Kinetics of swelling of cylindrical functionally graded temperature-responsive hydrogels
Document Type : Research Paper
Author
Department of mechanical engineering, Sharif university of technology, Tehran, Iran.
Abstract
Cylindrical hydrogels have a wide variety of applications in microfluidics; for example, they serve as micro-valves, micro-mixers, and micro-lenses. The main advantages of them can be mentioned as their autonomous functionality due to their responses to environmental stimuli and simple geometry. Furthermore, functionally graded hydrogels have recently found applications in hydrogel actuators. Therefore, in this work, the kinetics of swelling, shrinking, and force generation of cylindrical functionally graded temperature-responsive hydrogels are investigated. Kinetics of cylindrical structure is investigated analytically by developing a mathematical model based on available constitutive models of large deformation of hydrogels. The cross-link density of the hydrogel polymeric network varies along the radius of the cylinder linearly. In order to analyze the structure's behavior, the temperature is changed, and the response time of the structures with different distribution of cross-link density is investigated. In addition, to investigate the realistic actuators' performance, the cylindrical hydrogel is located inside a hollow cylinder, and the pressure of the hydrogel, which puts on the cylinder, is investigated. The results show that manipulation of cross-link density influences the response time of the cylindrical hydrogel; hence, it is a useful tool to manage the overall performance of cylindrical actuators.
Keywords
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[4] S. Zheng, Z. Liu, Constitutive model of salt concentration-sensitive hydrogel, Mechanics of Materials, Vol. 136, 2019.
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[8] C. Yang, W. Wang, C. Yao, R. Xie, X. J. Ju, Z. Liu, L. Y. Chu, Hydrogel Walkers with Electro-Driven Motility for Cargo Transport, Sci Rep, Vol. 5, pp. 13622, Aug 28, 2015.
[9] L. Ionov, Hydrogel-based actuators: possibilities and limitations, Materials Today, Vol. 17, No. 10, pp. 494-503, 2014.
[10] L. Dong, H. Jiang, Autonomous microfluidics with stimuli-responsive hydrogels, Soft Matter, Vol. 3, No. 10, 2007.
[11] L. D'Eramo, B. Chollet, M. Leman, E. Martwong, M. Li, H. Geisler, J. Dupire, M. Kerdraon, C. Vergne, F. Monti, Y. Tran, P. Tabeling, Microfluidic actuators based on temperature-responsive hydrogels, Microsystems & Nanoengineering, Vol. 4, 2018.
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[13] D. Kim, D. J. Beebe, A bi-polymer micro one-way valve, Sensors and Actuators A: Physical, Vol. 136, No. 1, pp. 426-433, 2007.
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[19] E. Yarali, R. Noroozi, A. Yousefi, M. Bodaghi, M. Baghani, Multi-Trigger Thermo-Electro-Mechanical Soft Actuators under Large Deformations, Polymers, Vol. 12, No. 2, pp. 489, 2020.
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[29] M. Shojaeifard, S. Tahmasiyan, M. Baghani, Swelling response of functionally graded temperature-sensitive hydrogel valves: Analytic solution and finite element method, Journal of Intelligent Material Systems and Structures, Vol. 31, No. 3, pp. 457-474, 2019.
[30] S. Cai, Y. Lou, P. Ganguly, A. Robisson, Z. Suo, Force generated by a swelling elastomer subject to constraint, Journal of Applied Physics, Vol. 107, No. 10, 2010.
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[33] D. Wang, M. S. Wu, Stress and displacement fields in soft cylindrical multilayers, International Journal of Solids and Structures, Vol. 50, No. 3-4, pp. 511-518, 2013.
[34] M. R. Bayat, A. Kargar-Estahbanaty, M. Baghani, A semi-analytical solution for finite bending of a functionally graded hydrogel strip, Acta Mechanica, Vol. 230, No. 7, pp. 2625-2637, 2019.
[35] H. Mazaheri, A. Ghasemkhani, S. Sabbaghi, Study of Fluid-Structure Interaction in a Functionally Graded Ph-Sensitive Hydrogel Micro-Valve, International Journal of Applied Mechanics, 2020.
[36] E. Sato Matsuo, T. Tanaka, Kinetics of discontinuous volume–phase transition of gels, The Journal of Chemical Physics, Vol. 89, No. 3, pp. 1695-1703, 1988.
