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Published in J. Environ. Qual. 33:1393-1402 (2004).
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TECHNICAL REPORTS

Plant and Environment Interactions

Phosphorus Desorption Dynamics in Soil and the Link to a Dynamic Concept of Bioavailability

G. F. Koopmansa,*, W. J. Chardona, P. de Willigena and W. H. van Riemsdijkb

a Alterra, Wageningen University and Research Centre (WUR), P.O. Box 47, 6700 AA, Wageningen, the Netherlands
b Department of Soil Quality, Wageningen University, WUR, P.O. Box 8005, 6700 EC, Wageningen, the Netherlands

* Corresponding author (gerwin.koopmans{at}wur.nl).

Received for publication October 22, 2003.

   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Soils under intensive livestock farming and heavily fertilized with animal manure may have elevated soil phosphorus (P) contents. We determined P desorption kinetics in batch experiments using soils from a pot experiment where grass was cropped on a P-rich noncalcareous sandy soil without P addition, to lower the soil P content. A diffusion model was used to describe P desorption kinetics from a spherical aggregate. The model was calibrated with data from the batch experiments. Simulation results show that in the pot experiment, P desorption from the solid phase of the inner layers was initially far from equilibrium with the rest of the aggregate, but desorption came closer to equilibrium as the soil P content decreased further. A simple tool is presented, referred to as the dynamic bioavailability index (DBI), to determine whether kinetics of P desorption limits plant uptake. This tool is the dimensionless ratio of the modeled maximal diffusive flux from soil aggregates to solution and the plant uptake rate measured in the pot experiment. The DBI was initially much larger than one; the maximal possible P desorption rate exceeded the uptake rate, so uptake was not limited by desorption. The DBI stabilized at a value somewhat larger than one after a while, due to soil transport limitations. This decrease coincided with a large decrease of the P content in the grass to a value (far) below what is considered as optimal; the supply rate of P from soil to the root cannot meet the demand needed for optimal P uptake. The DBI could be seen as a promising onset to a new dynamic approach of bioavailability.

Abbreviations: (Al + Fe)ox, sum of amorphous aluminum- and iron-(hydr)oxides • DBI, dynamic bioavailability index • Pox, ammonium oxalate–extractable phosphorus


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
IN AREAS with intensive livestock farming, soils are often enriched with P as a result of decades of P addition, via animal manure, exceeding P removal in harvested crops (e.g., Breeuwsma et al., 1995; Pautler and Sims, 2000). In the Netherlands, intensive livestock farming takes place mainly on noncalcareous sandy soils. In soils treated with large amounts of animal manure, P mainly accumulates in the inorganic form (Sharpley et al., 1984; Koopmans et al., 2003). Amorphous Al- and Fe-(hydr)oxides are the main reactive solid phases in noncalcareous sandy soils (Beek, 1979). The overall reaction of inorganic P with Al- and Fe-(hydr)oxides can be divided into a fast reversible adsorption reaction at surface sites with a reaction time of <1 d and a slow one, that is, (reactive) diffusion through the solid phase or through micropores of these metal-(hydr)oxides possibly followed by precipitation and/or adsorption inside the aggregates (van Riemsdijk and Lyklema, 1980; Barrow, 1983; van Riemsdijk et al., 1984; Madrid and De Arambarri, 1985). The total pool of sorbed P in noncalcareous sandy soils has been interpreted to be the sum of reversibly adsorbed P and quasi-irreversibly bound P (van der Zee et al., 1987; van der Zee and van Riemsdijk, 1988). Filter paper strips impregnated with iron oxide have been proposed to determine the amount of reversibly adsorbed phosphorus (FeO-P) (van der Zee et al., 1987). The acid ammonium oxalate extraction method of Schwertmann (1964) has been used to determine both the total pool of sorbed phosphorus (Pox) as well as amorphous (hydr)oxides of aluminum and iron [(Al + Fe)ox]. The sum of these metal-(hydr)oxides determines the total sorption capacity of inorganic P in noncalcareous sandy soils (Beek, 1979; van der Zee and van Riemsdijk, 1988). The reversibility of the overall reaction of P with the solid phase of the soil is of both agricultural and environmental interest. Because of the often limited availability of P for plant uptake in soils with a low input of P, a better understanding of the desorption kinetics of P from soil may help maintaining optimal soil fertility for crop production. On the other hand, in areas with intensive livestock farming, where soils have been enriched with P, accumulation of P can lead to saturation of the soil with P and environmental problems such as eutrophication of surface waters resulting from (subsurface) leaching of soil solution with a high P concentration (e.g., Breeuwsma et al., 1995; Sims et al., 1998; Schoumans and Groenendijk, 2000).

