Nanochannel Electroosmosis: Debye Layer Overlap & Ion Selectivity

Nanochannel Geometry

Channel height H 20 nm

Electrolyte

Salt concentration 1.00 mM

Wall zeta potential ζ -80 mV

Applied field E 200 V/cm

Live Readouts

Regime: —

Debye length λD

— nm

Overlap κh = h/λD

—

Centerline EOF speed

— µm/s

Cation:anion ratio

—

How it works

Two charged nanochannel walls (surface potential ζ, half-spacing h) sit in a 1:1 electrolyte of bulk concentration C. Screening length — the Debye length:

λD = sqrt( ε kT / (2 n0 e²) ),  n0 = C·NA

Linearized Poisson–Boltzmann gives the potential and ion profiles across the channel (y measured from the centerline):

ψ(y) = ζ · cosh(y/λD) / cosh(h/λD)
c±(y) = C · exp(∓ eψ(y) / kT)

Combining this body charge with Stokes flow under axial field E gives the electroosmotic velocity profile (Rice–Whitehead solution):

u(y) = -(ε ζ E / η) · [1 - cosh(y/λD)/cosh(h/λD)]

κh ≫ 1 (wide channel / high salt): thin, isolated double layers. The core is field-free and electroneutral, u(y) is a flat plug capped by thin shear layers — the classic Helmholtz–Smoluchowski limit u ≈ -εζE/η.
κh ≲ 1 (narrow channel / dilute salt): the two Debye layers overlap across the whole cross-section. Co-ions are excluded everywhere (Donnan exclusion), the channel becomes strongly permselective for counter-ions, and the flow profile turns parabolic-like with a reduced net speed — the signature of true nanofluidic (as opposed to microfluidic) transport.
The cation:anion ratio readout is the cross-sectional average of c₊/c₋ — the permselectivity a real nanofluidic diode or ion-current-rectifying pore exploits.

Sliders sweep H (2–200 nm), bulk salt (0.01 mM–100 mM), ζ (-150 to -5 mV) and the driving field E (10–1000 V/cm); particle color = charge sign, particle spacing near the walls visualizes the Boltzmann-weighted ion density, and particle drift speed visualizes u(y) directly.

Cations (counter-ions) Anions (co-ions)

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