This document summarizes research on how the physical interaction of water impacts phosphorus (P) desorption from soil. The researchers found that: 1) P desorption quantity and rate are dependent on time and water flow, with slower flow rates allowing for greater desorption over time. 2) P desorption follows two-stage first-order kinetics, with an initial rapid release followed by a slower secondary release. 3) Higher soil phosphorus content results in faster desorption rates initially and greater total desorption. 4) Clay soils show a greater difference in desorption between fast and slow flow rates compared to sandy soils, due to clay soils' greater buffering capacity and diffusion limitations being more overcome at

1. Phosphorus desorption kinetics under
flowing conditions: how physical and
chemical processes interact to control
concentrations and load
Chad Penn and Mark Williams
USDA Agricultural Research Service
National Soil Erosion Research Laboratory

2. Why we care about the
dissolved pool:
• It’s what plants truly uptake
• Stronger eutrophication agent
• More difficult to control or manipulate compared
to solid-bound/particulate P
– With regard to plant availability
– With regard to non-point drainage losses
• Dissolved P is dynamic
– Solubility varies with chemical conditions
– Behavior is a function of more than simple solubility
• Physical location, hydrology, kinetics

3. H+
H+
Quantity (Solid phase)
P-
H+
P2-
H+
H+
H+
P-
H+
H+
Precipitated minerals:
• Ca-P & Mg-P
• Al-P & Fe-P
Fe or Al
Oxygen
HPO4
2-
H2PO4
-
PO4
3-
sorption
precipitation
de-sorption
dissolution
Intensity
(solution phase)
Plant
uptake
Soil
Components
Iigand
exchange
Runoff
&leaching
precipitation
anion
exchange

4. • DP loss is flashy with most loss in large events
– True concentrations follows discharge flow rate
• Hydrology is partly controlling desorption from soil, not just loads!
• Current models cannot capture this variability. Why not?
King et al., 2017
Discharge
(m
3
s
-1
)
Field tile drain
(0.18 km2)
Portage River
(1100 km2)
Maumee River
(16000 km2)
Dissolved P is Dynamic

5. Movement between pools requires
time, not just thermodynamics
• Kinetics
• Depends on same properties that impact
equilibrium
Solid
Phase P
Solution P
A + B Y
𝑑 𝐴
𝑑𝑡
= −𝑘1 [𝐴][𝐵] + 𝑘−1[𝑌]
k1
k-1

6. It takes time and water to
desorb P
….Which is just another way of
saying “kinetics and
thermodynamic equilibrium”
+ =
P in water

7. Not just speed of chemical
reaction:
4. Chemical reaction (fast)
Weber, 1984
Chemical process of desorption is only
realized through physical processes

8. P desorption is not a purely
chemical process
Objective:
How does physical interaction of water impact
net measured desorption?
• Quantity
• Rate
We thoroughly studied a single high P soil to
understand this process before working on
other soils (Penn et al., 2022; Soil Processes)

9. Physio-chemical interaction
• Two most important physio-chemical
aspects to process of P desorption:
– Reaction order
• i.e. how does concentration affect desorption rate
• First-order is where thermodynamics meets
kinetics
– Dilution!
– Diffusion
• Both will impact P desorption quantity,
rate, and buffering

10. First-order means desorption
rate is concentration dependent
P desorption rate increases with disparity
between solid and solution phase concentration
– i.e. P desorption rate decreases with less dilution
or accumulation of solution P
• Lesser solution:soil ratio
Solid
Phase P
Slow desorption
rate
Solution P
concentration

11. Inflow from
Mariotte
bottle
Soil
0.45 𝜇m filter
Constant
water level
Peristaltic
pump
Outlet:
solution to
be analyzed
Tested a “fast” and “slow” flow rate (7 vs 0.13 mL/min)
Flow-Through Method

12. Flow rate makes a big
difference
0.0
0.5
1.0
1.5
2.0
2.5
0 5000 10000 15000 20000 25000 30000
P
desorbed
(mg
L
-1
)
Time (min)
Fast flow rate
Slow flow rate
Fast flow rate produces lower concentrations:

13. Flow rate makes a big
difference
BUT, higher flow rate desorbs P much faster than
the slow flow rate
0
50
100
150
200
250
300
350
400
0 5000 10000 15000 20000 25000
Cumulative
desorbed
P
(mg
kg-1)
Time (min)
Fast flow rate
Slow flow rate
Slope = P desorption rate
Desorption rate decreases as soil P is exhausted

14. Flow rate makes a big
difference
0
50
100
150
200
250
300
350
400
0 1 2 3 4 5 6
Cumulative
desorbed
P
(mg
kg-1)
Cumulative Volume (L)
However, slow flow rate desorbs a greater P
quantity at any given volume than fast flow rate
Fast flow rate
Slow flow rate

15. 0
100
200
300
400
500
600
0 5,000 10,000 15,000 20,000 25,000 30,000
Cumulative
desorbed
P
(mg
kg
-1
)
Time (min)
Initial rapid phase
Secondary gradual
phase
2-stage first-order kinetics:
• Initial rapid desorption depletes labile pool
• Secondary gradual desorption limited by less-labile
pool

