On the Mathematical Model of the Biomechanics of Green Plants

Main Article Content

N. O. Uka
J. D. Olisa


This study considers the biomechanics in the stem of green plants. The process of translocation and transpiration is discussed. The coupled non-linear differential equations governing the motion of the flow were non-dimensionlized and then solved using the homotopy perturbation method. The effects of various parameters such as Schmidt number, porosity, buoyancy forces (thermal and concentration Grashof numbers) and aspect ratio embedded in the flow were examined on the concentration field. The results showed that increasing the porosity, Schmidt number, Sherwood number and aspect ratio resulted to a decrease in the concentration field whereas increase in the buoyancy forces had a positive effect on the flow by increasing its concentration and hence enhancing the growth and productivity of the plant.

Biomechanics, xylem flow, phloem flow, Homotopy Perturbation Method (HPM).

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How to Cite
Uka, N. O., & Olisa, J. D. (2019). On the Mathematical Model of the Biomechanics of Green Plants. Asian Journal of Physical and Chemical Sciences, 7(3), 1-9. https://doi.org/10.9734/ajopacs/2019/v7i330097
Original Research Article


Knudson D. Fundamentals of Biomechanics. Springer Science + Business Media, LLC, 233 Spring Street, New York, NY 10013, USA; 2007.

Jensen KH, Berg-Sorensen K, Bruus H, Holbrook NM, Leische J, Schulz A, Zwieniecki MA, Bohr T. Sap flow and sugar transport in plant. Reviews of Modern Physics. 2016;88.

Rand RH. Fluid mechanics of green plants Ann. Rev. Fluid Mechanics. 1983;15:29-45.

Dolger J, Rademaker H, Liesche J, Schulz A, Bohr T. Diffusion and bulk flow in phloem loading: A theoretical analysis of the polymer trap mechanism for sugar transport in plants. Physical Review E. 2014;90.

Yu T. Translocation in the Phloem. Plant Physiology; 2008.

Bestman AR. Global models for the biomechanics of green plants part 1. International Journal of Energy Research. 1991;16:677-684.

Kililova NN. Long-distance liquid transport in plants. Proceeding of the Estonian Academy of Science. 2008;57(3):179-203.

Okuyade WIA, Abbey TM. Biomechanics of a bifurcating green plant, part 1. Asian Journal of Physics and Chemical. 2016; 1(2):1-22.

Muskat. Flow of fluids through porous media. Journal of Applied Physics. 1937; 8:274.

Zami-Pierre F, de Lonbens R, Quintard M, Davit Y. Transition in the flow of power–law fluids through isotropic porous media. Physical Review Letters. 2016; 117.

El-dabe NTM, Abou-zeid MY, Sayed HA. Pulsatile motion of Non-Newtonian fluid with heat and mass transfer THROUGH a porous medium in a solid cylindrical pipe in the presence of magnetic field. International Journal of Scientific and Innovative Mathematical Research (IJSIMR). 2014;2(10):844-854.

Okuyade WIA, Abbey TM. Biomechanics of a bifurcating green plant, part 2: Environmental thermal effects. Asian Journal of Physics and Chemical. 2017; 2(3):1-14

Bestman AR. Global models for the biomechanics of green plants part 2. International Journal of Energy Research, 1992;16:685-689.

Prakash O, Singh SP, Kumar D, Dwivedi YK. A study of effects of heat source on MHD blood flow through bifurcated arteries. AIP Advances. 2011;1:2158-3226.

Okuyade WIA. MHD blood flow in bifurcating porous fine capillaries. African Journal of Science Research. 2015; 4(4):56-59.

Tadjfar M, Smith FT. Direct simulations and modelling of basic three-dimensional bifurcating tube flow. J. Fluid Mech. 2004; 519:1-32.

Liou TM, Chang TW, Chang WC. Effects of bifurcation angle on the steady flow Structure in model Saccular Aneurysms. Experiments in Fluids. 1993;289-295.

Okuyade WIA, Abbey TM. Steady MHD fluid flow in a bifurcating rectangular porous channel. Advances in Research. 2016;8:3.

Rand RH, Cooke JR. Fluid dynamics of phloem flow: An axisymmetric model American Society of Agricultural Engineers; 1978.

Rand RH, Upadhyaya SK, Cooke JR. Fluid dynamics of phloem flow: part II. An approximate formula. American Society of Agricultural Engineers; 1980.

Jensen KH, Rio E, Hansen R, Clanet C, Bohr T. Osmotically driven pipe flows and their relation to sugar transport in plants. J. Fluid Mech. 2009;636:371-396.

Cabrita P, Thorpe M, Huber G. Hydrodynamics of steady state phloem transport with radial leakage of solute. Frontiers in Plant Science. 2013;4.

Payvandi S, Daly KR, Jones DL, Talboys P, Zygalakis KC, Roose T. A mathematical model of water and nutrients transport in xylem vessels of a wheat Plant. Bulletin of Mathematical Biology. 2014;76(3):566-596.

He JH. Computer methods in applied mechanics and engineering. 1999;178(3): 257-262.