Upon the removal of P from soil solution by plant uptake, a fast initial desorption reaction for P adsorbed to surface sites of Al- and Fe-(hydr)oxides is expected (van der Zee et al., 1987). The decrease of P adsorbed to surface sites may be replenished by desorption of P bound inside Al- and Fe-(hydr)oxides followed by diffusion of P to the outer layers of the aggregates (Barrow, 1983). Because intra-aggregate diffusion is slow, this P becomes available again only in the long term. The importance of intra-aggregate diffusion as the rate-limiting step in the mass transfer of reactive solutes between sorption sites inside porous sorbents and bulk solution was also demonstrated for various metals (Trivedi and Axe, 2000; Lin and Wu, 2001) and organic compounds (Wu and Gschwend, 1986; Rijnaarts et al., 1990). Therefore, this mechanism may be very important in controlling the bioavailability and transport of various reactive solutes in soils. Intra-aggregate diffusion should be considered if realistic models are to be used to model long-term (de)sorption processes of reactive solutes in soil.

Quantitative information about the reversibility of the overall reaction of P in P-enriched soils in the long term is scarce. A desorption isotherm, describing the long-term equilibrium relationship between P in soil solution and the total pool of sorbed P, can be used to estimate the total amount of P available for plant uptake and leaching. However, these relationships are difficult to determine experimentally, because of the slow desorption kinetics and other more practical problems (van der Zee et al., 1987; Freese et al., 1995). Furthermore, in the field, kinetic factors may lead to a lower availability of P than would be estimated from the equilibrium desorption isotherm. Knowledge about the equilibrium situation is nevertheless required before one can do a useful analysis of the P desorption kinetics. Koopmans et al. (2004) recently determined a desorption isotherm using a long-term pot experiment, where grass was cropped on a P-rich noncalcareous sandy soil without P addition as a means to lower the amount of P sorbed to the soil. The total pool of sorbed P, estimated by Pox, appeared to be close to equilibrium with P in 1:10 (w/v) 0.01 M CaCl2 extracts used to simulate conditions in the soil solution (McDowell and Sharpley, 2001). The Langmuir equation gave a very good description of the obtained relationship. These CaCl2 extracts were obtained from soil samples taken at various stages of the pot experiment using 2 h of very vigorous shaking (Houba et al., 1986). The vigor of shaking in batch systems is very important in the mass transfer of reactive solutes between sorption sites inside porous sorbents and bulk solution; at very vigorous shaking, only the reaction of the solute may be the rate-limiting step (Ogwada and Sparks, 1986a, 1986b). This may for instance be due to abrasion of soil aggregates leading to (much) shorter diffusion distances causing an increase of the mass transfer rate of the reactive solute, resulting in a faster establishment of equilibrium. This mechanism may have been responsible for the apparent equilibrium of P desorption in the CaCl2 extracts obtained from the soils of the pot experiment of Koopmans et al. (2004). This hypothesis is supported by results of van Erp et al. (1998); at an extraction time longer than 2 h, the P concentration measured in 1:10 (w/v) 0.01 M CaCl2 extracts determined according to Houba et al. (1986) did not further increase, indicating that equilibrium was reached. The apparent equilibrium of the P desorption isotherm cannot be used to determine whether the desorption processes of P from Al- and Fe-(hydr)oxides inside intact soil aggregates were near equilibrium during the growth of plants that continuously remove P from the soil solution. This requires a dynamic modeling approach of the P desorption kinetics for conditions where the soil aggregates are not degraded by vigorous shaking during the measurement of P desorption. Therefore, we decided to determine P desorption kinetics in batch experiments under more mild shaking conditions using some of the soils that were used to determine the equilibrium desorption isotherm in the pot experiment. For the modeling of the data, we used the simplifying assumption that the soil consists of a collection of spherical aggregates of equal size and composition. The reactive diffusive transport of P in the soil aggregates is calculated with the additional assumption that the diffusion in the soil aggregates is the rate-limiting step. The Langmuir equation is used to calculate the buffering behavior of P sorbed to the solid phase and the (local) solution in the micropores. In studies of Wu and Gschwend (1986), Rijnaarts et al. (1990), and Lin and Wu (2001), a similar modeling approach was used to simulate (de)sorption processes of reactive solutes in porous sorbents. The diffusion model was calibrated with the data from the batch experiments. The calibrated model was then used to simulate the distribution of P inside the soil aggregates during plant growth in the pot experiment using some simplifying assumptions. Whether or not kinetic factors may limit the bioavailability of P for plant uptake can be estimated using a dimensionless ratio of the maximal diffusive flux from the soil aggregates to the soil solution, which can be calculated with the model, and the flux that is required to obtain an optimal P content in the growing plants in the same units. This dimensionless ratio, which we will refer to as the dynamic bioavailability index (DBI), is expected to change during the long-term pot experiment. The same ratio can also be calculated by using the measured rate of plant uptake of P at a certain stage in the pot experiment instead of the flux that is required to obtain an optimal P content in the growing plants. Furthermore, the diffusion model is used to gain more insight in the 1:10 (w/v) 0.01 M CaCl2 method (Houba et al., 1986), which is a procedure to analyze the P status of agricultural soils.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Summary of the Pot Experiment
Koopmans et al. (2004) performed a pot experiment where ryegrass (Lolium perenne L.) was cropped over 978 d on a P-rich loamy noncalcareous sandy soil without P addition. The soil was sampled from the tillage layer (0–30 cm) of a plot from a long-term field experiment and received large applications of pig slurry in the past (see Del Castilho et al. [1993]). The pot experiment was performed in a greenhouse. There were two treatments: in a pot with a volume of 2.5 L, soil was placed in a layer of either 5 or 10 cm thickness. To prevent N and K limitation of plant growth, N and K were regularly added. Grass was harvested 31 times, at an interval of 19 to 47 d. Dry weight and total P content of the harvested grass were determined. At various stages of the pot experiment, soil of two pots per treatment (duplicate pots) was destructively sampled (22, 41, 88, 151, 236, 319, 692, and 978 d). Soil was dried at 40°C and passed through a 2-mm sieve. For an extensive description of the setup of the pot experiment, see Koopmans et al. (2004). The pH and organic matter content were determined according to Houba et al. (1997). Phosphorus in soil solution was estimated using 1:10 (w/v) 0.01 M CaCl2 extracts (Houba et al., 1986). The CaCl2 extracts were shaken on a reciprocating shaker at 165 strikes per minute (spm). After centrifugation (1800 x g), P was measured colorimetrically (Murphy and Riley, 1962). Reversibly adsorbed P was estimated using a modified FeO strip method of van der Zee et al. (1987); see Koopmans et al. (2004) for details. The total pool of sorbed P was estimated using the acid ammonium oxalate extraction method of Schwertmann (1964). Concentrations of P, Al, and Fe were measured using inductively coupled plasma atomic emission spectroscopy.

