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Electroosmotic flow (or electro-osmotic flow, often abbreviated EOF; synonymous with electroosmosis or electroendosmosis) is the motion of liquid induced by an applied potential across a porous material, capillary tube, membrane, microchannel, or any other fluid conduit. Because electroosmotic velocities are independent of conduit size, as long as the
electrical double layer A double layer (DL, also called an electrical double layer, EDL) is a structure that appears on the surface of an object when it is exposed to a fluid. The object might be a solid particle, a gas bubble, a liquid droplet, or a porous body. The D ...
is much smaller than the characteristic length scale of the channel, electroosmotic flow will have little effect. Electroosmotic flow is most significant when in small channels. Electroosmotic flow is an essential component in chemical separation techniques, notably
capillary electrophoresis Capillary electrophoresis (CE) is a family of electrokinetic separation methods performed in submillimeter diameter capillaries and in micro- and nanofluidic channels. Very often, CE refers to capillary zone electrophoresis (CZE), but other electr ...
. Electroosmotic flow can occur in natural unfiltered water, as well as
buffer Buffer may refer to: Science * Buffer gas, an inert or nonflammable gas * Buffer solution, a solution used to prevent changes in pH * Buffering agent, the weak acid or base in a buffer solution * Lysis buffer, in cell biology * Metal ion buffer * ...
ed solutions.


History

Electro-osmotic flow was first reported in 1807 by
Ferdinand Friedrich Reuss Ferdinand is a Germanic name composed of the elements "protection", "peace" (PIE "to love, to make peace") or alternatively "journey, travel", Proto-Germanic , abstract noun from root "to fare, travel" (PIE , "to lead, pass over"), and "co ...
(18 February 1778 (Tübingen, Germany) – 14 April 1852 (Stuttgart, Germany)) in an unpublished lecture before the Physical-Medical Society of Moscow; Reuss first published an account of electro-osmotic flow in 1809 in the ''Memoirs of the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 Moscow Society of Naturalists (russian: Московское общество испытателей природы (MOIP)) is one of Russia's oldest learned societies. In 1805 it was founded as the Imperial Society of Naturalists of Moscow (''So ...
''. He showed that water could be made to flow through a plug of
clay Clay is a type of fine-grained natural soil material containing clay minerals (hydrous aluminium phyllosilicates, e.g. kaolin, Al2 Si2 O5( OH)4). Clays develop plasticity when wet, due to a molecular film of water surrounding the clay par ...
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 An electrolyte is a medium containing ions that is electrically conducting through the movement of those ions, but not conducting electrons. This includes most soluble salts, acids, and bases dissolved in a polar solvent, such as water. Upon dis ...
(a fluid containing dissolved ions) and an insulating solid would generate electro-osmotic flow, though for water/
silica Silicon dioxide, also known as silica, is an oxide of silicon with the chemical formula , most commonly found in nature as quartz and in various living organisms. In many parts of the world, silica is the major constituent of sand. Silica is one ...
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).


Cause

Electroosmotic flow is caused by the
Coulomb force Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventiona ...
induced by an electric field on net mobile
electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
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 A double layer (DL, also called an electrical double layer, EDL) is a structure that appears on the surface of an object when it is exposed to a fluid. The object might be a solid particle, a gas bubble, a liquid droplet, or a porous body. The D ...
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.


