The Levich equation is written as: :I_L = (0.620) n F A D^\frac{2}{3} \omega^\frac{1}{2}\nu^\frac{-1}{6}C where
IL is the Levich current (A),
n is the number of moles of
electrons transferred in the
half reaction (number),
F is the
Faraday constant (C/mol),
A is the electrode area (cm2),
D is the diffusion coefficient (see
Fick's law of diffusion) (cm2/s),
ω is the angular rotation rate of the electrode (rad/s),
ν is the kinematic viscosity (cm2/s),
C is the
analyte concentration (mol/cm3). In this form of the equation, the constant with a value of 0.620 has units of rad-1/2. The leading term 0.620 is from the calculation of the velocity profile near the surface of the electrode. Using cylindrical coordinates, the von Karman and Cochran solution to the Navier-Stokes equations yields the two relevant profiles to electrochemical study: :v_y = -0.51\omega^\frac{3}{2} \nu^\frac{-1}{2} y^2 :v_r = 0.51 \omega^\frac{3}{2} \nu^\frac{-1}{2} ry The Levich equation can subsequently be derived by integrating the steady-state convection diffusion equation: :v_y \Big(\frac{\partial C}{\partial y}\Big) = D\frac{\partial^2 C}{\partial y^2} The leading numeric value varies with the units of
ω: 0.621 is referred to
ω in rad/s; other common values are 1.554 for
ω in Hz, and 0.201 for
ω in rpm. Whereas the Levich equation suffices for many purposes, improved forms based on derivations utilising more terms in the velocity expression are available. == Simplification ==