Phosphorus Desorption Kinetics
The initial soil and soils from the 5- and 10-cm treatments of the pot experiment sampled after 151 and 978 d of plant uptake of P were used. For the soils sampled after 151 and 978 d, the soil of only one of the duplicate pots was used. Soil was incubated in duplicate with 0.01 M CaCl2 at soil to solution ratios of 1:10, 1:50, 1:100, 1:500, and 1:1000 (w/v). To prevent biological activity, 0.5 mL of a 2% (w/v) sodium azide (NaN3) solution was added. Soil suspensions were shaken in a relatively mild motion on a reciprocating shaker at 75 spm for 3, 24, 48, 96, and 408 h. After filtration over a 0.45-µm filter, P was measured colorimetrically (Murphy and Riley, 1962).

Model
The numerical model was developed by Chardon and de Willigen (1997). The soil is assumed to consist of a collection of spherical aggregates of equal size and composition. Linquist et al. (1997) demonstrated the importance of the size of soil aggregates for P sorption. To represent the soil, the model uses one spherical aggregate divided into 50 concentric parts of equal mass. Sorption sites are distributed uniformly through the aggregate. Sorption or desorption of P occurs instantaneously according to the Langmuir equation:

[1]
where Q is the amount of P sorbed to the soil (mg P kg–1), Qmax is the sorption maximum (mg P kg–1), K is a constant describing the affinity of the soil for P (L mg–1), and C is the P concentration (mg P L–1). Intra-aggregate diffusion of P is considered as the rate-limiting step in P desorption. Transport of P within the aggregate is caused by diffusion described by Fick's first law:

[2]
where F is the flux of solute (mg P dm–2 s–1), De is the diffusion coefficient of P in water corrected for the volume of the micropores within the aggregate (dm2 s–1), and r is the radial coordinate (dm). The effective diffusion coefficient De is assumed to decrease with the volume of water-filled micropores according to:

