomogeneous diffusion and the formulas are given in the numerical study. Furthermore, the corresponding experiments are carried out to substantiate this theory. It can be observed that the theoretical prediction meets fairly well with our experimental data. Finally, we carry out a systematic parameter study to discuss the effect of three important parameters on the diffusion property. The increase of the interaction parameter is seen to constrain the diffusion while increase of the chemical potential is seen to facilitate the process. The change of the diffusion coefficient D, on the other hand, does not affect the process much. By comparing the conclusions above with the experimental data, we can narrow down the range of the values of χ and D.


Funded by

the National Natural Science Foundation of China(Grant,Nos.,11820101001,11572236)


Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11820101001, 11572236).


References

[1] Zheng S J, Liu Z S. Phase transition of temperature-sensitive hydrogel under mechanical constraint. J Appl Mech, 2018, 85: 021002 CrossRef ADS Google Scholar

[2] Qiu Y, Park K. Environment-sensitive hydrogels for drug delivery. Adv Drug Deliver Rev, 2001, 53: 321-339 CrossRef Google Scholar

[3] Drury J L, Mooney D J. Hydrogels for tissue engineering: Scaffold design variables and applications. Biomaterials, 2003, 24: 4337-4351 CrossRef Google Scholar

[4] Nguyen K T, West J L. Photopolymerizable hydrogels for tissue engineering applications. Biomaterials, 2002, 23: 4307-4314 CrossRef Google Scholar

[5] Harmon M E, Tang M, Frank C W. A microfluidic actuator based on thermoresponsive hydrogels. Polymer, 2003, 44: 4547-4556 CrossRef Google Scholar

[6] Augst A D, Kong H J, Mooney D J. Alginate hydrogels as biomaterials. Macromol Biosci, 2006, 6: 623-633 CrossRef PubMed Google Scholar

[7] Suo Z. Mechanics of stretchable electronics and soft machines. MRS Bull, 2012, 37: 218-225 CrossRef Google Scholar

[8] Zhang N, Zheng S, Pan Z, et al. Phase transition effects on mechanical properties of NIPA hydrogel. Polymers, 2018, 10: 358. Google Scholar

[9] Li Y, Liu Z. A novel constitutive model of shape memory polymers combining phase transition and viscoelasticity. Polymer, 2018, 143: 298-308 CrossRef Google Scholar

[10] Kosemund K, Schlatter H, Ochsenhirt J L, et al. Safety evaluation of superabsorbent baby diapers. Regulatory Toxicol Pharmacol, 2009, 53: 81-89 CrossRef PubMed Google Scholar

[11] Liu Z, Toh W, Ng T Y. Advances in mechanics of soft materials: A review of large deformation behavior of hydrogels. Int J Appl Mech, 2015, 7: 1530001 CrossRef ADS Google Scholar

[12] Zhang Y R, Tang L Q, Xie B X, et al. A Variable mass meso-model for the mechanical and water-expelled behaviors of PVA hydrogel in compression. Int J Appl Mech, 2017, 9: 1750044 CrossRef ADS Google Scholar

[13] Curatolo M, Nardinocchi P, Puntel E, et al. Transient instabilities in the swelling dynamics of a hydrogel sphere. J Appl Phys, 2017, 122: 145109 CrossRef ADS Google Scholar

[14] Kargar-Estahbanaty A, Baghani M, Shahsavari H, et al. A combined analytical-numerical investigation on photosensitive hydrogel micro-valves. Int J Appl Mech, 2017, 9: 1750103 CrossRef ADS Google Scholar

[15] Hong W, Zhao X, Zhou J, et al. A theory of coupled diffusion and large deformation in polymeric gels. J Mech Phys Solids, 2008, 56: 1779-1793 CrossRef ADS Google Scholar

[16] Hong W, Liu Z, Suo Z. Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load. Int J Solids Struct, 2009, 46: 3282-3289 CrossRef Google Scholar

