Nanoparticle Transport Through Soil

Nanoparticle & Flow

Particle diameter d_p 80 nm

Pore-water velocity v 2.0 m/day

Attachment efficiency α 0.05

Grain diameter d_c 0.50 mm

Live Filtration Readouts

Single-collector η₀

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Filter coeff. k_att

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Predicted C/C₀ (30 cm)

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Measured breakthrough

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Captured in column

Pore volumes elapsed

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Breakthrough curve C/C₀0%

How it works

Engineered nanoparticles moving through saturated soil are removed by attaching to sand grains — the same colloid filtration theory (CFT) used to design groundwater remediation barriers and predict how far a spill of nanomaterial can travel before it is trapped.

Single-collector efficiency (Yao, 1971):
η₀ = η_D + η_I + η_G

η_D = 4.04·Pe⁻²ᐟ³         Pe = dc·v / D        (diffusion)
η_I = 1.5·(dp/dc)²                              (interception)
η_G = g(ρp−ρf)dp² / (18μv)                      (gravity settling)

D  = kT / (3πμ·dp)         (Stokes–Einstein diffusion coeff.)

Filter coefficient:  k_att = [3(1−θ)/(2dc)]·α·η₀
Breakthrough:         C/C₀ = exp(−k_att·L)

d_p (particle size) — small particles diffuse fast (high η_D) and get caught; very large particles settle out (high η_G). Removal is weakest for particles around 100–500 nm, the classic CFT "minimum efficiency" window most engineered nanomaterials fall into.
v (velocity) — faster flow gives particles less time to diffuse or settle onto a grain, so it lowers η₀ and pushes more mass through.
α (attachment efficiency) — a stand-in for ionic strength / surface charge (DLVO). Low-salinity, highly-charged particles repel grains (α → 0, particles travel far); high ionic strength collapses that repulsion (α → 1, rapid capture near the inlet).
d_c (grain size) — fine sand has more surface area per volume and traps particles faster than coarse gravel.
Each injected particle is assigned a capture depth drawn from the exponential decay predicted by k_att — the same statistics a real packed-bed column experiment produces — then animated falling through the grain bed until it attaches or exits at the bottom outlet.

Real-world relevance: this is the mechanism regulators model when assessing whether nanoparticles released from consumer products, industrial waste or remediation nanomaterials will stay trapped in topsoil or reach an aquifer.

Mobile nanoparticle Captured (attached) Sand grain (collector)

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