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European Journal of Applied Sciences – Vol. 12, No. 3

Publication Date: June 25, 2024

DOI:10.14738/aivp.123.17017.

Mba, N. U., & Abbey, T. M. (2024). The Biomechanics of Green Plants in The Presence of Environmental Thermal Perturbations.

European Journal of Applied Sciences, Vol - 12(3). 424-440.

Services for Science and Education – United Kingdom

The Biomechanics of Green Plants in The Presence of

Environmental Thermal Perturbations

Nnenna Ude Mba

Department of Mathematics, Abia State University, Uturu

Tamunoimi Michael Abbey

Department of Physics, Applied Mathematics and

Theoretical Physics Group, University of Port-Harcourt, Nigeria

ABSTRACT

This study mimics the flow model of mineral salt solution in green plants when the

environmental temperature suddenly increased. The usual Navier stokes equation

in cylindrical coordinate is used to formulate the governing system of equations

for the flow model. The analysis is then carried out by means of the homotopy

perturbation method (HPM). The result obtained shows that the increase in the

thermal parameters caused a corresponding increase in the temperature, velocity

and the quantity of fluids being transported to the leaves of the plant. It further

reveals that when the aspect ratio of the plant is very large, that is for plant whose

length is far greater than its diameter, the flow profiles tend to be streamline,

laminar and Poiseuille. This understanding shows why some green plants of this

nature tend to strive during the period of heat waves and drought. It was further

seen that when the thermal parameter γ = 0, the model returns to that of Rand [1]

and Bestman [2].

Keywords: Biomechanics, Green plant, xylem flow, homotopy perturbation method

(HPM)

INTRODUCTION

In recent times there has been a growing concern among governmental organizations,

agencies, scientist, environmentalist and climatologist as well as medical experts on the issue

of global warming as a result of thermal perturbations; which has brought about

environmental temperature rise. The global change in environmental temperature has

resulted in climate changes as well as the ocean rise and water flooding. (Abbas et al. [3];

Shahzad [4]). In fact, the impact of global thermal perturbation on biotic life within the

biomass cannot be over emphasized. Its effect can be seen in areas where heat waves and

drought have caused a lot of impact on the livelihood of man, animals and plants.

The usefulness of plants, particularly green plants are numerous. In addition to serving as

source of food and energy for man and animals, they are source of air quality balance in the

atmosphere. Their economic value as a source of timber for building and infrastructure

development has enhanced the GDP of most countries.

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Mba, N. U., & Abbey, T. M. (2024). The Biomechanics of Green Plants in The Presence of Environmental Thermal Perturbations. European Journal

of Applied Sciences, Vol - 12(3). 424-440.

URL: http://dx.doi.org/10.14738/aivp.123.17017

Due to the above usefulness, several researchers in the literature have turned attention to the

study and investigation of plants and their applications. For example, Bestman [2,5]

investigated the effect of aspect ratio (valve) (which is the ratio of the length of the plant to its

diameter) and porosity on the concentration field of a fully developed xylem and phloem flow

in green plants using the Laplace transform method. For the case of non-fully (ie partially)

developed flow, the method of perturbation and finite Fourier sine and cosine technique were

adopted. It was discovered that the velocity near the walls of the plant were nearly zero for

the fully developed case. It was also observed that for very large values of the porosity

parameter, the concentration near the wall of the valve reduced and then increased when it

was far away from the wall. More so, for smaller values of the porosity parameter, the

concentration increased near the wall of the valve. More so, it was noticed that for the non- fully developed case and at a larger aspect ratio, the concentration was slightly less than that

of the fully developed flow when their aspect ratios were equal. They further observed that as

the aspect ratio increases, the concentration increases. The velocity of the non-fully developed

flow on the other hand was observed to be higher than that of the fully developed velocity

when the aspect ratio equals one. ( ie R = 1).

Bestman [6] also considered the transient case of the problem due to daily changes in the

stem diameters resulting from dehydration, neglecting environmental thermal differences

using the Laplace transform and Fourier sine and cosine transform method. Results showed

that concentration decreased exponentially with time. Thus, at lesser time, concentration

increased from zero and then decreased as time increases. The velocity on the other hand

became fully developed at small value of the aspect ratio. Similarly, Rand and Cooke [7]

studied the flow of viscous fluid through sieve tubes with sieve plates in the phloem of green

plants using an idealized single pore axisymmetrical model. The pressure drops encountered

by the viscous fluid moving through the series of sieve tube and plate were expressed using

the resistance formula. Result showed that the resistance formula gave a very small value for

pressure drop and was about two times smaller than the value obtained using the more

realistic idealized axisymmetric case. In the same vain, Rand et al. [8] used an approximate

formula to study the same flow problem. Their result gave a more exact solution for the

pressure drop.