Description

The resulting flow from applying a voltage is a
plug flow In fluid mechanics, plug flow is a simple model of the velocity profile of a fluid flowing in a pipe. In plug flow, the velocity of the fluid is assumed to be constant across any cross-section of the pipe perpendicular to the axis of the pipe. T ...
. 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 A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity, but it can be generalized to apply to any extensive quantity. S ...
:\nabla \cdot\mathbf = 0 and
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
:\rho \frac = -\nabla p + \mu \nabla^2 \mathbf + \rho_e \nabla \left( \psi + \phi \right), where is the velocity vector, is the density of the fluid, D/Dt is the
material derivative In continuum mechanics, the material derivative describes the time rate of change of some physical quantity (like heat or momentum) of a material element that is subjected to a space-and-time-dependent macroscopic velocity field. The material der ...
, 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 Zeta potential is the electrical potential at the slipping plane. This plane is the interface which separates mobile fluid from fluid that remains attached to the surface. Zeta potential is a scientific term for electrokinetic potential in coll ...
at the walls and is the fluid pressure.
Laplace’s equation In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties. This is often written as \nabla^2\! f = 0 or \Delta f = 0, where \Delta = ...
can describe the external electric field : \nabla^2 \phi = 0, while the potential within the electric double layer is governed by : \nabla^2 \psi = \frac, where is the dielectric constant of the electrolyte solution and is the
vacuum permittivity Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric consta ...
. This equation can be further simplified using the Debye-Hückel approximation : \nabla^2 \psi = k^2\psi, where is the
Debye Length In plasmas and electrolytes, the Debye length \lambda_ (also called Debye radius), is a measure of a charge carrier's net electrostatic effect in a solution and how far its electrostatic effect persists. With each Debye length the charges are in ...
, used to describe the characteristic thickness of the electric double layer. The equations for potential field within the double layer can be combined as :\rho_e = -\epsilon \epsilon_0 k^2 \psi. The transport of ions in space can be modeled using the
Nernst–Planck equation The Nernst–Planck equation is a conservation of mass equation used to describe the motion of a charged chemical species in a fluid medium. It extends Fick's law of diffusion for the case where the diffusing particles are also moved with respect t ...
: : = \nabla \cdot \left D\nabla c - c + c \left( \nabla \phi + \right) \right/math> Where \ c is the ion concentration, is the
magnetic vector potential In classical electromagnetism, magnetic vector potential (often called A) is the vector quantity defined so that its curl is equal to the magnetic field: \nabla \times \mathbf = \mathbf. Together with the electric potential ''φ'', the magnetic v ...
, D is the
diffusivity Diffusivity is a rate of diffusion, a measure of the rate at which particles or heat or fluids can spread. It is measured differently for different mediums. Diffusivity may refer to: *Thermal diffusivity, diffusivity of heat *Diffusivity of mass: ...
of the chemical species, z is the valence of ionic species, e is the
elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
, k_\text is the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, ...
, and T is the
absolute temperature Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics. Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic wor ...
.


Applications

Electro-osmotic flow is commonly used in
microfluidic Microfluidics refers to the behavior, precise control, and manipulation of fluids that are geometrically constrained to a small scale (typically sub-millimeter) at which surface forces dominate volumetric forces. It is a multidisciplinary field tha ...
devices, soil analysis and processing, and chemical analysis, all of which routinely involve systems with highly charged surfaces, often of
oxide An oxide () is a chemical compound that contains at least one oxygen atom and one other element in its chemical formula. "Oxide" itself is the dianion of oxygen, an O2– (molecular) ion. with oxygen in the oxidation state of −2. Most of the E ...
s. One example is
capillary electrophoresis Capillary electrophoresis (CE) is a family of electrokinetic separation methods performed in submillimeter diameter capillaries and in micro- and nanofluidic channels. Very often, CE refers to capillary zone electrophoresis (CZE), but other electr ...
, in which electric fields are used to separate chemicals according to their electrophoretic mobility by applying an electric field to a narrow capillary, usually made of
silica Silicon dioxide, also known as silica, is an oxide of silicon with the chemical formula , most commonly found in nature as quartz and in various living organisms. In many parts of the world, silica is the major constituent of sand. Silica is one ...
. In electrophoretic separations, the electroosmotic flow affects the
elution time In analytical and organic chemistry, elution is the process of extracting one material from another by washing with a solvent; as in washing of loaded ion-exchange resins to remove captured ions. In a liquid chromatography experiment, for exa ...
of the analytes. Electro-osmotic flow is actuated in a
FlowFET A flowFET is a microfluidic component which allows the rate of flow of liquid in a microfluidic channel to be modulated by the electrical potential applied to it. In this way, it behaves as a microfluidic analogue to the field effect transistor, ex ...
to electronically control fluid flow through a junction. It is projected that micro fluidic devices utilizing electroosmotic flow will have applications in medical research. Once controlling this flow is better understood and implemented, the ability to separate fluids on the atomic level will be a vital component for drug dischargers. Mixing fluids at the micro scale is currently troublesome. It is believed that electrically controlling fluids will be the method in which small fluids are mixed. A controversial use of electro-osmotic systems is the control rising damp in the walls of buildings. Available at
Springer.com
/ref> While there is little evidence to suggest that these systems can be useful in moving salts in walls, such systems are claimed to be especially effective in structures with very thick walls. However some claim that there is no scientific base for those systems, and cite several examples for their failure. Electro-osmosis can also be used for self-pumping pores powered by chemical reactions rather than electric fields. This approach, using , has been demonstrated and modeled with the Nernst-Planck-Stokes equations.


