scholarly journals A quadratic analytical solution of root pressure generation provides insights about bamboo and other species

2021 ◽  
Author(s):  
Dongmei Yang ◽  
Xiaolin Wang ◽  
Mengqi Yin ◽  
Yongjiang Zhang ◽  
Guoquan Peng ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Fine Roots ◽  
Soil Water Potential ◽  
Quadratic Function ◽  
Solute Concentration ◽  
Solute Flux ◽  
Root Pressure ◽  
Single Root ◽  
Whole Plant ◽  
Complex Roots

We derived a steady-state model of whole root pressure generation through the combined action of all parallel segments of fine roots. This may be the first complete analytical solution for root pressure, which can be applied to complex roots/shoots. The osmotic volume of a single root is equal to that of the vessel lumen in fine roots and adjacent apoplastic spaces. Water uptake occurs via passive osmosis and active solute uptake (J_s^*, osmol s-1), resulting in the osmolal concentration Cr (mol·kg-1 of water) at a fixed osmotic volume. Solute loss occurs via two passive processes: radial diffusion of solute Km (Cr-Csoil), where Km is the diffusional constant and Csoil is the soil-solute concentration) from fine roots to soil and mass flow of solute and water into the whole plant from the end of the fine roots. The proposed model predicts the quadratic function of root pressure P_r^2+bP_r+c=0, where b and c are the functions of plant hydraulic resistance, soil water potential, solute flux, and gravitational potential. The present study investigates the theoretical dependencies of Pr on the factors detailed above and demonstrates the root pressure-mediated distribution of water through the hydraulic architecture of a 6.8-m-tall bamboo shoot.

Diffusiophoresis of a charged drop

2018 ◽  
Vol 852 ◽  
pp. 37-59 ◽  
Author(s):  
Fan Yang ◽  
Sangwoo Shin ◽  
Howard A. Stone
Keyword(s):  
Analytical Solution ◽  
Oil Recovery ◽  
Electrolyte Solution ◽  
Solute Concentration ◽  
Solid Particles ◽  
Concentration Gradients ◽  
Charged Drop ◽  
Electric Stress ◽  
Potential Applications ◽  
Soft Objects

Diffusiophoresis describes the motion of colloids in an electrolyte or non-electrolyte solution where there is a concentration gradient. While most of the studies of diffusiophoresis focus on the motion of solid particles, soft objects such as drops and bubbles are also known to experience diffusiophoresis. Here, we investigate the diffusiophoresis of charged drops in an electrolyte solution both analytically and experimentally. The drop is assumed to remain spherical. An analytical solution of the diffusiophoretic velocity of drops is obtained by perturbation methods. We find that the flow inside the drop is driven by the tangential electric stress at the interface and it directly influences the diffusiophoretic speed of the drop. Using charged oil droplets, we measure the drop speed under solute concentration gradients and find good agreement with the analytical solution. Our findings have potential applications for oil recovery and drug delivery.

scholarly journals `Ben Lear' and `Stevens' Cranberry Root and Shoot Growth Response to Soil Water Potential

HortScience ◽  
2005 ◽  
Vol 40 (3) ◽  
pp. 795-798 ◽  
Author(s):  
Dana L. Baumann ◽  
Beth Ann Workmaster ◽  
Kevin R. Kosola
Keyword(s):  
Root Growth ◽  
Water Potential ◽  
Soil Water ◽  
Leaf Area ◽  
Growth Rates ◽  
Soil Water Potential ◽  
Relative Growth ◽  
Relative Growth Rates ◽  
Water Potentials ◽  
Whole Plant

Wisconsin cranberry growers report that fruit production by the cranberry cultivar `Ben Lear' (Vaccinium macrocarpon Ait.) is low in beds with poor drainage, while the cultivar `Stevens' is less sensitive to these conditions. We hypothesized that `Ben Lear' and `Stevens' would differ in their root growth and mortality response to variation in soil water potential. Rooted cuttings of each cultivar were grown in a green-house in sand-filled pots with three different soil water potentials which were regulated by a hanging water column below a fritted ceramic plate. A minirhizotron camera was used to record root growth and mortality weekly for five weeks. Root mortality was negligible (2% to 6%). Whole plant relative growth rates were greatest for both cultivars under the wettest conditions. Rooting depth was shallowest under the wettest conditions. Whole-plant relative growth rates of `Ben Lear' were higher than `Stevens' at all soil water potentials. `Stevens' plants had significantly higher root to shoot ratios and lower leaf area ratios than `Ben Lear' plants, and produced more total root length than `Ben Lear' at all soil water potentials. Shallow rooting, high leaf area ratio, and low allocation to root production by `Ben Lear' plants may lead to greater susceptibility to drought stress than `Stevens' plants in poorly drained cranberry beds.

