text: The resulting flow from applying a voltage is a plug flow. Unlike a parabolic profile flow generated from a pressure differential, a plug flow’s velocity profile is approximately planar, with slight variation near the electric double layer. This offers significantly less deleterious dispersive effects and can be controlled without valves, offering a high-performance method for fluid separation, although many complex factors prove this control to be difficult. Because of difficulties measuring and monitoring flow in microfluidic channels, primarily disrupting the flow pattern, most analysis is done through numerical methods and simulation.
  Electroosmotic flow through microchannels can be modeled after the Navier-Stokes equation with the driving force deriving from the electric field and the pressure differential. Thus it is governed by the continuity equation
  and momentum
  where  is the velocity vector,  is the density of the fluid,  is the material derivative,  is the viscosity of the fluid,  is the electric charge density,  is the applied electric field,  is the electric field due to the zeta potential at the walls and  is the fluid pressure.
  Laplace’s equation can describe the external electric field
  while the potential within the electric double layer is governed by
  where  is the dielectric constant of the electrolyte solution and  is the vacuum permittivity. This equation can be further simplified using the Debye-Hückel approximation
  where  is the Debye length, used to describe the characteristic thickness of the electric double layer. The equations for potential field within the double layer can be combined as
  The transport of ions in space can be modeled using the Nernst–Planck equation:
  Where  is the ion concentration,  is the magnetic vector potential,  is the diffusivity of the chemical species,  is the valence of ionic species,  is the elementary charge,  is the Boltzmann constant, and  is the absolute temperature.