An Analytical Solution and FEM Simulation for the Behavior of Sensitive FG micro-valve in Response to pH Stimuli

Document Type : Original Research Paper

Authors

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

Abstract

In this paper, an analytical solution and a numerical simulation of the pH-sensitive hydrogel micro-valves exposed to pH variation are proposed. Case studies consist of micro-valve with homogeneous single-layer and FG hydrogel as the active part. The results of both methods are in good agreement indicating the validity of both methods. In addition, The numerical and analytical solutions were compared between two ranges of cross-linking densities of hydrogels. In order to reach a convergent solution for the finite element model of the micro-valve, the hydrogel layer is considered to have a number of different layers, and an appropriate number of layers are considered. In the next step, parameters affecting the micro-valve behavior are studied, which are the dimensionless thickness ratio, the number of acidic groups in the network, and the salt molarity of the external solution. The findings show that as the thickness ratio, number of acidic groups, and salt concentration in the external solution result increases, the hydrogel part of the micro-valve experiences a higher degree of swelling and deformation, which should be considered when designing these devices. 

Keywords


[1] R. Marcombe, S. Cai, W. Hong, X. Zhao, Y. Lapusta, Z. Suo, A theory of constrained swelling of a pH-sensitive hydrogel, Soft Matter, 6(4) (2010) 784-793.
[2] W. Otto, L. Drahoslav, Cross-linked hydrophilic polymers and articles made therefrom, (1965), Google Patents.
[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(05) (2020) 2050057.
[4] T. Morimoto, F. Ashida, Temperature-responsive bending of a bilayer gel, Int. J. Solids Struct., 56 (2015) 20-28.
[5] F. Lai, H. Li, R. Luo, Chemo-electro-mechanical modeling of ionic-strength-sensitive hydrogel: Influence of Young’s modulus, Int. J. Solids Struct., 47(22-23) (2010) 3141-3149.
[6] X. Zhou, Y.C. Hon, S. Sun, A.F.T. Mak, Numerical simulation of the steady-state deformation of a smart hydrogel under an external electric field, Smart Mater. Struct., 11(3) (2002) 459-467.
[7] A. Kargar-Estahbanaty, M. Baghani, H. Shahsavari, Gh. Faraji, A combined analytical-numerical investigation on photosensitive hydrogel microvalves, Int. J. Appl. Mech., 9(07) (2017) 1750103. 
[8] M. Doi, Gel dynamics, J. Phys. Soc. Jpn., 78(5) (2009) 052001.
[9] H. Mazaheri, A.H. Namdar, A. Ghasemkhani, A model for inhomogeneous large deformation of photo-thermal sensitive hydrogels, Acta Mech., 232 (2021) 2955-2972.
[10] T.Y. Liu, S.H. Hu, T.Y. Liu, D.M. Liu, S.Y. Chen, Magnetic-sensitive behavior of intelligent ferrogels for controlled release of drug. Langmuir, 22(14) (2006) 5974-5978.
[11] P. Gupta, K. Vermani, S. Garg, Hydrogels: from controlled release to pH-responsive drug delivery, Drug Discov. Today, 7(10) (2002) 569-579.
[12] H. Mazaheri, A. Khodabandehloo, FSI and non-FSI studies on a functionally graded temperature-responsive hydrogel bilayer in a micro-channel, Smart Mater. Struct., 31(1) (2022) 015007.
[13] H. Mazaheri, A.H. 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.
[14] S.K. De, N.R. Aluru, B. Johnson, W.C. Crone, D.J. Beebe, J. Moore, Equilibrium swelling and kinetics of pH-responsive hydrogels: Models, experiments, and simulations, J. Microelectromechanical Syst., 11(5) (2002) 544-555.
[15] A. Drozdov, Swelling of pH-responsive cationic gels: Constitutive modeling and structure–property relations, Int. J. Solids Struct., 64 (2015) 176-190.
[16] H. Yan, B. Jin, S. Gao, L. Chen, Equilibrium swelling and electrochemistry of polyampholytic pH-sensitive hydrogel, Int. J. Solids Struct., 51(23-24) (2014) 4149-4156.
[17] 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) (2017) 1589-1602.
[18] S. Cai, Z. Suo, Mechanics and chemical thermodynamics of phase transition in temperature-sensitive hydrogels, J. Mech. Phys. Solids, 59(11) (2011) 2259-2278.
[19] 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.
[20] 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.
[21] R. Xiao, J. Qian, S. Qu, Modeling gel swelling in binary solvents: a thermodynamic approach to explaining cosolvency and cononsolvency effects, Int. J. Appl. Mech., 11(5) (2019) 1950050.
[22] S. Zheng, Z. Li, Z. Liu, The fast homogeneous diffusion of hydrogel under different stimuli, Int. J. Mech. Sci., 137 (2018) 263-270.
[23] Z. Liu, W. Toh, T.Y. Ng, Advances in mechanics of soft materials: A review of large deformation behavior of hydrogels, Int. J. Appl. Mech., 7(05) (2015) 1530001.
[24] W. Hong, X. Zhao, Z. Suo, Large deformation and electrochemistry of polyelectrolyte gels. J. Mech. Phys. Solids, 58(4) (2010) 558-577.
[25] A. Drozdov, J.D. Christiansen, The effects of pH and Ionic strength of swelling of cationic gels, Int. J. Appl. Mech., 8(5) (2016) 1650059.
[26] 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.
[27] 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.
[28] M. Guvendiren, J.A. Burdick, S. Yang, Kinetic study of swelling-induced surface pattern formation and ordering in hydrogel films with depth-wise cross-linking gradient, Soft Matter, 6(9) (2010) 2044-2049.
[29] M. Guvendiren, S. Yang, J.A. Burdick, Swelling‐induced surface patterns in hydrogels with gradient cross-linking density, Adv. Funct. Mater., 19(19) (2009) 3038-3045.
[30] M. Shojaeifard, F. Rouhani, M. Baghani, A combined analytical–numerical analysis on multidirectional finite bending of functionally graded temperature-sensitive hydrogels, J. Intell. Mater. Syst. Struct., 30(13) (2019) 1882-1895.
[31] 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.
[32] H. Mazaheri, A. Ghasemkhani, A.H. Namdar, Behavior of photo-thermal sensitive polyelectrolyte hydrogel micro-valve: Analytical and numerical approaches, J. Stress Anal., 5(1) (2020) 21-30.
[33] Z. Wu, N. Bouklas, R. Huang, Swell-induced surface instability of hydrogel layers with material properties varying in thickness direction, Int. J. Solids Struct., 50(3-4) (2013) 578-587.
[34] A.H. Namdar, Kinetics of swelling of cylindrical functionally graded temperature-responsive hydrogels, J. Comput. Appl. Mech., 51(2) (2020) 464-471.