[37] Z. Ding, W. Toh, J. Hu, Z. Liu, T. Y. Ng, A simplified coupled thermo-mechanical model for the transient analysis of temperature-sensitive hydrogels, Mechanics of Materials, Vol. 97, pp. 212-227, 2016.
[38] P. J. Flory, J. Rehner, Statistical Mechanics of Cross‐Linked Polymer Networks II. Swelling, The Journal of Chemical Physics, Vol. 11, No. 11, pp. 521-526, 1943.
[39] P. J. Flory, Thermodynamics of high polymer solutions, The Journal of chemical physics, Vol. 10, No. 1, pp. 51-61, 1942.
[40] M. L. Huggins, Solutions of long chain compounds, The Journal of chemical physics, Vol. 9, No. 5, pp. 440-440, 1941.
[41] F. Afroze, E. Nies, H. Berghmans, Phase transitions in the system poly (N-isopropylacrylamide)/water and swelling behaviour of the corresponding networks, Journal of Molecular Structure, Vol. 554, No. 1, pp. 55-68, 2000.
[42] T. Bertrand, J. Peixinho, S. Mukhopadhyay, C. W. MacMinn, Dynamics of swelling and drying in a spherical gel, Physical Review Applied, Vol. 6, No. 6, pp. 064010, 2016.
[43] M. Tokita, T. Tanaka, Friction coefficient of polymer networks of gels, The Journal of chemical physics, Vol. 95, No. 6, pp. 4613-4619, 1991.
[44] A. D. Drozdov, A. Papadimitriou, J. Liely, C.-G. Sanporean, Constitutive equations for the kinetics of swelling of hydrogels, Mechanics of Materials, Vol. 102, pp. 61-73, 2016.
[45] J. Yoon, S. Cai, Z. Suo, R. C. Hayward, Poroelastic swelling kinetics of thin hydrogel layers: comparison of theory and experiment, Soft Matter, Vol. 6, No. 23, 2010.
[46] W. Hong, Z. Liu, Z. Suo, Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load, International Journal of Solids and Structures, Vol. 46, No. 17, pp. 3282-3289, 2009.
[2] R. Marcombe, S. Cai, W. Hong, X. Zhao, Y. Lapusta, Z. Suo, A theory of constrained swelling of a pH-sensitive hydrogel, Soft Matter, Vol. 6, No. 4, 2010.
[3] S. K. De, N. R. Aluru, A chemo-electro-mechanical mathematical model for simulation of pH sensitive hydrogels, Mechanics of Materials, Vol. 36, No. 5-6, pp. 395-410, 2004.
[4] S. Zheng, Z. Liu, Constitutive model of salt concentration-sensitive hydrogel, Mechanics of Materials, Vol. 136, 2019.
[5] A. Suzuki, Phase transition in gels of sub-millimeter size induced by interaction with stimuli, in: Responsive gels: volume transitions II, Eds., pp. 199-240: Springer, 1993.
[6] N. A. Peppas, J. Z. Hilt, A. Khademhosseini, R. Langer, Hydrogels in Biology and Medicine: From Molecular Principles to Bionanotechnology, Advanced Materials, Vol. 18, No. 11, pp. 1345-1360, 2006.
[7] L. Dong, A. K. Agarwal, D. J. Beebe, H. Jiang, Adaptive liquid microlenses activated by stimuli-responsive hydrogels, Nature, Vol. 442, No. 7102, pp. 551-4, Aug 3, 2006.
[8] C. Yang, W. Wang, C. Yao, R. Xie, X. J. Ju, Z. Liu, L. Y. Chu, Hydrogel Walkers with Electro-Driven Motility for Cargo Transport, Sci Rep, Vol. 5, pp. 13622, Aug 28, 2015.
[9] L. Ionov, Hydrogel-based actuators: possibilities and limitations, Materials Today, Vol. 17, No. 10, pp. 494-503, 2014.
[10] L. Dong, H. Jiang, Autonomous microfluidics with stimuli-responsive hydrogels, Soft Matter, Vol. 3, No. 10, 2007.
[11] L. D'Eramo, B. Chollet, M. Leman, E. Martwong, M. Li, H. Geisler, J. Dupire, M. Kerdraon, C. Vergne, F. Monti, Y. Tran, P. Tabeling, Microfluidic actuators based on temperature-responsive hydrogels, Microsystems & Nanoengineering, Vol. 4, 2018.
