ORCID Profile
0000-0003-1855-7897
Current Organisation
University of Adelaide
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Publisher: Cambridge University Press (CUP)
Date: 11-07-2019
DOI: 10.1017/JFM.2019.466
Abstract: We consider the role of heating and cooling in the steady drawing of a long and thin viscous thread with an arbitrary number of internal holes of arbitrary shape. The internal holes and the external boundary evolve as a result of the axial drawing and surface-tension effects. The heating and cooling affects the evolution of the thread because both the viscosity and surface tension of the thread are assumed to be functions of the temperature. We use asymptotic techniques to show that, under a suitable transformation, this complicated three-dimensional free boundary problem can be formulated in such a way that the transverse aspect of the flow can be reduced to the solution of a standard Stokes flow problem in the absence of axial stretching. The solution of this standard problem can then be substituted into a system of three ordinary differential equations that completely determine the flow. We use this approach to develop a very simple numerical method that can determine the way that thermal effects impact on the drawing of threads by devices that either specify the fibre tension or the draw ratio. We also develop a numerical method to solve the inverse problem of determining the initial cross-sectional geometry, draw tension and, importantly, heater temperature to obtain a desired cross-sectional shape and change in cross-sectional area at the device exit. This precisely allows one to determine the pattern of air holes in the preform that will achieve the desired hole pattern in the stretched fibre.
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 04-07-2022
DOI: 10.21914/ANZIAMJ.V63.17079
Abstract: The chemical vapour deposition method is widely used to synthesise high quality graphene with a large surface area. However, the cooling process leads to the formations of ripples and wrinkles in the graphene structure. When a self-adhered wrinkle achieves the maximum height, it then folds onto the surface and leads to a collapsed wrinkle. The presence of such deformations often affects the properties of graphene. In this article, we describe a novel mathematical model to understand the formation and geometry of these wrinkles. The stability of these wrinkles is examined based on variational derivations for the energy of each structure. The model provides detailed explanations for the geometry of these wrinkles which would help in tuning their properties. References J. Aljedani, M. J. Chen, and B. J. Cox. Variational model for collapsed graphene wrinkles. Appl. Phys. A 127.11, 886 (2021), pp. 1–13. doi: 10.1007/s00339-021-05000-y A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau. Superior thermal conductivity of single-layer graphene. Nano Lett. 8.3 (2008), pp. 902–907. doi: 10.1021/nl0731872 S. Chen, Q. Li, Q. Zhang, Y. Qu, H. Ji, R. S. Ruoff, and W. Cai. Thermal conductivity measurements of suspended graphene with and without wrinkles by micro-Raman mapping. Nanotech. 23.36, 365701 (2012). doi: 10.1088/0957-4484/23/36/365701 on p. C85). B. J. Cox, T. Dyer, and N. Thamwattana. A variational model for conformation of graphene wrinkles formed on a shrinking solid metal substrate. Mat. Res. Express 7.8, 085001 (2020). doi: 10.1088/2053-1591/abaa8f A. K. Geim. Graphene: Status and prospects. Science 324.5934 (2009), pp. 1530–1534. doi: 10.1126/science.1158877 on p. C85). K. Kostarelos and K. S. Novoselov. Graphene devices for life. Nature Nanotech. 9 (2014), pp. 744–745. doi: 10.1038/nnano.2014.224 F. Long, P. Yasaei, R. Sanoj, W. Yao, P. Král, A. Salehi-Khojin, and R. Shahbazian-Yassar. Characteristic work function variations of graphene line defects. ACS Appl. Mat. Inter. 8.28 (2016), pp. 18360–18366. doi: 10.1021/acsami.6b04853 R. Muñoz and C. Gómez-Aleixandre. Review of CVD synthesis of graphene. Chem. Vapor Dep. 19.10–12 (2013), pp. 297–322. doi: 10.1002/cvde.201300051 L. Spanu, S. Sorella, and G. Galli. Nature and strength of interlayer binding in graphite. Phys. Rev. Lett. 103.19, 196401 (2009). doi: 10.1103/PhysRevLett.103.196401 T. Verhagen, B. Pacakova, M. Bousa, U. Hübner, M. Kalbac, J. Vejpravova, and O. Frank. Superlattice in collapsed graphene wrinkles. Sci. Rep. 9.1, 9972 (2019). doi: 10.1038/s41598-019-46372-9 C. Wang, Y. Liu, L. Li, and H. Tan. Anisotropic thermal conductivity of graphene wrinkles. Nanoscale 6.11 (2014), pp. 5703–5707. doi: 10.1039/C4NR00423J W. Wang, S. Yang, and A. Wang. Observation of the unexpected morphology of graphene wrinkle on copper substrate. Sci. Rep. 7.1 (2017), pp. 1–6. doi: 10.1038/s41598-017-08159-8 Y. Wang, R. Yang, Z. Shi, L. Zhang, D. Shi, E. Wang, and G. Zhang. Super-elastic graphene ripples for flexible strain sensors. ACS Nano 5.5 (2011), pp. 3645–3650. doi: 10.1021/nn103523t Y. Wei, B. Wang, J. Wu, R. Yang, and M. L. Dunn. Bending rigidity and Gaussian bending stiffness of single-layered graphene. Nano Lett. 13.1 (2013), pp. 26–30. doi: 10.1021/nl303168w Z. Xu and M. J. Buehler. Interface structure and mechanics between graphene and metal substrates: A first-principles study. J. Phys.: Cond. Mat. 22.48, 485301 (2010). doi: 10.1088/0953-8984/22/48/485301 Y. Zhang, N. Wei, J. Zhao, Y. Gong, and T. Rabczuk. Quasi-analytical solution for the stable system of the multi-layer folded graphene wrinkles. J. Appl. Phys. 114.6, 063511 (2013). doi: 10.1063/1.4817768 W. Zhu, T. Low, V. Perebeinos, A. A. Bol, Y. Zhu, H. Yan, J. Tersoff, and P. Avouris. Structure and electronic transport in graphene wrinkles. Nano Lett. 12.7 (2012), pp. 3431–3436. doi: 10.1021/nl300563h