[17] Yi C, Zhang X, Yan H, et al. Finite element simulation and the application of amphoteric pH-sensitive hydrogel. Int J Appl Mech, 2017, 9: 1750063 CrossRef ADS Google Scholar

[18] Toh W, Liu Z, Ng T Y, et al. Inhomogeneous large deformation kinetics of polymeric gels. Int J Appl Mech, 2013, 5: 1350001 CrossRef ADS Google Scholar

[19] Zheng S, Li Z, Liu Z. The fast homogeneous diffusion of hydrogel under different stimuli. Int J Mech Sci, 2018, 137: 263-270 CrossRef Google Scholar

[20] Bertrand T, Peixinho J, Mukhopadhyay S, et al. Dynamics of swelling and drying in a spherical gel. Phys Rev Appl, 2016, 6: 064010 CrossRef ADS arXiv Google Scholar

[21] Loussert C, Bouchaudy A, Salmon J B. Drying dynamics of a charged colloidal dispersion in a confined drop. Phys Rev Fluids, 2016, 1: 084201 CrossRef ADS arXiv Google Scholar

[22] Chester S A, Di Leo C V, Anand L. A finite element implementation of a coupled diffusion-deformation theory for elastomeric gels. Int J Solids Struct, 2015, 52: 1-18 CrossRef Google Scholar

[23] Brassart L, Liu Q, Suo Z. Mixing by shear, dilation, swap, and diffusion. J Mech Phys Solids, 2018, 112: 253-272 CrossRef ADS Google Scholar

[24] Wang Q M, Mohan A C, Oyen M L, et al. Separating viscoelasticity and poroelasticity of gels with different length and time scales. Acta Mech Sin, 2014, 30: 20-27 CrossRef ADS Google Scholar

[25] Flory P J. Thermodynamics of high polymer solutions. J Chem Phys, 1942, 10: 51-61 CrossRef ADS Google Scholar

[26] Bearman R J. Introduction to thermodynamics of irreversible processes. J Electroch Soc, 1955, 1: 4995–4996. Google Scholar

[27] Li Z, Liu Z. An algorithm for obtaining real stress field of hyperelastic materials based on digital image correlation system. Int J Comp Mat Sci Eng, 2017, 6: 1850003 CrossRef ADS Google Scholar

  • Figure 1

    (Color online) (a) Schematics of the profile of a spherical hydrogel in the solvent, undergoing the free swelling process from the dry state to the equilibrium state; (b)–(d) the water content, chemical potential and mean stress as a function of location with different time, which is normalized by the characteristic diffusion time τD=L2/D.

  • Figure 2

    (Color online) Schematics of the profile of a spherical hydrogel in the solvent (cross section), undergoing the free swelling process from the dry state to the equilibrium state. (a) Group-1 swells for 4 h; (b) Group-2 is immersed in water for 40 h; (c) hydrogel in Group-3 stays in water bath for 400 h.

  • Figure 3

    (Color online) The process of getting the experimental data based on the picture taken of the hydrogel slice.

  • Figure 4

    (Color online) (a) The experimental results of the diffusion of a spherical hydrogel; (b) the corresponding numerical simulation with a fitting parameter τD=20 h.

  • Figure 5

    (Color online) (a) The water content distribution with a varying χ when t/τD=0.1; (b) the water content distribution with a varying χ when t/τD=1.

  • Figure 6

    (Color online) (a) The water content distribution with a varying χ at three different locations when t/τD=0.1; (b) the water content distribution with a varying χ at three different locations when t/τD=1.

  • Figure 7

    (Color online) (a) The water content distribution with a varying D/D0 when t/τD=0.1; (b) the water content distribution with a varying D/D0 when t/τD=1.

  • Figure 8

    (Color online) (a) The water content distribution with a varying μ/kT when t/τD=0.1; (b) the water content distribution with a varying μ/kT when t/τD=1.

  • Figure 9

    (Color online) (a) The water content distribution with a varying μ/kT at three different locations when t/τD=0.1; (b) the water content distribution with a varying μ/kT at three different locations when t/τD=1.

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