Levich Equation: Rotating Disk Electrode (RDE) Limiting Current vs RPM

Replace decaying Cottrell transients with steady-state hydrodynamic RDE plateaus!

In fuel-cell ORR electrocatalysis and corrosion kinetics, spinning a flat disk electrode at angular velocity omega = 2 * PI() * RPM / 60 rad/s acts as a centrifugal pump—pulling fresh electrolyte axially toward the disk and flinging it outward radially to create a uniform, time-invariant hydrodynamic boundary layer! Veniamin Levich solved the von Karman convective-diffusion equations to derive the steady-state mass-transport limiting plateau current in CGS units: iL = 0.620 * n * F * A * (D^(2/3)) * (omega^(1/2)) * (nu^(-1/6)) * C0!

Here F = 96,485 C/mol, A is disk area (cm^2), D is diffusivity (cm^2/s), nu is electrolyte kinematic viscosity (cm^2/s, ~0.01 cm^2/s for water at 25 °C), and C0 is bulk concentration (mol/cm^3)! Because iL scales with SQRT(omega) (and therefore SQRT(RPM)), quadrupling rotation speed from 1,600 RPM to 6,400 RPM doubles steady-state limiting current from 257.95 uA to 515.89 uA!

Levich RDE Mass-Transport Limiting Current iL in Microamperes (uA)

Converts B5 RPM into omega = (2 * PI() * B5) / 60 rad/s and evaluates the full CGS Levich equation in microamperes.

=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0, B6 <= 0, B7 < 0), "Invalid RDE Parameters", ROUND(1000000 * 0.62 * B2 * 96485 * B3 * (B4 ^ (2 / 3)) * (((2 * PI() * B5) / 60) ^ 0.5) * (B6 ^ (-1 / 6)) * B7, 2))

Angular Velocity omega = 2 * PI() * RPM / 60 (rad/s)

Converts electrode shaft rotation speed from revolutions per minute (RPM) to radians per second.

=IF(B5 <= 0, "Invalid RDE Parameters", ROUND((2 * PI() * B5) / 60, 2))

Further reading

• Microsoft Support — PI function