Publisher: IOP Publishing
Date: 05-2021
Abstract: We present a novel analytical prediction for the effective bending rigidity γ eff of multi–layer graphene sheets. Our approach involves using a variational model to determine the folding conformation of multi–layer graphene sheets where the curvature of each graphene layer is taken into account. The Lennard–Jones potential is used to determine the van der Waals interaction energy per unit area and the spacing distance between graphene layers. The mid–line of the folded multi–layer graphene is described by a solution derived in previous work for folded single– and multi–layer graphene. Several curves are obtained for the single–layer solution using different values of the bending rigidity γ , and compared to the mid–line of the folded multi–layer graphene. The total area between these curves and the mid–line is calculated, and the value of γ eff is determined by the single–layer curve for which this area is minimized. While there is some disagreement in the literature regarding the relationship between the bending rigidity and the number of layers, our analysis reveals that the bending rigidity of multi–layer graphene follows an approximate square–power relationship with the number of layers N , where N 7. This trend is in line with theoretical and experimental studies reported in the literature.
Publisher: Cambridge University Press (CUP)
Date: 22-11-2018
DOI: 10.1017/S0956792518000657
Abstract: Tissue engineering aims to grow artificial tissues in vitro to replace those in the body that have been damaged through age, trauma or disease. A recent approach to engineer artificial cartilage involves seeding cells within a scaffold consisting of an interconnected 3D-printed lattice of polymer fibres combined with a cast or printed hydrogel, and subjecting the construct (cell-seeded scaffold) to an applied load in a bioreactor. A key question is to understand how the applied load is distributed throughout the construct. To address this, we employ homogenisation theory to derive equations governing the effective macroscale material properties of a periodic, elastic–poroelastic composite. We treat the fibres as a linear elastic material and the hydrogel as a poroelastic material, and exploit the disparate length scales (small inter-fibre spacing compared with construct dimensions) to derive macroscale equations governing the response of the composite to an applied load. This homogenised description reflects the orthotropic nature of the composite. To validate the model, solutions from finite element simulations of the macroscale, homogenised equations are compared to experimental data describing the unconfined compression of the fibre-reinforced hydrogels. The model is used to derive the bulk mechanical properties of a cylindrical construct of the composite material for a range of fibre spacings and to determine the local mechanical environment experienced by cells embedded within the construct.
Publisher: SAGE Publications
Date: 2019
Abstract: A key step in the tissue engineering of articular cartilage is the chondrogenic differentiation of mesenchymal stem cells (MSCs) into chondrocytes (native cartilage cells). Chondrogenesis is regulated by transforming growth factor- β (TGF- β), a short-lived cytokine whose effect is prolonged by storage in the extracellular matrix. Tissue engineering applications aim to maximise the yield of differentiated MSCs. Recent experiments involve seeding a hydrogel construct with a layer of MSCs lying below a layer of chondrocytes, stimulating the seeded cells in the construct from above with exogenous TGF- β and then culturing it in vitro. To investigate the efficacy of this strategy, we develop a mathematical model to describe the interactions between MSCs, chondrocytes and TGF- β. Using this model, we investigate the effect of varying the initial concentration of TGF- β, the initial densities of the MSCs and chondrocytes, and the relative depths of the two layers on the long-time composition of the tissue construct.
Publisher: Springer Science and Business Media LLC
Date: 11-2021
Publisher: Royal Society of Chemistry (RSC)
Date: 2020
DOI: 10.1039/C9RA10439A
Abstract: A variational model is proposed to describe rippled graphene on a substrate, and obtain the relationship between total energy and substrate length.
Publisher: IOP Publishing
Date: 30-12-2021
Abstract: A mathematical model is developed to study the folding behaviour of multi–layer graphene sheets supported on a substrate. The conformation of the fold is determined from variational considerations based on two energies, namely the graphene elastic energy and the van der Waals (vdW) interaction energy between graphene layers and the substrate. The model is nondimensionalized and variational calculus techniques are then employed to determine the conformation of the fold. The Lennard–Jones potential is used to determine the vdW interaction energy as well as the graphene–substrate and graphene–graphene spacing distances. The folding conformation is investigated under three different approximations of the total line curvature. Our findings show good agreement with experimental measurements of multi–layer graphene folds from the literature.
No related grants have been discovered for Michael Chen.