Similarly, Hoad [9] studied the translocation of plant hormones in the phloem of higher

plants. Problems associated with collection of sieve tube exudates and the analysis of samples

were discussed. More so, possible functions of the hormones were investigated. From the

study, it was established that mobile hormones played a part in controlling the structure of

the plant as their concentration in sieve tube have been shown to be influenced by the

environment at developmental stage. Peuke et al. [10] is reported to have used the nuclear

magnetic resonance (NMR) spectrometry to study the measurement of rates of flow in xylem

and phloem. The effects of light regime on water flows on xylem and phloem were monitored

using this same approach. It was observed that the presence of light did not change the flow of

water in the phloem very much whereas, it increased the velocity of flow in the xylem.

Transport of solutes were mainly affected by the solute concentration during loading and thus

resulting to changes in concentration. Rengel [11] studied the transport of micronutrients

(manganese and zinc) from leaves to roots, leaves and stems to developing grains and then

from one root to another in the xylem and phloem of a developing plant species. It was

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European Journal of Applied Sciences (EJAS) Vol. 12, Issue 3, June-2024

discovered that zinc solute was more mobile in phloem while manganese had poor mobility in

the phloem and therefore occurred mainly on the xylem vessel. Also, Jensen et al. [12]

presented an experimental and theoretical study of transient osmotically driven flows

through pipes with semi-permeable walls. The study considered the transport and decay of a

sudden loading of sugar in a closed water filled pipe. The equations of motion for the sugar

concentration and water velocity were solved using the method of characteristics. Result

showed that the concentration and velocity front decayed exponentially with time and the

dimensionless Munch number M. The applicability of the results to plants were discussed. It

was observed that the Munch mechanism could account for only short distance transport of

sugar in plants. Furthermore, Pitterman [13] studied the evolution of plant vascular system,

highlighted the recent developments that contributed to a better understanding of the xylem

evolution, discussed the functions of vascular structure in terms of support, drought and

freeze-thaw stress resistance and also discussed in details the impacts of plant transport on

hydrology and climate. Cabrita [14] investigated the magnitude of radial fluxes in the stem

(that is, water and solute exchanges along the long pathway) and what controlled them using

experiment and theory. A steady state model of phloem transport was constructed using the

Navier-Stokes and convection-diffusion equations. It was observed from the model that, radial

water exchange that affects the pressure gradient and solute exchange which depends on the

permeability of the phloem also affects the pressure gradient. Woodruff [15] examined how

the height of a tree together with water stress characteristics, that is, the sieve cell structural

characteristics and phloem sap composition influenced phloem transport capacity. It also

provided information on the relative contributions of changes in each of these characteristics

towards the impact of water stress on conductivity. De schepper et al. [16] carried out a

review on mechanisms and controls in phloem transport. Important differences on phloem

related data measured between trees and herbaceous species were revealed. It was observed

that not only do their loading strategies differ, but also the pressure was much higher in

herbaceous plant than in trees. The study gave a vital understanding of the phloem system on

how photosynthates/assimilates content is exchanged between sources and sinks and also,

how growth is regulated in plants. Payvandi et al. [17] studied the transport of water and

nutrient in xylem vessels of a wheat plant. Solutions to the transport of the nutrients were

obtained considering convection and diffusion. The diffusive transport showed a significant

effect. Jovanic et al. [18] investigated the effects of high pressure on the leaves of two green

plant species. It was observed that as pressure increased, the effectiveness of the

photosynthetic device decreased slowly and nonlinearly for both plant species, thus damaging

the leaf tissue. Knoblauch et al. [19] tested the Munch hypothesis of long-distance phloem

transport in plants. The aim of the study was to investigate whether the conductance of the

sieve tubes and sieve plate pore were sufficient to allow pressure flow. Observation showed

that as the distance between the source and the sink increased, the sieve tube conductance

and turgor increased dramatically thus providing a strong support for the Munch hypothesis.

Julius et al. [20] highlighted latest discoveries on the path of phloem loading of sugar

(sucrose) in rice and maize leaves and also discussed phloem loading pathways in stems and

roots and the sugars putatively involved. The study described how heat and drought stress

impact carbohydrate portioning and phloem transport; Illuminated how plant pathogens

hijack sugar transporters to obtain carbohydrate for pathogen survival and how plant

employs sugar transporters to defend against the pathogens and finally discussed the

different roles for sugar transporters in plant biology. Their discoveries provided valuable