In plants, the delivery of the products of photosynthesis is achieved through a hydraulic system labeled as phloem. This semi-permeable plant tissue consists of living cells that contract and expand in response to fluid pressure and flow velocity fluctuations. The Münch pressure flow theory, which is based on osmosis providing the necessary pressure gradient to drive the mass flow of carbohydrates, is currently the most accepted model for such sucrose transport. When this hypothesis is combined with the conservation of fluid mass and momentum as well as sucrose mass, many simplifications must be invoked to mathematically close the problem and to resolve the flow. This study revisits such osmotically driven flows by developing a new two-dimensional numerical model in cylindrical coordinates for an elastic membrane and a concentration-dependent viscosity. It is demonstrated that the interaction between the hydrodynamic and externally supplied geometrical characteristic of the phloem has a significant effect on the front speed of sucrose transport. These results offer a novel perspective about the evolutionary adaptation of plant hydraulic traits to optimize phloem soluble compounds transport efficiency.
more »
« less
Taylor dispersion in osmotically driven laminar flows in phloem
Sucrose is among the main products of photosynthesis that are deemed necessary for plant growth and survival. It is produced in the mesophyll cells of leaves and translocated to different parts of the plant through the phloem. Progress in understanding this transport process remains fraught with experimental difficulties, thereby prompting interest in theoretical approaches and laboratory studies. The Münch pressure and mass flow model is one of the accepted hypotheses describing the physics of sucrose transport in the phloem. It is based on osmosis creating an energy potential difference between the source and the sink. The flow responding to this energy potential is assumed laminar and described by the Hagen–Poiseuille equation. This study revisits such osmotically driven flows in tubes with membrane walls by including the effects of Taylor dispersion on mass transport. This effect has been overlooked in phloem flow studies. Taylor dispersion can increase the effective transport of solutes by increasing the apparent diffusion coefficient. It is shown that, in addition to the conventional diffusive correction derived for impermeable tube walls, a new adjustment to the mean advective terms arises because of osmotic effects. Because the molecular Schmidt number is very large for sucrose in water, the sucrose front speed and travel times have a direct dependence on the Péclet number for different ranges of the Münch number. This study establishes upper limits on expected Taylor dispersion enhancement of sucrose transport.
more »
« less
- NSF-PAR ID:
- 10217417
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 913
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
more » « less
Abstract The significance of phloem hydrodynamics to plant mortality and survival, which impacts ecosystem‐scale carbon and water cycling, is not in dispute. The phloem provides the conduits for products of photosynthesis to be transported to different parts of the plant for consumption or storage. The M
nch pressure flow hypothesis (PFH) is the leading framework to mathematically represent this transport. It assumes that osmosis provides the necessary pressure differences to drive water and sucrose within the phloem. Mathematical models utilizing the PFH approximate the phloem by a relatively rigid slender semi‐permeable tube. However, the phloem consists of living cells that contract and expand in response to pressure fluctuations. The effect of membrane elasticity on osmotically driven sucrose front speed has rarely been considered and frames the scope here. Laboratory experiments were conducted to elucidate the elastic‐to‐plastic pressure‐deformation relation in membranes and their effect on sucrose front speeds. It is demonstrated that membrane elasticity acts to retard the sucrose front speed. The retardation emerges because of two effects: (a) part of the osmotic pressure is diverted to perform mechanical work to expand the membrane instead of pressurizing water, and (b) expansion of the membrane reduces the sucrose concentration driving osmotic potential due to volume increases and concomitant dilution effects. These results offer a novel perspective about the much discussed presence of sieve plates throughout the phloem acting as structural expansion dampers. -
more » « less
Summary A robust understanding of phloem functioning in tall trees evades us because current methods for collecting phloem sap do not lend themselves to measuring actively photosynthesizing canopy leaves.
We show that Raman spectroscopy can be used as a quantitative tool to assess sucrose concentration in leaf samples. Specifically, we found that Raman spectroscopy can predict physiologically relevant sucrose concentrations (adjusted
R 2of 0.9) in frozen leaf extract spiked with sucrose.We then apply this method to estimate sieve element sucrose concentration in rapidly frozen petioles of canopy red oak (
Quercus rubra) trees and found that sucrose concentrations are > 1100 mM at midday and midnight. This concentration is predicted to generate a sieve element turgor pressure high enough to generate bulk flow through the phloem, but is potentially too high to allow for sucrose diffusion from photosynthetic cells.Our findings support the Münch hypothesis for phloem transport once the carbon is in the phloem and challenge the passive‐loading hypothesis for carbon movement into the phloem for red oak. This study provides the first ˜
in‐situ (frozen in the functioning state) source sieve element sucrose concentration characterization in any plant, opening a new avenue for investigation of phloem functioning. -
Radial–axial transport coordination enhances sugar translocation in the phloem vasculature of plantsmore » « less
Abstract Understanding mass transport of photosynthates in the phloem of plants is necessary for predicting plant carbon allocation, productivity, and responses to water and thermal stress. Several hypotheses about optimization of phloem structure and function and limitations of phloem transport under drought have been proposed and tested with models and anatomical data. However, the true impact of radial water exchange of phloem conduits with their surroundings on mass transport of photosynthates has not been addressed. Here, the physics of the Munch mechanism of sugar transport is re-evaluated to include local variations in viscosity resulting from the radial water exchange in two dimensions (axial and radial) using transient flow simulations. Model results show an increase in radial water exchange due to a decrease in sap viscosity leading to increased sugar front speed and axial mass transport across a wide range of phloem conduit lengths. This increase is around 40% for active loaders (e.g. crops) and around 20% for passive loaders (e.g. trees). Thus, sugar transport operates more efficiently than predicted by previous models that ignore these two effects. A faster front speed leads to higher phloem resiliency under drought because more sugar can be transported with a smaller pressure gradient.
-
Permeable and porous surfaces are common in natural and engineered systems. Flow and transport above such surfaces are significantly affected by the surface properties, e.g. matrix porosity and permeability. However, the relationship between such properties and macroscopic solute transport is largely unknown. In this work, we focus on mass transport in a two-dimensional channel with permeable porous walls under fully developed laminar flow conditions. By means of perturbation theory and asymptotic analysis, we derive the set of upscaled equations describing mass transport in the coupled channel–porous-matrix system and an analytical expression relating the dispersion coefficient with the properties of the surface, namely porosity and permeability. Our analysis shows that their impact on the dispersion coefficient strongly depends on the magnitude of the Péclet number, i.e. on the interplay between diffusive and advective mass transport. Additionally, we demonstrate different scaling behaviours of the dispersion coefficient for thin or thick porous matrices. Our analysis shows the possibility of controlling the dispersion coefficient, i.e. transverse mixing, by either active (i.e. changing the operating conditions) or passive mechanisms (i.e. controlling matrix effective properties) for a given Péclet number. By elucidating the impact of matrix porosity and permeability on solute transport, our upscaled model lays the foundation for the improved understanding, control and design of microporous coatings with targeted macroscopic transport features.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2021.56
