Electro-osmosis

Last updated October 21, 2024

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.

History

Electro-osmotic flow was first reported in 1807 by Ferdinand Friedrich Reuss (18 February 1778 (Tübingen, Germany) – 14 April 1852 (Stuttgart, Germany))^[1] in an unpublished lecture before the Physical-Medical Society of Moscow;^[2] Reuss first published an account of electro-osmotic flow in 1809 in the Memoirs of the Imperial Society of Naturalists of Moscow .^[3]^[4] 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).^[5]^[6]

Cause

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.

Description

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.^[7]

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

\nabla \cdot \mathbf {U} =0

and momentum

\rho {\frac {D\mathbf {U} }{Dt}}=-\nabla p+\mu \nabla ^{2}\mathbf {U} +\rho _{e}\nabla \left(\psi +\phi \right),

where $U$ is the velocity vector, $ρ$ is the density of the fluid, $D/Dt$ 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.

Laplace’s equation 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 {-\rho _{e}}{\epsilon \epsilon _{0}}},

where $ε$ is the dielectric constant of the electrolyte solution and $ε 0$ is the vacuum permittivity. This equation can be further simplified using the Debye-Hückel approximation

\nabla ^{2}\psi =k^{2}\psi ,

where $1 / k$ 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

\rho _{e}=-\epsilon \epsilon _{0}k^{2}\psi .

The transport of ions in space can be modeled using the Nernst–Planck equation:^[8]

{\partial c \over {\partial t}}=\nabla \cdot \left[D\nabla c-c{\bf {v}}+{Dze \over {k_{\text{B}}T}}c\left(\nabla \phi +{\partial {\bf {A}} \over {\partial t}}\right)\right]

Where $\ c$ is the ion concentration, ${\bf {A}}$ is the magnetic vector potential, $D$ is the diffusivity of the chemical species, $z$ is the valence of ionic species, $e$ is the elementary charge, $k_{\text{B}}$ is the Boltzmann constant, and $T$ is the absolute temperature.

Applications

Electro-osmotic flow is commonly used in microfluidic devices,^[9]^[10] soil analysis and processing,^[11] and chemical analysis,^[12] all of which routinely involve systems with highly charged surfaces, often of oxides. One example is capillary electrophoresis,^[10]^[12] 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. In electrophoretic separations, the electroosmotic flow affects the elution time of the analytes.

Electro-osmotic flow is actuated in a FlowFET 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.^[13] 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.^[13]

A controversial use of electro-osmotic systems is the control rising damp in the walls of buildings.^[14] 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.^[15]

Electro-osmosis can also be used for self-pumping pores powered by chemical reactions rather than electric fields. This approach, using H₂O₂, has been demonstrated^[16] and modeled with the Nernst-Planck-Stokes equations.^[8]

Physics

In fuel cells, electro-osmosis causes protons moving through a proton exchange membrane (PEM) to drag water molecules from one side (anode) to the other (cathode).

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 that differs from the cohesion-tension theory supplied in the mass flow hypothesis and others, such as cytoplasmic streaming.^[17] Companion cells 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 in pressure, and results in polar water molecules and other solutes present moved upward through the phloem.^[17]

In 2003, St Petersburg University graduates applied direct electric current 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.^[18]

Disadvantages

Maintaining an electric field in an electrolyte requires Faradaic reactions to occur at the anode and cathode. This is typically electrolysis of water, which generates hydrogen peroxide, hydrogen ions (acid) and hydroxide (base) as well as oxygen and hydrogen 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 systems. These problems can be alleviated by using alternative electrode materials such as conjugated polymers which can undergo the Faradaic reactions themselves, dramatically reducing electrolysis.^[19]

Related Research Articles

Electrophoresis is the motion of charged dispersed particles or dissolved charged molecules relative to a fluid under the influence of a spatially uniform electric field. As a rule, these are zwitterions.

In plasmas and electrolytes, the Debye length, 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 increasingly electrically screened and the electric potential decreases in magnitude by 1/e. A Debye sphere is a volume whose radius is the Debye length. Debye length is an important parameter in plasma physics, electrolytes, and colloids. The corresponding Debye screening wave vector $for particles of density, charge at a temperature is given by in Gaussian units. Expressions in MKS units will be given below. The analogous quantities at very low temperatures are known as the Thomas-Fermi length and the Thomas-Fermi wave vector. They are of interest in describing the behaviour of electrons in metals at room temperature.$

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.