16. Diffusion and buffering
• Interruption tests indicate P desorption is
diffusion-limited
– Less diffusion limitation with slow flow rate
• Diffusion IS buffering
Start of run: A, A1, A2, A3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 200 400 600 800 1000 1200 1400
Desorption
rate
(mg
P
kg
-1
min
-1
)
Flow time (min)
Rep 1
Rep 2
A
A1
A2
A3
B B1
B2
B3
Flow interruption

17. Mineral
Film
Solution
sorption-
desorption

18. P
Labile P
Less-Labile P
P leaching
P
Slow Flow
• More effective diffusion to
replenish labile pool
• Labile pool depleted slowly
– Less-labile pool replenishment
“keeps up” for a time
Solution P

19. P
Labile P
Less-Labile P
P leaching
P
• Less effective diffusion
• Labile pool depleted rapidly
– Labile pool depleted MUCH
faster than it can be replenished
Fast Flow
Solution P

20. What we know
• P desorption quantity and rate are a
function of:
– Time and Water!
• Both captured by flow rate
• Physio-chemical process
• 2-stage first-order kinetics
– Initial rapid rate, secondary gradual release
– Dilution: via thermodynamics increases rate
• Desorption and buffering limited by diffusion
• Slow flow desorbs more P than fast flow,
but does it at a slower rate

21. How do soil properties affect
how flow rate influence P
desorption degree and kinetics?

22. > 30 soils
Soil property range mean max min median
Clay content (%) 16.7 6.5 17.5 0.8 6.0
pH 3.54 6.57 8.25 4.71 6.42
Soluble C (mg/kg) 501 284 616 115 207
Total C (g/kg) 34 20 39 5 18
M3-P 1378 260 1394 31.2 180
Water soluble P (mg/kg) 44.2 11.3 45.4 1.2 8.3
Pox (mg/kg) 7456 4003 7596 140 5379
Pox Saturation (%) 94 25.3 96.3 2.31 19.4
M3-P Saturation (%) 120 31.0 120 2.45 22.9
Total P desorbed at 2 L:
fast flow rate (mg/kg)
218 50.3 228 9.7 37.3
Total P desorbed at 2 L:
slow flow rate (mg/kg)
452 98.0 459 6.6 64.1

23. y = 0.36x + 8.9177
R² = 0.91
y = 0.16x + 9.1971
R² = 0.88
0
50
100
150
200
250
300
350
400
450
500
0 500 1000 1500
P
desorbed
after
2
L
inflow
(mg/kg)
M3-P (mg/kg)
Slow
Fast
Desorption quantity:
– Clearly more P released with slow flow and from soils
with greater soil M3-P
– Difference in P released between fast and slow flow
increased with increasing soil M3-P content

24. y = 0.001x + 0.0228
R² = 0.88
y = 0.0003x + 0.0212
R² = 0.91
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 500 1000 1500
desorption
rate
(mg/kg/min)
M3-P (mg/kg)
Initial rapid phase
Secondary gradual
phase
Desorption rate:
– Increased soil P concentration means faster P release
• i.e. First order kinetics
• Difference in P desorption rate between initial rapid phase and secondary
gradual phase increased with increasing soil M3-P content

25. Stepwise analysis (take it with a
grain of salt)
Significant variables identified:
– P desorbed at fast flow rate:
M3-P, WSP, pH, clay
– P desorbed at slow flow rate:
M3-P, clay, pH, DPS
– % difference between fast and slow rate:
WSP and clay

26. M3-P is obvious. What about
clay?
Contrast analysis
– Divided soils into two groups: sand
• (<10% clay) and clay (>10% clay)
– Removed 3 outliers with excessive M3-P
• (>550 mg/kg)
– Between the two texture groups, compared:
• M3-P, and P desorption quantity and rate for fast and
slow

27. M3-P
Clay Sand
vs.
M3-P M3-P
NS

28. Total P desorbed at fast FR
Clay Sand
vs.
P desorbed (Fast FR) P desorbed (Fast FR)
47 vs 32 mg/kg (p = 0.07)
Not much difference!

29. Total P desorbed at slow FR
Clay Sand
vs.
P desorbed (Slow FR) P desorbed (Slow FR)
105 vs. 53 mg/kg (p = 0.02)
BIG difference!
• Changes in FR may have a more dramatic
effect on clay soils than sandy. Why?

30. P desorbed: Initial rapid release rate
(mg/kg min and mg/kg hr)
Clay Sand
vs.
Fast FR Slow FR Fast FR Slow FR
joint
0.21 vs 0.20 mg/kg min (NS)
0.71 vs 0.42 mg/kg h (p = 0.03)
• Again, slow flow rate
allows for the desorption
potential of clays to be
more fully realized
– Differences become more
apparent

31. Why the differences between clay and
sand, especially at slow flow rate?
Clay soils are more buffered and
therefore a much larger less-labile pool
– Have much more total P for a given level of M3-
P compared to sandy soils
– Less-labile pool able to keep feeding the labile
pool faster for clays because of first order
kinetics (bigger pool = faster)
• BUT this potential is more fully realized at slower flow rates
– Clay soils have much more physical restrictions than sand, and therefore
are diffusion limited
» You overcome diffusion limitations at slower flow rates
» i.e. fast flow rates do not allow for less-labile P and diffusion as much

32. Who Cares?
• Understanding the nature of P behavior
will help us
– Improve transport models
– Create new P fertility recommendations
– Better target best management practices
• …..Because water-soil interactions matter!

33. Questions?
Chad.penn@ars.usda.gov
Twitter Handle: House of Phos