Derivation of a dual porosity model for the uptake of nutrients by root hairs

Root hairs are thought to play an important role in mediating nutrient uptake by plants. We develop a mathematical model for the nutrient transport and uptake in the root hair zone of a single root in the soil. Nutrients are assumed to diffuse both in the soil fluid phase and within the soil particles. Nutrients can also be bound to the soil particle surfaces by reversible reactions. Using homogenization techniques we derive a macroscopic dual porosity model for nutrient diffusion and reaction in the soil which includes the effect of all root hair surfaces

Homogenization of two fluid flow in porous media

The macroscopic behavior of air and water in porous media is often approximated using Richards’ equation for the fluid saturation and pressure. This equation is parametrized by the hydraulic conductivity and water release curve. In this paper, we use homogenization to derive a general model for saturation and pressure in porous media based on an underlying periodic porous structure. Under an appropriate set of assumptions, i.e., constant gas pressure, this model is shown to reduce to the simpler form of Richards’ equation. The starting point for this derivation is the Cahn-Hilliard phase field equation coupled with Stokes equations for fluid flow. This approach allows us, for the first time, to rigorously derive the water release curve and hydraulic conductivities through a series of cell problems. The method captures the hysteresis in the water release curve and ties the macroscopic properties of the porous media to the underlying geometrical and material properties

Mathematical models of avascular cancer

This review will outline a number of illustrative mathematical models describing the growth of avascular tumours. The aim of the review is to provide a relatively comprehensive list of existing models in this area and discuss several representative models in greater detail. In the latter part of the review, some possible future avenues of mathematical modelling of avascular tumour development are outlined together with a list of key questions

Mathematical models of avascular cancer

This review will outline a number of illustrative mathematical models describing the growth of avascular tumours. The aim of the review is to provide a relatively comprehensive list of existing models in this area and discuss several representative models in greater detail. In the latter part of the review, some possible future avenues of mathematical modelling of avascular tumour development are outlined together with a list of key questions

PCBs in cod (<i>Gadus morhua</i>), flounder (<i>Platichthys flesus</i>), blue mussel (<i>Mytilus edulis</i>) and brown shrimp (<i>Crangon crangon</i>) from the Belgian Continental Shelf: relation to biological parameters and trend analysis

PCB levels in cod, flounder, mussel and shrimp, covering a ten-year period, were assessed for temporal trends and their relation to biological parameters. A significant relation was found between the PCB levels on a wet weight basis and the total lipid content. Normalising on the total lipid content reduced the differences in PCB levels between the organisms and between different tissues within the organisms. A general downward trend was observed for the PCB levels on the Belgian continental shelf

PCBs in cod (<i>Gadus morhua</i>), flounder (<i>Platichthys flesus</i>), blue mussel (<i>Mytilus edulis</i>) and brown shrimp (<i>Crangon crangon</i>) from the Belgian Continental Shelf: relation to biological parameters and trend analysis

PCB levels in cod, flounder, mussel and shrimp, covering a ten-year period, were assessed for temporal trends and their relation to biological parameters. A significant relation was found between the PCB levels on a wet weight basis and the total lipid content. Normalising on the total lipid content reduced the differences in PCB levels between the organisms and between different tissues within the organisms. A general downward trend was observed for the PCB levels on the Belgian continental shelf

Adsorption and desorption dynamics of citric acid anions in soil

The functional role of organic acid anions (e.g. citrate, oxalate, malonate, etc) in soil has been intensively investigated with special focus either on (i) microbial respiration and soil carbon dynamics, (ii) nutrient solubilization, or (iii) metal detoxification. Considering the potential impact of sorption processes on the functional significance of these effects, comparatively little is known about the adsorption and desorption dynamics of organic acid anions in soils. The aim of this study therefore was to experimentally characterize the adsorption and desorption dynamics of organic acid anions in different soils using citrate as a model carboxylate. Results showed that both adsorption and desorption processes were fast, reaching a steady state equilibrium solution concentration within approximately 1 hour. However, for a given total soil citrate concentration(ctot) the steady state value obtained was critically dependent on the starting conditions of the experiment (i.e. whether most of the citrate was initially present in solution (cl) or held on the solid phase (cs)). Specifically, desorption-led processes resulted in significantly lower equilibrium solution concentrations than adsorption led processes indicating time-dependent sorption hysteresis. As it is not possible to experimentally distinguish between different sorption pools in soil (i.e. fast, slow, irreversible adsorption/desorption), a new dynamic hysteresis model was developed that relies only on measured soil solution concentrations. The model satisfactorily explained experimental data and was able to predict dynamic adsorption and desorption behaviour. To demonstrate its use we applied the model to two relevant scenarios (exudation and microbial degradation), where the dynamic sorption behaviour of citrate occurs. Overall, this study highlights the complex nature of citrate sorption in soil and concludes that existing models need to incorporate both a temporal and sorption hysteresis component to realistically describe the role and fate of organic acids in soil processes