[3]
where {theta} is the water-filled pore volume fraction of the aggregate (unitless) and D is the diffusion coefficient of P in free water (dm2 s–1). Furthermore, there is no external limitation in the mass transfer of P from the aggregate to the bulk solution. Under static conditions in batch experiments, diffusion of P through a nonturbulent external film of water adhering to and surrounding porous sorbents may be the rate-limiting step in the mass transfer of reactive solutes. However, under nonstatic conditions resulting from shaking, the effect of film diffusion as the rate-limiting step may be strongly decreased (Ogwada and Sparks, 1986a, 1986b; Rijnaarts et al., 1990). Table 1 shows the parameters used in the model. The values of Qmax and K used in the model were derived from the desorption isotherm determined in the pot experiment.


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  		Table 1. Parameter values used in the diffusion model.

 
For the total amount of P initially present in the aggregate, we used the sum of the total pool of sorbed P and P desorbed in the CaCl2 extract of the initial soil. The total pool of sorbed P was calculated from the Langmuir equation determined in the pot experiment where the measured P concentration in the CaCl2 extract of the initial soil was used as an input variable. The initial distribution of the total amount of P over the solution in the micropores and the solid phase of the aggregate was calculated from the mass balance:

[4]
where T is the total amount of P initially present (mg P), g is the weight of the aggregate (kg), and v is the volume of the micropores (L). The Langmuir equation can be substituted for Q in the mass balance (van Noordwijk et al., 1990), after which Eq. [4] can be solved analytically for C (see Koopmans et al. [2002]). Subsequently, the initial P concentration in the micropores and the corresponding amount of P sorbed to the solid phase were calculated.

The ratio {alpha} between Pox and (Al + Fe)ox (both expressed in mmol kg–1) is a measure of the degree of P saturation of a soil with respect to its content of amorphous Al- and Fe-(hydr)oxides (van der Zee and van Riemsdijk, 1988). The {alpha} of the initial soil was 0.42, which is close to the {alpha}max of 0.46 derived from the Langmuir equation determined in the pot experiment (Koopmans et al., 2004). The Al- and Fe-(hydr)oxides of the initial soil were thus nearly saturated with P, indicating that the P initially present was distributed uniformly through the aggregate.

In the model, P desorption with time can be simulated by the presence of an external solution surrounding the aggregate with an initially zero P concentration. The soil to solution ratio of the external solution can be varied. The data from the batch experiments, where the kinetics of P desorption from the initial soil were determined, were used to calibrate the model using the pore volume fraction of the aggregate as a fitting parameter. Plant uptake of P measured in the 5- and 10-cm treatments of the pot experiment was simulated to determine whether P desorption from Al- and Fe-(hydr)oxides inside soil aggregates reached equilibrium. Phosphorus desorbed to the soil solution was removed in the model with a rate according to the measured plant uptake of P. Soil solution was simulated by the addition of an external solution with a soil to solution ratio of 1:0.3 (w/v), which may be representative for conditions in the soil. To calculate the maximal P desorption rate, the P concentration in an external solution with a soil to solution ratio of 1:0.3 (w/v) was maintained at zero to facilitate continuous maximal P desorption. To simulate the results of the batch experiments and to calculate the maximal P desorption rate for the soils sampled after 151 and 978 d of plant uptake of P, the same procedures were followed as described above for an aggregate after 151 and 978 d of simulation of plant uptake.


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
CONCLUSIONS
 REFERENCES
 
Pot Experiment
Table 2 shows some results of soil extractable P obtained in the pot experiment of Koopmans et al. (2004). In the soils of the 5- and 10-cm treatments, the P concentration in the 1:10 (w/v) 0.01 M CaCl2 extracts measured according to Houba et al. (1986) had decreased by 93 and 91% after 978 d of continuous cropping of grass. The amount of P extractable with an FeO strip decreased by 83 and 72%, respectively. The relative decrease of Pox was much smaller; Pox decreased by 48 and 32% in the soils of the 5- and 10-cm treatments, respectively. The (Al + Fe)ox content remained relatively constant as expected. The ratio {alpha} between Pox and (Al + Fe)ox of the initial soil was 0.42 and decreased with time to 0.23 and 0.28, respectively.