[12] D. J. Beebe, J. S. Moore, J. M. Bauer, Q. Yu, R. H. Liu, C. Devadoss, B.-H. Jo, Functional hydrogel structures for autonomous flow control inside microfluidic channels, Nature, Vol. 404, No. 6778, pp. 588, 2000.
[13] D. Kim, D. J. Beebe, A bi-polymer micro one-way valve, Sensors and Actuators A: Physical, Vol. 136, No. 1, pp. 426-433, 2007.
[14] H. Mazaheri, M. Baghani, R. Naghdabadi, S. Sohrabpour, Inhomogeneous swelling behavior of temperature sensitive PNIPAM hydrogels in micro-valves: analytical and numerical study, Smart Materials and Structures, Vol. 24, No. 4, 2015.
[15] A. Agarwal, S. Sridharamurthy, T. Pearce, G. Mensing, D. Beebe, H. Jiang, Magnetically-driven actuation using liquid-phase polymerization (LPP) and its application: a programmable mixer, in Proceeding of, 121-4.
[16] R. Noroozi, M. Bodaghi, H. Jafari, A. Zolfagharian, M. Fotouhi, Shape-adaptive metastructures with variable bandgap regions by 4D printing, Polymers, Vol. 12, No. 3, pp. 519, 2020.
[17] L. D'Eramo, B. Chollet, M. Leman, E. Martwong, M. Li, H. Geisler, J. Dupire, M. Kerdraon, C. Vergne, F. Monti, Y. Tran, P. Tabeling, Microfluidic actuators based on temperature-responsive hydrogels, Microsystems & Nanoengineering, Vol. 4, No. 1, pp. 1-7, 2018.
[18] H. Mazaheri, A. H. Namdar, A. Amiri, Behavior of a smart one-way micro-valve considering fluid–structure interaction, Journal of Intelligent Material Systems and Structures, Vol. 29, No. 20, pp. 3960-3971, 2018.
[19] E. Yarali, R. Noroozi, A. Yousefi, M. Bodaghi, M. Baghani, Multi-Trigger Thermo-Electro-Mechanical Soft Actuators under Large Deformations, Polymers, Vol. 12, No. 2, pp. 489, 2020.
[20] E. Yarali, R. Noroozi, A. Moallemi, A. Taheri, M. Baghani, Developing an analytical solution for a thermally tunable soft actuator under finite bending, Mechanics Based Design of Structures and Machines, pp. 1-15, 2020.
[21] S. A. Chester, L. Anand, A coupled theory of fluid permeation and large deformations for elastomeric materials, Journal of the Mechanics and Physics of Solids, Vol. 58, No. 11, pp. 1879-1906, 2010.
[22] W. Hong, X. Zhao, J. Zhou, Z. Suo, A theory of coupled diffusion and large deformation in polymeric gels, Journal of the Mechanics and Physics of Solids, Vol. 56, No. 5, pp. 1779-1793, 2008.
[23] F. P. Duda, A. C. Souza, E. Fried, A theory for species migration in a finitely strained solid with application to polymer network swelling, Journal of the Mechanics and Physics of Solids, Vol. 58, No. 4, pp. 515-529, 2010.
[24] H. Mazaheri, M. Baghani, R. Naghdabadi, Inhomogeneous and homogeneous swelling behavior of temperature-sensitive poly-(N-isopropylacrylamide) hydrogels, Journal of Intelligent Material Systems and Structures, Vol. 27, No. 3, pp. 324-336, 2015.
[25] S. A. Chester, L. Anand, A thermo-mechanically coupled theory for fluid permeation in elastomeric materials: Application to thermally responsive gels, Journal of the Mechanics and Physics of Solids, Vol. 59, No. 10, pp. 1978-2006, 2011.
[26] N. Arbabi, M. Baghani, J. Abdolahi, H. Mazaheri, M. Mosavi-Mashhadi, Study on pH-sensitive hydrogel micro-valves: A fluid–structure interaction approach, Journal of Intelligent Material Systems and Structures, Vol. 28, No. 12, pp. 1589-1602, 2017.
[27] A. Kargar-Estahbanaty, M. Baghani, H. Shahsavari, G. Faraji, A combined analytical–numerical investigation on photosensitive hydrogel micro-valves, International Journal of Applied Mechanics, Vol. 9, No. 07, pp. 1750103, 2017.
