A meshfree model for plant tissue deformations during drying

Chaminda Prasad Karunasena Helambage, Wijitha Senadeera, Richard J Brown, Yuan Tong Gu

Abstract


Plant tissue has a complex cellular structure which is an aggregate of individual cells bonded by middle lamella. During drying processes, plant tissue undergoes extreme deformations which are mainly driven by moisture removal and turgor loss. Numerical modelling of this problem becomes challenging when conventional grid-based modelling techniques such as finite element and finite difference methods are considered due to grid-based limitations. This work presents a meshfree approach to model and simulate the deformations of plant tissue during drying. This method demonstrates the fundamental capabilities of meshfree methods in handling extreme deformations of multiphase systems. A simplified two-dimensional tissue model is developed by aggregating individual cells while accounting for the stiffness of the middle lamella. Each individual cell is simply treated as consisting of two main components: cell fluid and cell wall. The cell fluid is modelled using smoothed particle hydrodynamics and the cell wall is modelled using a discrete element method. Drying is accounted for by the reduction of cell fluid and wall mass, and turgor pressure, which causes local deformations of cells, eventually leading to tissue scale shrinkage. The cellular deformations are quantified using several cellular geometrical parameters and a good agreement is observed when compared to experiments on apple tissue. The model is also capable of visually replicating dried tissue structures. The proposed model can be used as a step in developing complex tissue models to simulate extreme deformations during drying.