Nitrogen stress alters root proliferation in Douglas-fir seedlings

1990 ◽  
Vol 20 (9) ◽  
pp. 1524-1529 ◽  
Author(s):  
Alexander L. Friend ◽  
Marvin R. Eide ◽  
Thomas M. Hinckley
Keyword(s):  
Root Growth ◽  
Root System ◽  
Fine Roots ◽  
Fine Root ◽  
Douglas Fir ◽  
Chemical Activity ◽  
Nitrogen Stress ◽  
Root Proliferation ◽  
Whole Plant ◽  
Proliferation Response

The proliferation of roots in soil microenvironments was studied to gain an understanding of how nitrogen (N) stress affects root growth. By placing one major lateral root (<10% of the root system) of a Douglas-fir (Pseudotsugamenziesii (Mirb.) Franco) seedling into a small pot (microenvironment) and the remaining roots into a large pot, it was possible to manipulate the growth of a small part of the root system while having only minor effects on the growth of the entire seedling. Nitrogen stress was successfully induced by large-pot treatments and resulted in greatly decreased foliage growth and slightly decreased total fine (<2 mm diam.) root growth. Nitrogen stress had minimal effects on total fine root growth, but large effects on the distribution of growth within the root system. Fine roots grew preferentially in high compared with low N microenvironments, and root proliferation in high N microenvironments was enhanced twofold in N-stressed compared with nonstressed seedlings. The root proliferation response of Douglas-fir seedlings to N stress illustrates a potential means of N-stress compensation. It also implies that root distribution among soil microenvironments may depend not only upon chemical activity of nutrient ions in the rooting environment, but also upon nutrient stress in the whole plant.

Mathematical models of plant–soil interaction

2008 ◽  
Vol 366 (1885) ◽  
pp. 4597-4611 ◽  
Author(s):  
Tiina Roose ◽  
Andrea Schnepf
Keyword(s):  
Mathematical Models ◽  
Single Root ◽  
Advantages And Disadvantages ◽  
Plant Soil ◽  
Whole Plant ◽  
Scale Models ◽  
Food Shortages ◽  
Mathematical Techniques ◽  
Homogenization Methods

In this paper, we set out to illustrate and discuss how mathematical modelling could and should be applied to aid our understanding of plants and, in particular, plant–soil interactions. Our aim is to persuade members of both the biological and mathematical communities of the need to collaborate in developing quantitative mechanistic models. We believe that such models will lead to a more profound understanding of the fundamental science of plants and may help us with managing real-world problems such as food shortages and global warming. We start the paper by reviewing mathematical models that have been developed to describe nutrient and water uptake by a single root. We discuss briefly the mathematical techniques involved in analysing these models and present some of the analytical results of these models. Then, we describe how the information gained from the single-root scale models can be translated to root system and field scales. We discuss the advantages and disadvantages of different mathematical approaches and make a case that mechanistic rather than phenomenological models will in the end be more trustworthy. We also discuss the need for a considerable amount of effort on the fundamental mathematics of upscaling and homogenization methods specialized for branched networks such as roots. Finally, we discuss different future avenues of research and how we believe these should be approached so that in the long term it will be possible to develop a valid, quantitative whole-plant model.

scholarly journals Groundwater Solute Transport Modeling:Effects of Transport and Fate

2019 ◽  
Vol 8 (2) ◽  
pp. 3541-3544
Keyword(s):  
Analytical Solution ◽  
Solute Transport ◽  
Test Problem ◽  
Transport Model ◽  
Sorption Process ◽  
Solute Concentration ◽  
Matlab Software ◽  
Advection Dispersion ◽  
Saturated Media ◽  
Fate And Transport Modeling

In this paper, the solution of the advection-dispersion equation with different sorption values is used for the prediction of solute concentration in groundwater. Sorption process in the groundwater is complex, due to increasing the groundwater pollution the effect of different chemical transport plotted. The fate and sorption process of different chemical different degradation constant. We used the analytical solution to evaluate the transport phenomenon and analysis of the chemical dissolved in groundwater. The solute transport model simulated with the analytical solution and final result obtained using MATLAB software. The solution of a test problem based on the sequential degradation of the different chemical in the groundwater. This solution of equilibrium and rate of sorption dynamics of processes is imperative for accurate fate and transport modeling. The present study shows the effects of advection, dispersion/diffusion, and sorption equation on the saturated media of soil. MATLAB software used for analyzing the solution of groundwater and showing the different case taking care of saturated aquifer and with different void ratio of soil its shows that the soil parameter is also impotent parameter and its effect can see in plot between concertation vs time. The solute transport model simulated with the analytical solution and final result obtained using MATLAB software. The solution of a test problem based on the sequential degradation of the different chemical in the groundwater. This study compares the solute concentration with respect to distance and its different hydraulics conductivity of dense sad and lose.