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  		Table 2. Selected characteristics and soil extractable P from the initial soil and soils of the 5- and 10-cm treatments.{dagger}

 
Phosphorus Desorption Isotherm and Desorption Kinetics
Figure 1 shows the desorption isotherm using the soils from the pot experiment, where the uptake of P by the growing plants leads to P desorption. The isotherm was constructed by plotting Pox of the initial soil and the soils of the 5- and 10-cm treatments after various periods of plant growth against P measured in 1:10 (w/v) 0.01 M CaCl2 extracts. The Langmuir equation fitted very well to these data points. The CaCl2 extracts were obtained after 2 h of very vigorous shaking. The vigor of shaking in batch systems is very important in the mass transfer of reactive solutes between sorption sites inside porous sorbents and bulk solution (Ogwada and Sparks, 1986a, 1986b). This was also demonstrated in a P sorption study of Barrow and Shaw (1979); vigorous shaking caused abrasion of soil particles leading to the exposure of new surface sites and greater P sorption. Vigorous shaking thus leads to shorter diffusion distances causing an increase of P (de)sorption rates, resulting in a faster establishment of equilibrium. Vigorous shaking during the CaCl2 extraction may thus have caused the equilibrium of the desorption isotherm. The fact that equilibrium may have been reached in the CaCl2 extracts is thus not necessarily indicative that P desorption from Al- and Fe-(hydr)oxides inside intact soil aggregates was near equilibrium. The situation prevailing in the soil will be later analyzed using the diffusion model. Furthermore, Fig. 1 shows the results of the batch experiments where the kinetics of P desorption were determined. Similar to the isotherm, Pox was plotted against P desorbed in 1:10 (w/v) 0.01 M CaCl2 extracts as a function of time. To prevent abrasion of soil aggregates, we chose a relatively mild shaking method in the batch experiments. Under these shaking conditions, intra-aggregate diffusion may be expected to act as the rate-limiting step in P desorption. Thus, the most important experimental difference between the data points used to construct the isotherm and the data points representing the results of the batch experiments is the vigor of shaking. The kinetics of P desorption is most clearly visible for a higher P concentration in the CaCl2 extracts, where the equilibrium isotherm is approached only for the batch experiment with the longest duration (408 h). However, at a low P concentration, kinetic effects are hardly visible.



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  		Fig. 1. Desorption isotherm of the soils of the pot experiment (Koopmans et al., 2004) describing the relationship between the P concentration measured in 1:10 (w/v) 0.01 M CaCl2 extracts (vigorous shaking) and the total pool of sorbed P (open symbols). The Langmuir equation was fitted to the data. Furthermore, the total pool of sorbed P is plotted against the P concentration as a function of time measured in 1:10 (w/v) 0.01 M CaCl2 extracts obtained under mild shaking conditions in the batch experiments (closed symbols).

 
In Fig. 2, experimental and model results are shown for the P desorption kinetics of the initial soil at varying soil to solution ratios, whereas Fig. 3 shows results of the 1:10 (w/v) 0.01 M CaCl2 extracts obtained from the soils taken from the pot experiment after plant uptake of P for 151 and 978 d. The model was calibrated with the pore volume fraction of the aggregate as a fitting parameter to predict the data presented in Fig. 2. We assumed a uniform radius of the soil aggregates of 1 mm, because the soil was sieved through a 2-mm sieve. The model describes the increase in the P concentration with time, using a radius of 1.0 mm and a fitted pore volume fraction of 0.035, quite well for the 1:10, 1:50, and 1:100 (w/v) 0.01 M CaCl2 extracts obtained from the initial soil. For the soil to solution ratios of 1:500 and 1:1000 (w/v), the model predictions are less accurate. The model gives a reasonable prediction of the P concentration in the 1:10 (w/v) 0.01 M CaCl2 extracts obtained from the soils of the 5- and 10-cm treatments sampled after 151 and 978 d of plant uptake of P.



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  		Fig. 2. Measured (symbols) and predicted P concentrations (lines) in 0.01 M CaCl2 extracts with varying soil to solution ratios as a function of time at a fitted pore volume fraction of 0.035. The CaCl2 extracts were obtained from the initial soil under mild shaking conditions in the batch experiments. The open triangle represents the P concentration measured in the 1:10 (w/v) 0.01 M CaCl2 extract with vigorous shaking. The dotted line represents the predicted P concentration at a soil to solution ratio of 1:10 (w/v) whereby the radius of the spherical aggregate was set at 0.1 mm.

 


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  		Fig. 3. Measured (symbols) and predicted P concentrations (lines) in 1:10 (w/v) 0.01 M CaCl2 extracts as a function of time. The CaCl2 extracts were obtained from the soils of the 5- and 10-cm treatments sampled after 151 and 978 d of plant uptake of P in the batch experiments.