References
  • S. V. Jangam. An overview of recent developments and some RandD challenges related to drying of foods. Dry. Technol., 29(12):1343–1357, 2011. doi:10.1080/07373937.2011.594378
  • L. Mayor and A. M. Sereno. Modelling shrinkage during convective drying of food materials: a review. J. Food Eng., 61(3):373–386, 2004. doi:10.1016/s0260-8774(03)00144-4
  • M. S. Rahman, I. Al-Zakwani, and N. Guizani. Pore formation in apple during air-drying as a function of temperature: porosity and pore-size distribution. J. Sci. Food Agr., 85(6):979–989, 2005. doi:10.1002/jsfa.2056
  • M. K. Bartlett, C. Scoffoni, and L. Sack. The determinants of leaf turgor loss point and prediction of drought tolerance of species and biomes: a global meta-analysis. Ecol. Lett., 15(5):393–405, 2012. doi:10.1111/j.1461-0248.2012.01751.x
  • L. Mayor, M. A. Silva, and A. M. Sereno. Microstructural changes during drying of apple slices. Dry. Technol., 23(9–11):2261–2276, 2005. doi:10.1080/07373930500212776
  • G. H. Crapiste, S. Whitaker, and E. Rotstein. Drying of cellular material–-I. A mass transfer theory. Chem. Eng. Sci., 43(11):2919–2928, 1988. doi:10.1016/0009-2509(88)80045-9
  • H. X. Zhu and J. R. Melrose. A mechanics model for the compression of plant and vegetative tissues. J. Theor. Biol., 221(1):89–101, 2003. doi:10.1006/jtbi.2003.3173
  • C. X. Wang, L. Wang, and C. R. Thomas. Modelling the mechanical properties of single suspension-cultured tomato cells. Ann. Bot.-London, 93(4):443–453, 2004. doi:10.1093/aob/mch062
  • N. Wu and M. J. Pitts. Development and validation of a finite element model of an apple fruit cell. Postharvest Biol. Tec., 16(1):1–8, 1999. doi:10.1016/S0925-5214(98)00095-7
  • G. R. Liu and M. B. Liu. Smoothed Particle Hydrodynamics: A Meshfree Particle Method. World Scientific Publishing Co., Singapore, 2003. http://www.worldscientific.com/worldscibooks/10.1142/5340
  • G. R. Liu and Y. T. Gu. An Introduction to Meshfree Methods and Their Programming. Springer, 2005. http://www.springer.com/engineering/computational+intelligence+and+complexity/book/978-1-4020-3228-8
  • Y. T. Gu and G. R. Liu. Hybrid boundary point interpolation methods and their coupling with the element free galerkin method. Eng. Anal. Bound. Elem., 27(9):905–917, 2003. doi:10.1016/S0955-7997(03)00045-6
  • Y. Gu and L. C. Zhang. Coupling of the meshfree and finite element methods for determination of the crack tip fields. Eng. Fract. Mech., 75:986–1004, 2008. doi:10.1016/j.engfracmech.2007.05.003
  • R. A. Gingold and J. J. Monaghan. Smoothed particle hydrodynamics - theory and application to non-spherical stars. Mon. Not. R. Astron. Soc., 181:375–389, 1977. http://adsabs.harvard.edu/full/1977MNRAS.181..375G
  • P. Van Liedekerke, P. Ghysels, E. Tijskens, G. Samaey, D. Roose, and H. Ramon. Mechanisms of soft cellular tissue bruising. a particle based simulation approach. Soft Matter, 7:3580–3591, 2011. doi:10.1039/C0SM01261K
  • P. Van Liedekerke, P. Ghysels, E. Tijskens, G. Samaey, B. Smeedts, D. Roose, and H. Ramon. A particle-based model to simulate the micromechanics of single-plant parenchyma cells and aggregates. Phys. Biol., 7:026006, 2010. doi:10.1088/1478-3975/7/2/026006
  • H. C. P. Karunasena, W. Senadeera, Y. T. Gu, and R. J. Brown. A particle based micromechanics model to simulate drying behaviors of vegetable cells. In Y. T. Gu, S. C. Saha, editor, 4th International Conference on Computational Methods (ICCM 2012), Gold Coast, Australia, 25–28 November, 2012. http://eprints.qut.edu.au/55471/1/A_Particle_Based_Micromechanics_Model(ICCM_Gold_Coast).pdf
  • H. C. P. Karunasena, W. Senadeera, Y. T. Gu, and R. J. Brown. A coupled SPH-DEM model for fluid and solid mechanics of apple parenchyma cells during drying. In P. A. Brandner, B. W. Pearce, editor, 18th Australasian Fluid Mechanics Conference, Launceston, Australia, 2012. http://eprints.qut.edu.au/55469/
  • H. C. P. Karunasena, W. Senadeera, Y. T. Gu, and R. J. Brown. A coupled SPH-DEM model for micro-scale structural deformations of plant cells during drying. Appl. Math. Model., 2014. doi:10.1016/j.apm.2013.12.004
  • H. C. P. Karunasena, W. Senadeera, R. J. Brown, and Y. T. Gu. Simulation of plant cell shrinkage during drying - a SPH-DEM approach. Eng. Anal. Bound. Elem., 44:1–18, 2014. doi:10.1016/j.enganabound.2014.04.004
  • H. C. P. Karunasena, P. Hesami, W. Senadeera, Y. T. Gu, R. J. Brown, and A. Oloyede. Scanning electron microscopic study of microstructure of gala apples during hot air drying. Dry. Technol., 32(4):455–468, 2014. doi:10.1080/07373937.2013.837479
  • A. Stukowski. Visualization and analysis of atomistic simulation data with OVITO–-the open visualization tool. Model. Simul. Mater. Sc., 18:015012, 2010. doi:10.1088/0965-0393/18/1/015012
  • P. W. Cleary and J. J. Monaghan. Conduction modelling using smoothed particle hydrodynamics. J. Comput. Phys., 148(1):227–264, 1999. doi:10.1006/jcph.1998.6118
  • L. Taiz and E. Zeiger. Plant Physiology, chapter Water and Plant Cells, pages 73–84. Sinauer Associates, Sunderland, USA, 2010.
  • H. C. P. Karunasena, W. Senadeera, R. J. Brown, and Y. T. Gu. A particle based model to simulate microscale morphological changes of plant tissues during drying. Soft Matter, 2014. doi:10.1039/C4SM00526K

Keywords


discrete element method;drying;meshfree;plant tissue;shrinkage;smoothed particle hydrodynamics;

Full Text:

PDF BIB


DOI: http://dx.doi.org/10.21914/anziamj.v55i0.7857



Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.