Behavior of Photo-thermal Sensitive Polyelectrolyte Hydrogel Micro-valve: Analytical and Numerical Approaches

Document Type : Original Research Paper


1 Mechanical Engineering Department, Bu-Ali Sina University, Hamedan, Iran.

2 Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran.


In this paper, the swelling of the photo-thermal sensitive cylindrical polyelectrolyte hydrogel micro-valve has been studied. For this purpose, a modified constitutive model that considers the polyelectrolyte nature of the photothermal sensitive hydrogels is used. The analytical solution for swelling of the hydrogel cylinder due to temperature and light intensity changes was presented. Then, in order to confront problems with realistic complicated boundary conditions, the finite element (FE) tool was implemented in ABAQUS software by scripting a UHYPER subroutine. Using the FE tool, the swelling of the hydrogel cylinder and contact of the micro-valve with the wall of the channel was investigated. Then, the temperature and the light intensity at which the channel was closed was obtained. Finally, opening valve parameter was studied for analyzing the geometrical influence of the under-study actuator, and the obtained results were discussed.


[1] E. Birgersson, H. Li, S. Wu, Transient analysis of temperature-sensitive neutral hydrogels, J. Mech. Phys. Solids, 56(2) (2008) 444-466.
[2] A.D. Drozdov, Swelling of pH-responsive cationic gels: Constitutive modeling and structure-property relations, Int. J. Solids Struct., 64-65 (2015) 176-190.
[3] H. Mazaheri, A. Ghasemkhani, S. Sabbaghi, Study of fluid-structure interaction in a functionally graded pH-sensitive hydrogel micro-valve, Int. J. Appl. Mech., 12(5) (2020) 2050057.
[4] W. Toh, T.Y. Ng, J. Hu, Z. Liu, Mechanics of inhomogeneous large deformation of photo-thermal sensitive hydrogels. Int. J. Solids Struct., 51(25-26) (2014) 4440-4451.
[5] S. Sugiura, K. Sumaru, K. Ohi, K. Hiroki, T. Takagi, T. Kanamori, Photoresponsive polymer gel microvalves controlled by local light irradiation, Sens. Actuators, A: Physical, 140(2) (2007) 176-184.
[6] W. Hong, X. Zhao, J. Zhou, Z. Suo, A theory of coupled diffusion and large deformation in polymeric gels, J. Mech. Phys. Solids, 56(5) (2008) 1779-1793.
[7] W. Hong, X. Zhao, Z. Suo, Large deformation and electrochemistry of polyelectrolyte gels, J. Mech. Phys. Solids, 58(4) (2010) 558-577.
[8] S. Zheng, Z. Liu, Constitutive model of salt concentration-sensitive hydrogel, Mech. Mater., 136 (2019) 103092.
[9] D. Kim, D.J. Beebe, Hydrogel-based reconfigurable components for microfluidic devices, Lab Chip, 7(2) (2007) 193-198.
[10] D.T. Eddington, D.J. Beebe, Flow control with hydrogels, Adv. Drug Deliv. Rev., 56(2) (2004) 199-210.
[11] L.E. Freed, G.C. Engelmayr Jr., J.T. Borenstein, F.T. Moutos, F. Guilak, Advanced material strategies for tissue engineering scaffolds, Adv. Mater., 21(32-33) (2009) 3410-3418.
[12] F.P. Duda, A.C. Souza, E. Fried, A theory for species migration in a finitely strained solid with application to polymer network swelling, J. Mech. Phys. Solids, 58(4) (2010) 515-529.
[13] S.A. Chester, L. Anand, A coupled theory of fluid permeation and large deformations for elastomeric materials, J. Mech. Phys. Solids, 58(11) (2010) 1879-1906.
[14] S. Cai, Z. Suo, Mechanics and chemical thermodynamics of phase transition in temperature-sensitive hydrogels, J. Mech. Phys. Solids, 59(11) (2011) 2259-2278.
[15] S.A. Chester, L. Anand, A thermo-mechanically coupled theory for fluid permeation in elastomeric materials: Application to thermally responsive gels, J. Mech. Phys. Solids, 59(10) (2011)1978-2006.
[16] Z. Ding, Z. Liu, J. Hu, S. Swaddiwudhipong, Z. Yang, Inhomogeneous large deformation study of temperature-sensitive hydrogel, Int. J. Solids Struct., 50(16-17) (2013) 2610-2619.
[17] H. Mazaheri, M. Baghani, R. Naghdabadi, Inhomogeneous and homogeneous swelling behavior of temperature-sensitive poly-(Nisopropylacrylamide) hydrogels, J. Intell. Mater. Syst. Struct., B, 27(3) (2016) 324-336.
[18] H. Mazaheri, Study of swelling behavior of temperature sensitive hydrogels considering inextensibility of network, Scientia Iranica B, 26(2) (2019) 887-896.
[19] R. Marcombe, S. Cai, W. Hong, X. Zhao, Y. Lapusta, Z. Sou, A theory of constrained swelling of a pH-sensitive hydrogel, Soft Matter., 6(4) (2010) 784-793.
[20] A. Suzuki, T. Tanaka, Phase transition in polymer gels induced by visible light, Nature, 346(6282) (1990) 345-347.
[21] A. Suzuki, Phase Transition in Gels of Submillimeter Size Induced by Interaction with Stimuli, In: K. Dusek, (eds) Advances in Polymer Sience, Heidelbery, (1993) 199-240.
[22] 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, 404(6778) (2000) 588-590.
[23] D. Kim, D.J. Beebe, A bi-polymer micro one-way valve, Sens. Actuators, A: Physical, 136(1) (2007) 426-433.
[24] H. Mazaheri, M. Baghani, R. Naghdabadi, S. Sohrabpour, Inhomogeneous swelling behavior of temperature sensitive PNIPAM hydrogels in microvalves: analytical and numerical study, Smart Mater. Struct., 24(4) (2015) 045004.
[25] N. Arbabi, M. Baghani, J. Abdolahi, H. Mazaheri, M. Mosavi-Mashhadi, Study on pH-sensitive hydrogel micro-valves: A fluid–structure interaction approach, J. Intell. Mater. Syst. Struct., 28(12) (2016) 1589-1602.
[26] H. Mazaheri, A. Namdar, A. Amiri, Behavior of a smart one-way micro-valve considering fluid–structure interaction, J. Intell. Mater. Syst. Struct., 29(20) (2018) 3960-3971.
[27] P.J. Flory, J. Rehner Jr, Statistical mechanics of cross-linked polymer networks II. Swelling, J. Chem. Phys., 11(11) (1943) 521-526.
[28] M.L. Huggins, Some properties of solutions of long-chain compounds, J. Chem. Phys., 46(1) (1942) 151-158.
[29] F. Afroze, E. Nies, H. Berghmans, Phase transitions in the system poly(Nisopropylacrylamide)/water and swelling behaviour of the corresponding networks, J. Mol. Struct., 554(1) (2000) 55-68.
[30] H. Mazaheri, M. Baghani, R. Naghdabadi, S. Sohrabpour, Coupling behavior of the pH/temperature sensitive hydrogels for the inhomogeneous and homogeneous swelling, Smart Mater. Struct., 25(8) (2016) 085034.
[31] W. Hong, Z. Liu, Z. Suo, Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load, Int. J. Solids Struct., 46(17) (2009) 3282-3289.
[32] H. Mazaheri, A. Ghasemkhani, Analytical and numerical study of the swelling behavior in functionally graded temperature-sensitive hydrogel shell, J. Stress Anal. 3(2) (2019) 29-35.