Physics

In
fuel cell A fuel cell is an electrochemical cell that converts the chemical energy of a fuel (often hydrogen) and an oxidizing agent (often oxygen) into electricity through a pair of redox reactions. Fuel cells are different from most batteries in requ ...
s, electro-osmosis causes
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
s moving through a
proton exchange membrane A proton-exchange membrane, or polymer-electrolyte membrane (PEM), is a semipermeable membrane generally made from ionomers and designed to conduct protons while acting as an electronic insulator and reactant barrier, e.g. to oxygen and hydrogen g ...
(PEM) to drag water molecules from one side (
anode An anode is an electrode of a polarized electrical device through which conventional current enters the device. This contrasts with a cathode, an electrode of the device through which conventional current leaves the device. A common mnemonic is ...
) to the other (
cathode A cathode is the electrode from which a conventional current leaves a polarized electrical device. This definition can be recalled by using the mnemonic ''CCD'' for ''Cathode Current Departs''. A conventional current describes the direction in whi ...
).


Vascular plant biology

In vascular plant biology, electro-osmosis is also used as an alternative or supplemental explanation for the movement of polar liquids via the
phloem Phloem (, ) is the living biological tissue, tissue in vascular plants that transports the soluble organic compounds made during photosynthesis and known as ''photosynthates'', in particular the sugar sucrose, to the rest of the plant. This tran ...
that differs from the
cohesion-tension theory Xylem is one of the two types of transport tissue in vascular plants, the other being phloem. The basic function of xylem is to transport water from roots to stems and leaves, but it also transports nutrients. The word ''xylem'' is derived from ...
supplied in the mass flow hypothesis and others, such as
cytoplasmic streaming Cytoplasmic streaming, also called protoplasmic streaming and cyclosis, is the flow of the cytoplasm inside the cell, driven by forces from the cytoskeleton. It is likely that its function is, at least in part, to speed up the transport of mol ...
.Clegg, C. J., Mackean, D. G. (2006) "''Advanced Biology – principles & applications''" Hodder Stoughton Publishers, pp. 340–343.
Companion cells Phloem (, ) is the living tissue in vascular plants that transports the soluble organic compounds made during photosynthesis and known as ''photosynthates'', in particular the sugar sucrose, to the rest of the plant. This transport process is c ...
are involved in the "cyclic" withdrawal of ions (K+) from sieve tubes, and their secretion parallel to their position of withdrawal between sieve plates, resulting in polarisation of sieve plate elements alongside
potential difference Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
in pressure, and results in polar water molecules and other solutes present moved upward through the phloem. In 2003,
St Petersburg University Saint Petersburg State University (SPBU; russian: Санкт-Петербургский государственный университет) is a public research university in Saint Petersburg, Russia. Founded in 1724 by a decree of Peter the G ...
graduates applied direct
electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving pa ...
to 10 mm segments of mesocotyls of maize seedlings alongside one-year linden shoots; electrolyte solutions present in the tissues moved toward the cathode that was in place, suggesting that electro-osmosis might play a role in solution transport through conductive plant tissues.


