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Research Papers

Wrinkling of a Polymeric Gel During Transient Swelling

[+] Author and Article Information
William Toh

School of Mechanical
and Aerospace Engineering,
Nanyang Technological University,
50 Nanyang Avenue,
639798, Singapore
e-mail: wtoh1@e.ntu.edu.sg

Zhiwei Ding

Institute of High Performance Computing,
1 Fusionopolis Way,
#16-16 Connexis,
138632, Singapore
e-mail: dingzw@ihpc.a-star.edu.sg

Teng Yong Ng

Mem. ASME
School of Mechanical
and Aerospace Engineering,
Nanyang Technological University,
50 Nanyang Avenue,
639798, Singapore
e-mail: mtyng@ntu.edu.sg

Zishun Liu

Mem. ASME
International Center for Applied Mechanics,
State Key Laboratory for Strength
and Vibration of Mechanical Structures,
Xi'an Jiaotong University,
No. 28, West Xianning Road,
Xi'an Shaanxi 710049, China
e-mail: zishunliu@mail.xjtu.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 22, 2015; final manuscript received April 2, 2015; published online April 30, 2015. Editor: Yonggang Huang.

J. Appl. Mech 82(6), 061004 (Jun 01, 2015) (8 pages) Paper No: JAM-15-1039; doi: 10.1115/1.4030327 History: Received January 22, 2015; Revised April 02, 2015; Online April 30, 2015

When exposed to an external solvent, a dry polymeric network imbibes the solvent and undergoes large deformation. The resulting aggregate is known as a hydrogel. This swelling process is diffusion driven and thus results in differential swelling during transient swelling. When subjected to external geometrical constraints, such as being rigidly fixed or attachment to a compliant substrate, wrinkles have been shown to appear due to mechanical instabilities. In the case of free swelling, there are no external constraints to induce the instabilities accounting for wrinkling patterns. However, during the transient swelling process, the swelling differential between the gel on the exterior and the interior causes compressive stresses and gives rise to mechanical instabilities. It is also observed that the time dependence of the swelling profile causes the wrinkles to evolve with time. In this work, we investigate this interesting phenomenon of transient wrinkle mode evolution using the finite element and state-space methods. From our simulations and prediction, we find that there is an inverse relation between critical wave number and time, which has earlier been observed in experiments.

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Figures

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Fig. 1

Schematics of a gel exposed to solvent of chemical potential μs during (a) initial state of homogeneous swelling at chemical potential of μ0 and (b) onset of wrinkling at the surface at time t

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Fig. 2

(a) Compressive stresses experienced by a gel (Nν=0.001,χ=0.1,and μ0=-1) swelling under lateral constrains in kinetic analysis and (b) stretch ratio at various times

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Fig. 3

(a) Discretization of a single waveform into eight elements and (b) imposition of MPC at surface nodes

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Fig. 4

(a) Full finite element model of the gel, with thickness 1 and width of 10. (b)–(d) Different meshes with top layer mesh thickness of 0.01 H, 0.005 H, and 0.001 H, respectively. Note that meshes (b)–(d) are shortened with width to illustrate the graded mesh used in simulations.

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Fig. 5

Time of onset of wrinkling with increasing refinement of mesh for models with 10 and 15 waves within the width of the gel

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Fig. 6

Evolution of surface wrinkles of a hydrogel layer. Time of onset of wrinkling increases from (a) to (f).

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Fig. 7

(a) wave number versus time and (b) wavelength versus time for gels of crosslink densities at Nν=0.001 and Nν=0.01; Flory-interaction parameter χ=0.1; and initial chemical potential of μ0=-1

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Fig. 8

Comparison between state-space predictions for different discretization of gel layers

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Fig. 9

Normalized wave number versus time for finite element method and state-space methods for Nν=0.01,χ=0.1,and μ0=-1

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