 
Figure 4 shows the simulation of the P concentration in the micropores of the 50 concentric parts of the aggregate representing the initial soil incubated at a soil to solution ratio of 1:10 (w/v) as a function of time for relatively mild shaking conditions. The P concentration in the outer layers of the aggregate shows a fast decrease, due to an initially high P desorption rate. After 41 h, the P concentration in the outer layer decreased by 42%. This can be explained by the initially large difference between the P concentration in the outer layer of the aggregate and the P concentration in the external solution, which is the driving force of the P efflux; after 0.1 h, the P concentration in the outer layer is 25 times larger than the P concentration in the external solution (results not shown). Initially, P desorption from the solid phase of the inner layers is thus far from equilibrium with the rest of the aggregate. The concentration gradient at the interface between the outer layer of the aggregate and the external solution decreases with time. Desorption of P comes closer to equilibrium, because the concentration gradient along the radius of the aggregate is relatively small. This results in a low P flux from the aggregate to the external solution. However, there is still a concentration gradient along the radius of the aggregate, which reaches equilibrium only very slowly. After 10000 h, equilibrium is clearly reached, because there is no concentration gradient anymore in the system. The model shows that after 10000 h, the same P concentration is reached in the external solution (results not shown) as was obtained for 2 h of vigorous shaking (Fig. 2), which was shown to lead to almost equilibrium (van Erp et al., 1998).



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  		Fig. 4. Profile of the P concentration along the radius of the spherical aggregate simulated for P desorption from the initial soil to an external solution with a soil to solution ratio of 1:10 (w/v) (x = 0 mm corresponds with the center of the spherical aggregate).

 
We used the model to see how much abrasion of soil aggregates is needed to reproduce the results of 1:10 (w/v) 0.01 M CaCl2–extractable P from the initial soil with vigorous shaking. We again simulated P desorption to an external solution with a soil to solution ratio of 1:10 (w/v) for 408 h. Instead of a 1-mm radius of the aggregate, we now used a radius of 0.1 mm, supposing that vigorous shaking caused a 10-times reduction of the size of the soil aggregates. Desorption of P after 2 h was now close to equilibrium as the P concentration in the external solution amounted to 84% of the P concentration in the CaCl2 extract measured with vigorous shaking (Fig. 2). This suggests that the soil aggregates were relatively unstable.

Dynamic Simulation of the Behavior of Phosphorus in Soil Aggregates in the Pot Experiment
Figure 5 shows the simulation of the P concentration and the corresponding amount of P sorbed to the solid phase of the 50 concentric parts of the aggregate as a function of time, resulting from plant uptake of P measured in the 5-cm treatment. Simulation of the behavior of P in soil aggregates of the 10-cm treatment shows similar results (results not shown). The P concentration in the outer layers of the aggregate shows a fast decrease, due to an initially high P desorption rate. After 1000 h, the P concentration in the outer layer had decreased by 60%. As discussed above, this can be explained by the initially large concentration gradient at the interface between the outer layer of the aggregate and the external solution, which is stimulated by plant uptake of P from the soil solution. After 0.1 h, the P concentration in the outer layer is 1.5 times larger than the P concentration in the external solution (results not shown). The concentration gradient decreases with time; from 1000 h onward, the P concentration in the outer layer of the aggregate almost equals the P concentration in the external solution, resulting in lower P efflux. Nevertheless, in the initial stage of the pot experiment, the soil can easily meet the demand of the plant due to uptake of P. This will be demonstrated later using the diffusion model. In the initial stage of the simulation, the relative decrease of the amount of P sorbed to the solid phase of the outer layers of the aggregate is much smaller than what is observed for the P concentration. This is easily explained by the fact that initially the soil is nearly saturated with P, implicating that the slope of the isotherm is rather small, leading to a large response of the P concentration on a relatively small decrease of the amount of sorbed P (Fig. 1 and Table 2). The initial fast decrease of the P concentration in the outer layers of the aggregate is only slowly replenished by P desorbed from the solid phase of the inner layers, due to slow intra-aggregate diffusion, resulting in a very steep concentration gradient along the radius of the aggregate. Desorption of P from the solid phase of the inner layers is thus far from equilibrium with the rest of the aggregate. The concentration gradient clearly becomes much less steep with time in both treatments. Apparently, desorption of P inside the aggregate comes closer to equilibrium as the soil P content is further lowered by plant uptake. This explains why kinetic effects on P desorption in the 1:10 (w/v) 0.01 M CaCl2 extracts obtained from the soils of the 5- and 10-cm treatments taken from the pot experiment after plant uptake of P for 978 d are hardly visible for relatively mild shaking conditions in the batch experiments (Fig. 1).