[28] H. Mazaheri, A. Ghasemkhani, Analytical and numerical study of the swelling behavior in functionally graded temperature-sensitive hydrogel shell, Journal of Stress Analysis, Vol. 3, No. 2, pp. 29-35, 2019.
[29] M. Shojaeifard, S. Tahmasiyan, M. Baghani, Swelling response of functionally graded temperature-sensitive hydrogel valves: Analytic solution and finite element method, Journal of Intelligent Material Systems and Structures, Vol. 31, No. 3, pp. 457-474, 2019.
[30] S. Cai, Y. Lou, P. Ganguly, A. Robisson, Z. Suo, Force generated by a swelling elastomer subject to constraint, Journal of Applied Physics, Vol. 107, No. 10, 2010.
[31] Y. Liu, H. Zhang, J. Zhang, Y. Zheng, Transient swelling of polymeric hydrogels: A new finite element solution framework, International Journal of Solids and Structures, Vol. 80, pp. 246-260, 2016.
[32] M. Guvendiren, S. Yang, J. A. Burdick, Swelling‐induced surface patterns in hydrogels with gradient crosslinking density, Advanced Functional Materials, Vol. 19, No. 19, pp. 3038-3045, 2009.
[33] D. Wang, M. S. Wu, Stress and displacement fields in soft cylindrical multilayers, International Journal of Solids and Structures, Vol. 50, No. 3-4, pp. 511-518, 2013.
[34] M. R. Bayat, A. Kargar-Estahbanaty, M. Baghani, A semi-analytical solution for finite bending of a functionally graded hydrogel strip, Acta Mechanica, Vol. 230, No. 7, pp. 2625-2637, 2019.
[35] H. Mazaheri, A. Ghasemkhani, S. Sabbaghi, Study of Fluid-Structure Interaction in a Functionally Graded Ph-Sensitive Hydrogel Micro-Valve, International Journal of Applied Mechanics, 2020.
[36] E. Sato Matsuo, T. Tanaka, Kinetics of discontinuous volume–phase transition of gels, The Journal of Chemical Physics, Vol. 89, No. 3, pp. 1695-1703, 1988.
[37] Z. Ding, W. Toh, J. Hu, Z. Liu, T. Y. Ng, A simplified coupled thermo-mechanical model for the transient analysis of temperature-sensitive hydrogels, Mechanics of Materials, Vol. 97, pp. 212-227, 2016.
[38] P. J. Flory, J. Rehner, Statistical Mechanics of Cross‐Linked Polymer Networks II. Swelling, The Journal of Chemical Physics, Vol. 11, No. 11, pp. 521-526, 1943.
[39] P. J. Flory, Thermodynamics of high polymer solutions, The Journal of chemical physics, Vol. 10, No. 1, pp. 51-61, 1942.
[40] M. L. Huggins, Solutions of long chain compounds, The Journal of chemical physics, Vol. 9, No. 5, pp. 440-440, 1941.
[41] F. Afroze, E. Nies, H. Berghmans, Phase transitions in the system poly (N-isopropylacrylamide)/water and swelling behaviour of the corresponding networks, Journal of Molecular Structure, Vol. 554, No. 1, pp. 55-68, 2000.
[42] T. Bertrand, J. Peixinho, S. Mukhopadhyay, C. W. MacMinn, Dynamics of swelling and drying in a spherical gel, Physical Review Applied, Vol. 6, No. 6, pp. 064010, 2016.
[43] M. Tokita, T. Tanaka, Friction coefficient of polymer networks of gels, The Journal of chemical physics, Vol. 95, No. 6, pp. 4613-4619, 1991.
[44] A. D. Drozdov, A. Papadimitriou, J. Liely, C.-G. Sanporean, Constitutive equations for the kinetics of swelling of hydrogels, Mechanics of Materials, Vol. 102, pp. 61-73, 2016.
[45] J. Yoon, S. Cai, Z. Suo, R. C. Hayward, Poroelastic swelling kinetics of thin hydrogel layers: comparison of theory and experiment, Soft Matter, Vol. 6, No. 23, 2010.
[46] W. Hong, Z. Liu, Z. Suo, Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load, International Journal of Solids and Structures, Vol. 46, No. 17, pp. 3282-3289, 2009.
)
Volume 51, Issue 2
December 2020Pages 464-471
- Receive Date: 07 July 2020
- Revise Date: 10 August 2020
- Accept Date: 16 August 2020