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SoilLiquid‐Phase(Solute)Diffusion

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DefinitionofDiffusion:Masstransportbyrandomatomicmotion

Fick’slaws:

Fick’s1stlaw: steady‐stateconditions

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Fick’s2ndlaw: transientconditions

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J=solutediffusiveflux

D=diffusivityordiffusioncoefficient

Subscriptl=indicatesliquid‐phasesystem

C=soluteconcentration

x=distanceinthexdirection

t=time

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Whenisdiffusionimportant?

 Duringlowadvectiveflowandshortdistancesofasystem

o Engineeringexample

 Human‐madewasterepositories(i.e.dumps)haveacompactedsoil

liningatthebottomtominimizeadvectiveflow.Therefore,ifthelining

wassuccessfullyconstructedandnoadvectiveflowoccursthesolutes

couldthenonlypassthroughthelinerbydiffusion.Importantfor

environmentalcontamination.

o Agricultureexample

 Nitrogenfertilizationinawellaggregatedsoil.Foramildlywetsoil(i.e.

waterfilmsalongtheoutsideofbothsoilparticlesandsoilaggregatesbut

theinter‐aggregatespacesaremostlyfilledwithair),immediatelyaftera

nitrogenproductisinjectedintothesoilalargeconcentrationgradientof

soilwaternitrogenfromtheoutsidetotheinsideofasoilaggregate,

assumingthatallthenitrogenwasreadilydissolvedinthesoilwateror

wasalreadyinanaqueousstate.SowhatdidwelearnedfromDr.A.

Fick?....Adiffusivefluxcanberelatedtoaconcentrationgradient.

Therefore,thenitrogenwilldiffusetotheinsideofthesoilaggregate.

However,ifthesoilissaturatedandyouinjectyournitrogenproduct

thenthenitrogen,wherewillthenitrogendiffuseto?...diffuseintothe

soilaggregatewhereyouhaveonlyafractionalvolumeandtortuosityor

diffuseacrosstheopenwateroftheinter‐aggregatespace?Thenitrogen

willmorereadilydiffuseacrosstheinter‐aggregatespaceandtheninto

thesoilaggregate;butyouhavereducedyourconcentrationgradientat

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Soil Liquid‐Phase (Solute) Diffusion

Definition of Diffusion: Mass transport by random atomic motion Fick’s laws: Fick’s 1 st law: steady‐state conditions Fick’s 2 nd law: transient conditions J = solute diffusive flux D = diffusivity or diffusion coefficient Subscript l = indicates liquid‐phase system C = solute concentration x = distance in the x direction t = time When is diffusion important?  During low advective flow and short distances of a system o Engineering example  Human‐made waste repositories (i.e. dumps) have a compacted soil lining at the bottom to minimize advective flow. Therefore, if the lining was successfully constructed and no advective flow occurs the solutes could then only pass through the liner by diffusion. Important for environmental contamination. o Agriculture example  Nitrogen fertilization in a well aggregated soil. For a mildly wet soil (i.e. water films along the outside of both soil particles and soil aggregates but the inter‐aggregate spaces are mostly filled with air), immediately after a nitrogen product is injected into the soil a large concentration gradient of soil water nitrogen from the outside to the inside of a soil aggregate, assuming that all the nitrogen was readily dissolved in the soil water or was already in an aqueous state. So what did we learned from Dr. A. Fick?.... A diffusive flux can be related to a concentration gradient. Therefore, the nitrogen will diffuse to the inside of the soil aggregate. However, if the soil is saturated and you inject your nitrogen product then the nitrogen, where will the nitrogen diffuse to?... diffuse into the soil aggregate where you have only a fractional volume and tortuosity or diffuse across the open water of the inter‐aggregate space? The nitrogen will more readily diffuse across the inter‐aggregate space and then into the soil aggregate; but you have reduced your concentration gradient at

the soil aggregate surface and consequently reduce the diffusive flux and the amount of nitrogen within the soil aggregate. So why is this important? It’s important because infiltrating water during a precipitation event in a well‐aggregated soil will have both flowing water in the inter‐aggregate spaces and stagnant water in the intra‐ aggregate spaces. Thus, the more nitrogen product diffused into the soil aggregate, where the stagnant water is present, and then you will minimize the loss of nitrogen due to leaching. Important for the plant nitrogen needs, nitrogen use efficiency, environmental water quality. Diffusion in soil  Standard equation for soil liquid‐phase diffusivity D = soil diffusivity D (^) w = diffusivity in bulk water θ = volumetric water content = tortuosity  However, similar to that of soil‐gas phase diffusivity, many mathematical models have been developed for liquid‐phase diffusivity.  is difficult to quantify  Soil particle surfaces can affect diffusivity. Soil particles are dominantly negatively charged. Therefore cations will accumulate near the soil particle and soil aggregate surfaces. This accumulation changes the fluid properties of the media your solute is diffusing through. Hillel gives α, that can be linearly applied to diffusivity, as a factor accounting for the increased viscosity near the solid surface. Though one may argue that visocity is not an active mechanism when advection is not present, the fluid properties near the soil particle surface are different than that farther away and you would expect the diffusivity to change. Important in soil with large fraction of small pores. H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O H 2 O Negatively charged soil particle Soil Water Cation Solute Solute Solute Solute

 Nerst equation D = diffusivity R = Molar gas constant T = Kelvins = Faraday constant (electric charge carried by one mole of electrons) = electrical conductivity = valence of ion However, ions typically may travel in pairs with differ ions, if present. Anion solutes will commonly pair with some cation solute and travel together (Ex: NO 3 ‐ may travel with free Ca 2+^ or Na +). Each are attracted to each other due to electrostatic forces. Each are likely to give a different diffusivity. However they will travel at some average. D (^0) D (^1) D (^2)

Soil Liquid Phase Diffusion - Soil Physics - Lecture Notes, Study notes of Soil Physics

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Soil Liquid‐Phase (Solute) Diffusion