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  		Fig. 5. Profile of the P concentration (A) and the amount of P sorbed to the solid phase (B) along the radius of the spherical aggregate simulated for the measured plant uptake of P in the 5-cm treatment (x = 0 mm corresponds with the center of the spherical aggregate).

 
Dynamic Bioavailability Index
Soil analysis is commonly used as a means to estimate the bioavailability of elements for plants or other organisms. Relationships between the measured concentration in a certain extract and the yield of plants growing in the field can be established by comparing both sets of data. Such relationships are widely used as a basis for fertilizer recommendations (Tunney et al., 1997). Plant growth is a dynamic process, and for optimal growth, a certain flux of a given nutrient at the interface between the soil solution and the root is needed to satisfy the demand of the growing plant. Whether or not the soil can provide for the needs of the plant depends on the amount of the nutrient present in soil, on plant factors, and on physical and chemical soil characteristics determining the supply (van Noordwijk et al., 1990; Jungk and Claassen, 1997; Hinsinger, 2001). One often simplifies the bioavailability concept by considering that a certain fraction of the total amount of an element is bioavailable. However, this notion of bioavailability is rather static, and we propose here to use instead a dynamic concept of bioavailability that still can be applied in a rather simple way. The plant requirement can be derived by measuring the uptake under conditions that are considered optimal for plant growth in a pot or field experiment, or from literature data on the plant uptake rate of a nutrient. One can then calculate the average supply rate expressed as amount of the nutrient per unit of weight of soil per unit of time that has to be delivered by the soil to be able to satisfy the demand. The challenge is then to be able to estimate the potential of a given soil to fulfill this using data that can be readily collected in routine soil analysis in combination with some modeling of physical, chemical, and biological processes governing the rate of release of the nutrient from the soil and the rate of transport to the root. One can then estimate to what extent bioavailability may be limiting plant growth and, if so, what action needs to be taken to optimize the situation. This approach was used before by van Noordwijk et al. (1990) to develop a mechanistic model of P transport in the soil to calculate the so-called Pw value required for optimal P uptake by crops within a growing season on the basis of plant and root density data and some physical and chemical soil characteristics. In the Netherlands, Pw (water-extractable P at a soil to solution ratio of 1:60 [v/v]) (Sissingh, 1971) is used in agricultural practice as a soil test for P fertilizer recommendations of arable land. In the approach of van Noordwijk et al. (1990), however, the emphasis was put on P transport from the soil to the root, the desorption itself being assumed to occur instantaneously. In the approach presented here, we will use the diffusion model to develop a simple tool that can be used to determine to what extent P desorption kinetics may be limiting plant uptake of P. This approach is based on what we will call the DBI. This DBI is analogous to the dimensionless Damköhler number, which is used in the chemical engineering literature to determine the rate-limiting step in reactive flow, that is, flow accompanied by a chemical reaction, in chemical reactors and bioreactors (van 't. Riet and Tramper, 1991). The Damköhler number relates the rate of the reaction with the physical transport rate of the reactant. The DBI is the ratio of the maximal desorption rate of a given nutrient from the soil divided by the plant uptake rate, both expressed in the same units. For the plant uptake rate, one can either use a constant value related to optimal plant growth as discussed above, or the actual plant uptake rate measured in a pot or field experiment. The ratio can both be larger or smaller than one when a constant optimal plant uptake rate is used in the calculation of the index. When the index is much larger than one, the kinetics of desorption is most likely not limiting optimal plant growth for the nutrient considered, whereas values smaller than one are indicative that optimal plant uptake will not be reached unless corrective action is taken. Using the actual plant uptake rate to calculate the dynamic bioavailability index is expected to lead to values larger than or equal to one. When the kinetics of P desorption is limiting plant growth, the maximal desorption rate and the actual plant uptake rate are expected to be rather similar. However, this situation will apply only for an infinitely high root density where all soil aggregates are in direct contact with the plant root (van Noordwijk et al., 1990). The calculated maximal desorption rate will not be reached for soil aggregates that are not in direct contact with the roots, due to transport limitations in the soil matrix. This may cause the buildup of a concentration gradient toward the root, limiting further P desorption (Jungk and Claassen, 1997). Even at a dense rooting, like in pot experiments, the volume of soil that is in direct contact with the plant root is relatively small (Geelhoed et al., 1997). For a finite root density, one may thus expect that the actual plant uptake rate is consistently lower than the maximal possible desorption rate. The difference between the maximal possible desorption rate and actual uptake rate is the amount remaining in the soil, due to transport limitations in the soil between aggregates (van Noordwijk et al., 1990). The extent to which the maximal desorption kinetics and the actual plant uptake approach each other is thus a function of root density, but also of physical characteristics, like the water content and tortuosity of the soil, determining the rate of transport in the soil (Jungk and Claassen, 1997).

