text: To analyze the transport of ions in the channel, behaviors of system in electrochemistry as well as fluid mechanics need to be considered. The Poisson–Nernst–Planck (PNP) equations are utilized to describe ionic current flowing through a channel, and the Navier–Stokes (NS) equations are used to represent the fluid dynamics in the channel.
  The PNP equations consist of the Poisson equation:
  and the Nernst–Planck equations, which gives the particle flux of ion species  due to a concentration gradient and electric potential gradient:
  where  is the electrostatic potential,  is the unit charge of electron,  is the permittivity in vacuum, and  is the dielectric constant of solution; ,  and  are the diffusivity, the number density of ions, and the valence of ion species .
  The solution in steady-state satisfies the continuity equation. To describe fluid velocity field in the channel, using Navier–Stokes equations:
  where , , , and  are pressure, velocity vector, viscosity, and density of fluid, respectively. The equations above are usually solved with numerical algorithm to determine the velocity, pressure, electric potential, and ionic concentration in the fluid, as well as the electric current flow through the channel.