Electro-osmosis

In chemistry, electro-osmotic flow (EOF, hyphen optional; synonymous with electro-osmosis or electro-endosmosis) is the motion of liquid induced by an applied potential across a porous material, capillary tube, membrane, microchannel, or any other fluid conduit. Because electro-osmotic velocities are independent of conduit size, as long as the electrical double layer is much smaller than the characteristic length scale of the channel, electro-osmotic flow will have little effect. Electro-osmotic flow is most significant when in small channels, and is an essential component in chemical separation techniques, notably capillary electrophoresis. Electro-osmotic flow can occur in natural unfiltered water, as well as buffered solutions.

Electro-osmotic flow was first reported in 1807 by Ferdinand Friedrich Reuss (18 February 1778 (Tübingen, Germany) – 14 April 1852 (Stuttgart, Germany)) in an unpublished lecture before the Physical-Medical Society of Moscow; Reuss first published an account of electro-osmotic flow in 1809 in the Memoirs of the Imperial Society of Naturalists of Moscow. He showed that water could be made to flow through a plug of clay by applying an electric voltage. Clay is composed of closely packed particles of silica and other minerals, and water flows through the narrow spaces between these particles just as it would through a narrow glass tube. Any combination of an electrolyte (a fluid containing dissolved ions) and an insulating solid would generate electro-osmotic flow, though for water/silica the effect is particularly large. Even so, flow speeds are typically only a few millimeters per second.

Electro-osmosis was discovered independently in 1814 by the English chemist Robert Porrett Jr. (1783–1868).

Electroosmotic flow is caused by the Coulomb force induced by an electric field on net mobile electric charge in a solution. Because the chemical equilibrium between a solid surface and an electrolyte solution typically leads to the interface acquiring a net fixed electrical charge, a layer of mobile ions, known as an electrical double layer or Debye layer, forms in the region near the interface. When an electric field is applied to the fluid (usually via electrodes placed at inlets and outlets), the net charge in the electrical double layer is induced to move by the resulting Coulomb force. The resulting flow is termed electroosmotic flow.

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 U is the velocity vector, ρ is the density of the fluid, ${\displaystyle D/Dt}$ is the material derivative, μ is the viscosity of the fluid, ρ_e is the electric charge density, ϕ is the applied electric field, ψ is the electric field due to the zeta potential at the walls and p is the fluid pressure.