The two-dimensional oscillations of straight vortex filaments with a power-law distribution of vorticity

1982 ◽  
Vol 384 (1786) ◽  
pp. 1-29 ◽  
Keyword(s):  
Asymptotic Analysis ◽  
Cross Section ◽  
Power Law ◽  
Circular Cross Section ◽  
Azimuthal Velocity ◽  
Two Dimensional ◽  
Power Law Distribution ◽  
Vortex Filaments ◽  
Single Root ◽  
Complex Roots

Straight vortex filaments are considered with a circular cross section, with zero vorticity outside a given radius a , and with a power-law distribution of vorticity within the radius a such that the azimuthal velocity varies like r β as a function of the radius r . It is shown that the vortices are stable to a two-dimensional disturbance if –1 < β < 1 and unstable if β > 1. Numerical values are given for the eigenvalue and compared with results obtained from asymptotic analysis in some limiting cases. The behaviour near β = 1 is discussed in some detail. Results are found for different values of the mode number m , but for each m and β it was only possible to find a single root or pair of conjugate complex roots.

Flow dependence of nonelectrolyte absorption in the nephron

1979 ◽  
Vol 236 (2) ◽  
pp. F163-F174 ◽  
Author(s):  
D. W. Barfuss ◽  
J. A. Schafer
Keyword(s):  
Lower Bound ◽  
Solute Transport ◽  
Axial Flow ◽  
Solute Concentration ◽  
Solute Flux ◽  
Perfusion Rate ◽  
Volume Absorption ◽  
Flow Dependence ◽  
Solute Absorption ◽  
Glomerulotubular Balance

The axial flow dependence of nonelectrolyte absorption was examined in terms of a model incorporating interactions between net volume absorption and both saturable and nonsaturable solute absorption. The model solutions demonstrated that changes in transepithelial solute transport are produced by changes in the average luminal solute concentration. Even passive non-saturable solute absorption was shown to exhibit dependence on the perfusion rate, and, therefore, on the solute delivery rate, which could be incorrectly interpreted as demonstrating the presence of a saturable absorptive mechanism. For a unidirectional lumen-to-bath solute flux mediated in part by a saturable mechanism, the observed flux is dependent on the permeability of any parallel nonsaturable permeation pathway. This permeability also sets a lower bound on the luminal solute concentration which may be achieved during active net solute absorption by determining the rate of passive solute backleak. Extension of the model to incorporate dependence of net volume absorption on the delivery of nonelectrolytes predicted a relationship between perfusion rate and net volume absorption equivalent to approximately one-third of complete glomerulotubular balance.

scholarly journals A Two-dimensional, Dynamic Model for Root Growth Distribution of Potted Plants

1993 ◽  
Vol 118 (2) ◽  
pp. 181-187 ◽  
Author(s):  
De-Xing Chen ◽  
J. Heinrich Lieth
Keyword(s):  
Spatial Distribution ◽  
Root Growth ◽  
Soil Water Potential ◽  
Extension Rate ◽  
Root Weight ◽  
Two Dimensional ◽  
Weight Density ◽  
Whole Plant ◽  
Root Weight Density ◽  
Growth Distribution

A two-dimensional mathematical model was developed to describe the time course of root growth and its spatial distribution for container-grown plants, using chrysanthemum [Dendranthema ×grandiflorum (Ramat.) Kitamura] as the model system. Potential root growth was considered as consisting of several concurrent processes, including branching, extension, and death. Branching rate was assumed to be related sigmoidally to existing root weight density. Root growth extension rate was assumed to be proportional to the existing root weight density above some threshold root weight density in adjacent cells. The senescence rate of root weight density was assumed to be proportional to existing root mass. The effects of soil matric potential and temperature on root growth were quantified with an exponential function and the modified Arrhenius equation, respectively. The actual root growth rate was limited by the amount of carbohydrate supplied by the canopy to roots. Parameters in the model were estimated by fitting the model to experimental data using nonlinear regression. Required inputs into the model included initial root dry weight density distribution, soil temperature, and soil water potential data. Being a submodel of the whole-plant growth model, the supply of carbohydrates from canopy to roots was required; the total root weight incremental rate was used to represent this factor. Rather than linking to a complex whole-plant C balance model, the total root weight growth over time was described by a logistic equation. The model was validated by comparing the predicted results with independently measured data. The model described root growth dynamics and its spatial distribution well. A sensitivity analysis of modeled root weight density to the estimated parameters indicated that the model was more sensitive to carbohydrate supply parameters than to root growth distribution parameters.