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 electrophoretic techniques including capillary gel electrophoresis (CGE), capillary isoelectric focusing (CIEF), capillary isotachophoresis and micellar electrokinetic chromatography (MEKC) belong also to this class of methods. In CE methods, analytes migrate through electrolyte solutions under the influence of an electric field. Analytes can be separated according to ionic mobility and/or partitioning into an alternate phase via non-covalent interactions. Additionally, analytes may be concentrated or "focused" by means of gradients in conductivity and pH.

Electrohydrodynamics (EHD), also known as electro-fluid-dynamics (EFD) or electrokinetics, is the study of the dynamics of electrically charged fluids. Electrohydrodynamics (EHD) is a joint domain of electrodynamics and fluid dynamics mainly focused on the fluid motion induced by electric fields. EHD, in its simplest form, involves the application of an electric field to a fluid medium, resulting in fluid flow, form, or properties manipulation. These mechanisms arise from the interaction between the electric fields and charged particles or polarization effects within the fluid. The generation and movement of charge carriers (ions) in a fluid subjected to an electric field are the underlying physics of all EHD-based technologies.

A surface charge is an electric charge present on a two-dimensional surface. 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 distribution on the surface. The electric potential is continuous across a surface charge and the electric field is discontinuous, but not infinite; this is unless the surface charge consists of a dipole layer. In comparison, the potential and electric field both diverge at any point charge or linear charge.

In plasma physics, the Hasegawa–Mima equation, named after Akira Hasegawa and Kunioki Mima, is an equation that describes a certain regime of plasma, where the time scales are very fast, and the distance scale in the direction of the magnetic field is long. In particular the equation is useful for describing turbulence in some tokamaks. The equation was introduced in Hasegawa and Mima's paper submitted in 1977 to Physics of Fluids, where they compared it to the results of the ATC tokamak.

A streaming current and streaming potential are two interrelated electrokinetic phenomena studied in the areas of surface chemistry and electrochemistry. They are an electric current or potential which originates when an electrolyte is driven by a pressure gradient through a channel or porous plug with charged walls.

Electroacoustic phenomena arise when ultrasound propagates through a fluid containing ions. The associated particle motion generates electric signals because ions have electric charge. This coupling between ultrasound and electric field is called electroacoustic phenomena. The fluid might be a simple Newtonian liquid, or complex heterogeneous dispersion, emulsion or even a porous body. There are several different electroacoustic effects depending on the nature of the fluid.

The Dukhin number is a dimensionless quantity that characterizes the contribution of the surface conductivity to various electrokinetic and electroacoustic effects, as well as to electrical conductivity and permittivity of fluid heterogeneous systems. The number was named after Stanislav and Andrei Dukhin.

In surface science, a double layer 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 DL refers to two parallel layers of charge surrounding the object. The first layer, the surface charge, consists of ions which are adsorbed onto the object due to chemical interactions. The second layer is composed of ions attracted to the surface charge via the Coulomb force, electrically screening the first layer. This second layer is loosely associated with the object. It is made of free ions that move in the fluid under the influence of electric attraction and thermal motion rather than being firmly anchored. It is thus called the "diffuse layer".

Surface conductivity is an additional conductivity of an electrolyte in the vicinity of the charged interfaces. Surface and volume conductivity of liquids correspond to the electrically driven motion of ions in an electric field. A layer of counter ions of the opposite polarity to the surface charge exists close to the interface. It is formed due to attraction of counter-ions by the surface charges. This layer of higher ionic concentration is a part of the interfacial double layer. The concentration of the ions in this layer is higher as compared to the ionic strength of the liquid bulk. This leads to the higher electric conductivity of this layer.

Electrokinetic phenomena are a family of several different effects that occur in heterogeneous fluids, or in porous bodies filled with fluid, or in a fast flow over a flat surface. The term heterogeneous here means a fluid containing particles. Particles can be solid, liquid or gas bubbles with sizes on the scale of a micrometer or nanometer. There is a common source of all these effects—the so-called interfacial 'double layer' of charges. Influence of an external force on the diffuse layer generates tangential motion of a fluid with respect to an adjacent charged surface. This force might be electric, pressure gradient, concentration gradient, or gravity. In addition, the moving phase might be either continuous fluid or dispersed phase.

Sedimentation potential occurs when dispersed particles move under the influence of either gravity or centrifugation or electricity in a medium. This motion disrupts the equilibrium symmetry of the particle's double layer. While the particle moves, the ions in the electric double layer lag behind due to the liquid flow. This causes a slight displacement between the surface charge and the electric charge of the diffuse layer. As a result, the moving particle creates a dipole moment. The sum of all of the dipoles generates an electric field which is called sedimentation potential. It can be measured with an open electrical circuit, which is also called sedimentation current.