We used the DBI to determine whether or not P desorption kinetics limited the bioavailability of P for plant uptake in the pot experiment during some time. The index was calculated as the ratio of the simulated maximal flux from the aggregate to the soil solution and the measured plant uptake rate (Table 3). Figure 6 shows the simulated maximal P desorption rate and actual plant uptake rate measured in the 10-cm treatment as a function of time; the results of the 5-cm treatment give a similar picture (results not shown). The maximal P desorption rate shows a fast decrease with time. This can be explained by the decrease of the concentration gradient between the outer layer of the aggregate and the external solution, which is the driving force of the P efflux. The measured plant uptake rate shows an irregular but much slower decrease. In the period between 0 and 236 d, the DBI is much larger than one (Fig. 6), since the maximal possible P desorption rate is much larger than the measured plant uptake rate, which may result in a buildup of P in soil solution causing an increased risk of P leaching. This high value of the DBI was caused by the large amount of desorbable P in the soil we used. The P content measured in the grass harvested in the period between 0 and 236 d is (much) larger than what may be considered as optimal (4 g P kg–1 of dry matter) in conventional agricultural practice in the Netherlands (Agterberg and Henkens, 1995). Apparently, plant uptake of P is initially not limited by P desorption, but is governed by other factors like biological constraints in the uptake of P by the root (Jungk and Claassen, 1997). The curves for the variation of the maximal desorption rate and the actual plant uptake rate approach each other after a while and run parallel in the later stage of the pot experiment. The curve for the P content of the harvested grass and that of the calculated maximal desorption rate show interestingly a high similarity as a function of time (Fig. 6). The DBI fluctuates around a constant value of two after 236 d, so the measured plant uptake rate is half of the maximal possible desorption rate in this period. During the pot experiment, not all soil aggregates may have been in direct contact with the roots, which explains why the DBI stabilizes at a value somewhat larger than one, due to additional transport limitations, as discussed above. The decrease of the DBI to a value of around two coincides with a large decrease of the P content in the harvested grass to a value (far) below 3 g P kg–1 of dry matter (Table 3). For optimal nutritional value of grass to serve as feed for high yielding dairy cows, it should not contain less than 3 g P kg–1 of dry matter if grass is the only component of the diet (Valk et al., 1999). This implies that the grass harvested in the period between 236 and 978 d would have too little nutritional value. Apparently, the supply rate of P from soil to the root in this period cannot meet the demand needed for optimal P uptake by the grass. Corrective action like the application of P fertilizer thus seems to be necessary to restore the optimal plant uptake rate. To apply this dynamic concept of bioavailability in the field, one needs to account for the lower root density and a less optimal water content. Both factors would lower the bioavailability of P for a given soil compared with the pot experiment. The dimensionless bioavailability index needed for optimal plant growth may thus be higher than two. However, the plant can explore a larger volume of soil in the field than in those of the 5- or 10-cm treatments used in the pot experiment. This leads to a lowering of the desorption rate from the aggregates per unit of weight of soil that is required for optimal plant growth, which improves the bioavailability situation. How these two opposing effects work out in practice with respect to the application of the proposed bioavailability index requires more research. The concept presented here could be seen as a promising onset that needs to be developed further.


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  		Table 3. Phosphorus content of the harvested grass{dagger}, the plant uptake rate of P, the calculated maximal P desorption rate from the spherical aggregate, and the dimensionless dynamic bioavailability index (DBI){ddagger}.

 


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  		Fig. 6. Simulated maximal P desorption rate from the spherical aggregate, the actual plant uptake rate, and the P content measured in the grass harvested in the 10-cm treatment as a function of time. The inserted figure shows the dynamic bioavailability index (DBI) as a function of time.

 

   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
REFERENCES
 


   ACKNOWLEDGMENTS
 
The authors thank Jan Dolfing and Oene Oenema for their valuable comments on a previous version of this manuscript.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 


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