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In this paper we derive a model for the diffusion of strongly sorbed solutes in soil taking into account diffusion within both the soil fluid phase and the soil particles. The model takes into account the effect of solutes being bound to soil particle surfaces by a reversible nonlinear reaction. Effective macroscale equations for the solute movement in the soil are derived using homogenization theory. In particular, we use the unfolding method to prove the convergence of nonlinear reaction terms in our system. We use the final, homogenized model to estimate the effect of solute dynamics within soil particles on plant phosphate uptake by comparing our double-porosity model to the more commonly used single-porosity model. We find that there are significant qualitative and quantitative differences in the predictions of the models. This highlights the need for careful experimental and theoretical treatment of plant-soil interaction when trying to understand solute losses from the soil

Topics:
TA

Year: 2010

OAI identifier:
oai:eprints.soton.ac.uk:145121

Provided by:
e-Prints Soton

Downloaded from
http://dx.doi.org/10.1137/080729591

- (1989). A general Convergence Result for a Functional related to the Theory of Homogenization.
- (2001). A mathematical model of plant nutrient uptake.
- (1996). Convergence of the homogenization process for a double-porosity model of immiscible two-phase ﬂow.
- (2008). Derivationo fam a c r o s c o p i cr e c e p t o r - b a s e dm o d e lu s i n gh o m o g e -nization techniques.
- (2009). Di usion of strongly-sorbed solutes in soil: experimental testing of dual porosity model.
- (2009). Di usion ofs t r o n g l ys o r b e ds o l u t e si ns o i l :ad u a lp o r o s i t ym o d e l allowing for slow access to sorption sites and time-dependent sorption reactions.
- (1991). Di usion, Convection, Adsorption and Reaction of Chemicals in Porous Media.
- (2007). E ective transmission conditions for reaction-di usion processes in domains separated by an interface.
- (1992). Homogenization and two-scale convergence.
- (1979). Homogenization in Open Sets with Holes.
- (1968). Linear and Quasi-linear Equations of Parabolic Type.A m e r i c a nM a t h e m a t i c a lS o c i e t y .
- (1991). Modeling of naturally fractured reservoirs by formal homogenization techniques. Frontiers in Pure and
- (1972). Non-homogeneous boundary values problems and applications.
- (2000). On an extension of the method of two-scale convergence and its applications.
- (2006). Periodic unfolding and Robin problems in perforated domains.
- (2002). Periodicu n f o l d i n ga n dh o m o g e n i z a t i o n .C.
- (1969). Quelques m´ ethodes de r´ esolution des probl` emes aux limites non lin´ eaires.D u n o d ,P a r i s .
- (1994). Reactive transport through an array of cells with semi-permeable membranes.
- (1994). Shock-Waves and Reaction-Di usion Equations.S p r i n g e r - V e r l a g ,N e wY o r k .
- (1984). Soil Nutrient Bioavailability. A Mechanistic Approach.
- (2000). Solute movement in the rhizosphere.O x f o r dU n i v e r s i t yP r e s s ,N e wY o r kO x f o r d .
- (1996). Some extensions of two-scale convergence.
- (1994). The self-di usion of strongly adsorbed anions in soil: two-path model to simulate restricted access to exchange sites.
- (1996). Two-scalec o n v e r g e n c eo np e r i o d i cs u r f a c e sa n da p p l i c a t i o n s .

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