A Layer-Integrated Model of Solute Transport in Heterogeneous Media

2014 ◽  
Vol 6 (06) ◽  
pp. 699-717
Author(s):  
Hung-En Chen ◽  
Hui-Ping Lee ◽  
Shih-Wei Chiang ◽  
Tung-Lin Tsai ◽  
Jinn-Chuang Yang
Keyword(s):  
Solute Transport ◽  
Heterogeneous Media ◽  
Three Dimensional ◽  
Concentration Field ◽  
Quadratic Function ◽  
Integrated Approach ◽  
Solute Concentration ◽  
Two Dimensional ◽  
One Dimensional ◽  
Proposed Model

AbstractThis study presents a numerical solution to the three-dimensional solute transport in heterogeneous media by using a layer-integrated approach. Omitting vertical spatial variation of soil and hydraulic properties within each layer, a three-dimensional solute transport can be simplified as a quasi-three-dimensional solute transport which couples a horizontal two-dimensional simulation and a vertical one-dimensional computation. The finite analytic numerical method was used to discretize the derived two-dimensional governing equation. A quadratic function was used to approximate the vertical one-dimensional concentration distribution in the layer to ensure the continuity of concentration and flux at the interface between the adjacent layers. By integration over each layer, a set of system of equations can be generated for a single column of vertical cells and solved numerically to give the vertical solute concentration profile. The solute concentration field was then obtained by solving all columns of vertical cells to achieve convergence with the iterative solution procedure. The proposed model was verified through examples from the published literatures including four verifications in terms of analytical and experimental cases. Comparison of simulation results indicates that the proposed model satisfies the solute concentration profiles obtained from experiments in time and space.

scholarly journals Phoretic self-propulsion at large Péclet numbers

2015 ◽  
Vol 768 ◽  
Author(s):  
Ehud Yariv ◽  
Sébastien Michelin
Keyword(s):  
Boundary Layer ◽  
Rate Constant ◽  
Particle Velocity ◽  
Fourier Transforms ◽  
Solute Concentration ◽  
Solute Flux ◽  
Nonlinear Transport ◽  
Fixed Rate ◽  
Range Interaction ◽  
Advection Diffusion Equation

We analyse the self-diffusiophoresis of a spherical particle animated by a non-uniform chemical reaction at its boundary. We consider two models of solute absorption, one with a specified distribution of interfacial solute flux and one where this flux is governed by first-order kinetics with a specified distribution of rate constant. We employ a macroscale model where the short-range interaction of the solute with the particle boundary is represented by an effective slip condition. The solute transport is governed by an advection–diffusion equation. We focus upon the singular limit of large Péclet numbers, $\mathit{Pe}\gg 1$. In the fixed-flux model, the excess-solute concentration is confined to a narrow boundary layer. The scaling pertinent to that limit allows the problem governing the solute concentration to be decoupled from the flow field. The resulting nonlinear boundary-layer problem is handled using a transformation to stream-function coordinates and a subsequent application of Fourier transforms, and is thereby reduced to a nonlinear integral equation governing the interfacial concentration. Its solution provides the requisite approximation for the particle velocity, which scales as $\mathit{Pe}^{-1/3}$. In the fixed-rate model, large Péclet numbers may be realized in different limit processes. We consider the case of large swimmers or strong reaction, where the Damköhler number $\mathit{Da}$ is large as well, scaling as $\mathit{Pe}$. In that double limit, where no boundary layer is formed, we obtain a closed-form approximation for the particle velocity, expressed as a nonlinear functional of the rate-constant distribution; this velocity scales as $\mathit{Pe}^{-2}$. Both the fixed-flux and fixed-rate asymptotic predictions agree with the numerical values provided by computational solutions of the nonlinear transport problem.

Sign in / Sign up

Export Citation Format

Share Document