Diffusiophoresis is the spontaneous motion of colloidal particles or molecules in a fluid, induced by a concentration gradient of a different substance. In other words, it is motion of one species, A, in response to a concentration gradient in another species, B. Typically, A is colloidal particles which are in aqueous solution in which B is a dissolved salt such as sodium chloride, and so the particles of A are much larger than the ions of B. But both A and B could be polymer molecules, and B could be a small molecule. For example, concentration gradients in ethanol solutions in water move 1 μm diameter colloidal particles with diffusiophoretic velocities $of order 0.1 to 1 μm/s, the movement is towards regions of the solution with lower ethanol concentration. Both species A and B will typically be diffusing but diffusiophoresis is distinct from simple diffusion: in simple diffusion a species A moves down a gradient in its own concentration.$

Nanofluidic circuitry is a nanotechnology aiming for control of fluids in nanometer scale. Due to the effect of an electrical double layer within the fluid channel, the behavior of nanofluid is observed to be significantly different compared with its microfluidic counterparts. Its typical characteristic dimensions fall within the range of 1–100 nm. At least one dimension of the structure is in nanoscopic scale. Phenomena of fluids in nano-scale structure are discovered to be of different properties in electrochemistry and fluid dynamics.

In chemical analysis, capillary electrochromatography (CEC) is a chromatographic technique in which the mobile phase is driven through the chromatographic bed by electro-osmosis. Capillary electrochromatography is a combination of two analytical techniques, high-performance liquid chromatography and capillary electrophoresis. Capillary electrophoresis aims to separate analytes on the basis of their mass-to-charge ratio by passing a high voltage across ends of a capillary tube, which is filled with the analyte. High-performance liquid chromatography separates analytes by passing them, under high pressure, through a column filled with stationary phase. The interactions between the analytes and the stationary phase and mobile phase lead to the separation of the analytes. In capillary electrochromatography capillaries, packed with HPLC stationary phase, are subjected to a high voltage. Separation is achieved by electrophoretic migration of solutes and differential partitioning.

Double layer forces occur between charged objects across liquids, typically water. This force acts over distances that are comparable to the Debye length, which is on the order of one to a few tenths of nanometers. The strength of these forces increases with the magnitude of the surface charge density. For two similarly charged objects, this force is repulsive and decays exponentially at larger distances, see figure. For unequally charged objects and eventually at shorted distances, these forces may also be attractive. The theory due to Derjaguin, Landau, Verwey, and Overbeek (DLVO) combines such double layer forces together with Van der Waals forces in order to estimate the actual interaction potential between colloidal particles.

Induced-charge electrokinetics in physics is the electrically driven fluid flow and particle motion in a liquid electrolyte. Consider a metal particle in contact with an aqueous solution in a chamber/channel. If different voltages apply to the end of this chamber/channel, electric field will generate in this chamber/channel. This applied electric field passes through this metal particle and causes the free charges inside the particle migrate under the skin of particle. As a result of this migration, the negative charges move to the side which is close to the positive voltage while the positive charges move to the opposite side of the particle. These charges under the skin of the conducting particle attract the counter-ions of the aqueous solution; thus, the electric double layer (EDL) forms around the particle. The EDL sign on the surface of the conducting particle changes from positive to negative and the distribution of the charges varies along the particle geometry. Due to these variations, the EDL is non-uniform and has different signs. Thus, the induced zeta potential around the particle, and consequently slip velocity on the surface of the particle, vary as a function of the local electric field. Differences in magnitude and direction of slip velocity on the surface of the conducting particle effects the flow pattern around this particle and causes micro vortices. Yasaman Daghighi and Dongqing Li, for the first time, experimentally illustrated these induced vortices around a 1.2 mm diameter carbon-steel sphere under the 40V/cm direct current (DC) external electric filed. Chenhui Peng et al. also experimentally showed the patterns of electro-osmotic flow around an Au sphere when alternating current (AC) is involved . Electrokinetics here refers to a branch of science related to the motion and reaction of charged particles to the applied electric filed and its effects on its environment. It is sometimes referred as non-linear electrokinetic phenomena as well.

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, except that in the flowFET the flow of liquid takes the place of the flow of electric current. Indeed, the name of the flowFET is derived from the naming convention of electronic FETs.

References

↑ Biographical information about F.F. Reuss is available (in German) at: Deutsche Biographie
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↑ Reuss, F. F. (1809). "Notice sur un nouvel effet de l'électricité galvanique" [Notice of a new effect of galvanic electricity]. Mémoires de la Société Impériale des Naturalistes de Moscou (in French). 2: 327–337.
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