Disadvantages

Maintaining an electric field in an electrolyte requires Faradaic reactions to occur at the anode and cathode. This is typically
electrolysis of water Electrolysis of water, also known as electrochemical water splitting, is the process of using electricity to decompose water into oxygen and hydrogen gas by electrolysis. Hydrogen gas released in this way can be used as hydrogen fuel, or remi ...
, which generates
hydrogen peroxide Hydrogen peroxide is a chemical compound with the formula . In its pure form, it is a very pale blue liquid that is slightly more viscous than water. It is used as an oxidizer, bleaching agent, and antiseptic, usually as a dilute solution (3% ...
,
hydrogen ion A hydrogen ion is created when a hydrogen atom loses or gains an electron. A positively charged hydrogen ion (or proton) can readily combine with other particles and therefore is only seen isolated when it is in a gaseous state or a nearly particle ...
s (acid) and
hydroxide Hydroxide is a diatomic anion with chemical formula OH−. It consists of an oxygen and hydrogen atom held together by a single covalent bond, and carries a negative electric charge. It is an important but usually minor constituent of water. I ...
(base) as well as
oxygen Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as wel ...
and
hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, an ...
gas bubbles. The hydrogen peroxide and/or pH changes generated can adversely affect biological cells and biomolecules such as proteins, while gas bubbles tend to "clog"
microfluidic Microfluidics refers to the behavior, precise control, and manipulation of fluids that are geometrically constrained to a small scale (typically sub-millimeter) at which surface forces dominate volumetric forces. It is a multidisciplinary field tha ...
systems. These problems can be alleviated by using alternative electrode materials such as
conjugated polymers In theoretical chemistry, a conjugated system is a system of connected p-orbitals with delocalized electrons in a molecule, which in general lowers the overall energy of the molecule and increases stability. It is conventionally represented as ...
which can undergo the Faradaic reactions themselves, dramatically reducing electrolysis.


See also

*
Surface charge Surface charge is a two-dimensional surface with non-zero electric charge. These electric charges are constrained on this 2-D surface, and surface charge density, measured in coulombs per square meter (C•m−2), is used to describe the charge di ...
*
Capillary electrophoresis Capillary electrophoresis (CE) is a family of electrokinetic separation methods performed in submillimeter diameter capillaries and in micro- and nanofluidic channels. Very often, CE refers to capillary zone electrophoresis (CZE), but other electr ...
*
Electrical double layer A double layer (DL, also called an electrical double layer, EDL) is a structure that appears on the surface of an object when it is exposed to a fluid. The object might be a solid particle, a gas bubble, a liquid droplet, or a porous body. The D ...
*
Streaming current Streaming media is multimedia that is delivered and consumed in a continuous manner from a source, with little or no intermediate storage in network elements. ''Streaming'' refers to the delivery method of content, rather than the content it ...
*
Induced-charge Electrokinetics Induced-charge electrokinetics in physics is the electrically driven fluid flow and particle motion in a liquid electrolyte.V. G. Levich, Physicochemical Hydrodynamics. Englewood Cliffs, N.J., Prentice-Hall, (1962) Consider a metal particle (whi ...
*
Streaming potential Streaming media is multimedia that is delivered and consumed in a continuous manner from a source, with little or no intermediate storage in network elements. ''Streaming'' refers to the delivery method of content, rather than the content it ...
*
Zeta potential Zeta potential is the electrical potential at the slipping plane. This plane is the interface which separates mobile fluid from fluid that remains attached to the surface. Zeta potential is a scientific term for electrokinetic potential in coll ...
*
Electroosmotic pump An electroosmotic pump (EOP), or EO pump, is used for generating flow or pressure by use of an electric field. One application of this is removing liquid flooding water from channels and gas diffusion layers and direct hydration of the proton excha ...
*
Electrical double layer A double layer (DL, also called an electrical double layer, EDL) is a structure that appears on the surface of an object when it is exposed to a fluid. The object might be a solid particle, a gas bubble, a liquid droplet, or a porous body. The D ...
*
Microfluidics Microfluidics refers to the behavior, precise control, and manipulation of fluids that are geometrically constrained to a small scale (typically sub-millimeter) at which surface forces dominate volumetric forces. It is a multidisciplinary field tha ...
*
Electrochemistry Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential difference, as a measurable and quantitative phenomenon, and identifiable chemical change, with the potential difference as an outco ...


References


Further reading

* * * * {{DEFAULTSORT:Electro-Osmosis Fluid dynamics Electrochemistry