Electroosmotic motion

Isoelectric An ionic macromolecule that exhibits no electrophoretic or electroosmotic motion. 

Isoelectric Point The solution pH or condition for which the electro-kinetic or zeta potential is zero. Under this condition, a colloidal system will exhibit no electrophoretic or electroosmotic motions. See also Point of Zero Charge. 

Consider electroosmotic motion in a porous medium. We can model this medium by a system of parallel cylindrical microcapillaries. Consider one of such capillaries and assume that its wall carries a charge. The motion of Uquid in the... 

Note that in the small double layer thickness approximation, the character of motion of liquid in the capillary is that of plug flow with the velocity U. If the thickness of the double layer is small, but finite, the velocity profile looks like the one shown in Fig. 7.9. For the characteristic values C = 0.1 V, = 10 m, we have for water U = m/s. Thus, electroosmotic motion has a very low velocity. 

Note that the liquid flow rate during electroosmotic motion is = na U, while the hydraulic flow rate of liquid due to a given pressure gradient be equal to Qkfdr = na dp/dx)/%n. Hence, Qa/Qhydr 1/a. It means that as the capillary radius gets smaller, the motion of the liquid becomes predominantly electroosmotic, rather than hydraulic. This conclusion is true only for a Ad. 

Another hmiting case, Xd a, is mostly realized in disperse systems. In particular, for colloidal systems a ranges between 0.1 and 1 pm, and at Xp 10 pm we have Xo/a 10 -10 . In this case the curvature of the particle s surface can be neglected, and the diffusion layer may be considered as locally flat. In this approximation, the electric field in the double layer is parallel to the surface. The motion of charged ions in the double layer may be considered as an electroosmotic motion along the surface just as in paragraph 7.5. It follows from (7.72) that... 

The electrophoresis retardation is motion of ions in the double layer in direction opposite to particles motion. Due to forces of viscous friction, the ions cause the electroosmotic motion of liquid, which retards the particle s motion. Following the approach presented in [48], consider the electrophoresis motion of a particle, assuming that the double layer remains spherical during the motion, and the potential of the particle s surface is small enough, so Debye-Huckel approximation is valid. The motion is supposed to be inertialess. Introduce a coordinate system moving with the particle s velocity U so that in the chosen system of coordinates the particle is motionless, and the flow velocity at infinity is equal to - 17 (Fig. 9.2). 

Streaming Potential When the solution is forced through the porous solid under the effect of an external pressure P, the character of liquid motion in the cylindrical pores will be different from that in electroosmotic transport. Since the external pressure acts uniformly on the full pore cross section, the velocity of the liquid will be highest in the center of the pore, and it will gradually decrease with decreasing distance from the pore walls (Fig. 31.5). The velocity distribution across the pore is quantitatively described by the Poiseuille equation. 

The electroosmotic pumping is executed when an electric field is applied across the channel. The moving force comes from the ion moves in the double layer at the wall towards the electrode of opposite polarity, which creates motion of the fluid near the walls and transfer of the bulk fluid in convection motion via viscous forces. The potential at the shear plane between the fixed Stem layer and Gouy-Champmon layer is called zeta potential, which is strongly dependent on the chemistry of the two phase system, i.e. the chemical composition of both solution and wall surface. The electroosmotic mobility, xeo, can be defined as follow,... 

FIGURE 11.32 Flow profiles in microchannels, (a) A pressure gradient, - AP, along a channel generates a parabolic or Poiseuille flow profile in the channel. The velocity of the flow varies across the entire cross-sectional area of the channel. On the right is an experimental measurement of the distortion of a volume of fluid in a Poiseuille flow. The frames show the state of the volume of fluid 0, 66, and 165 ms after the creation of a fluorescent molecule, (b) In electroosmotic flow in a channel, motion is induced by an applied electric field E. The flow speed only varies within the so-called Debye screening layer, of thickness D. On the right is an experimental measurement of the distortion of a volume of fluid in an electroosmotic flow. The frames show the state of the fluorescent volume of fluid 0, 66, and 165 ms after the creation of a fluorescent molecule [165], Source http //www.niherst.gov.tt/scipop/sci-bits/microfluidics.htm (see Plate 12 for color version). 

Using the SI units, the velocity of the EOF is expressed in meters/second (m s ) and the electric held in volts/meter (V m ). Consequently, the electroosmotic mobility has the dimension of m V s. Since electroosmotic and electrophoretic mobility are converse manifestations of the same underlying phenomena, the Helmholtz-von Smoluchowski equation applies to electroosmosis, as well as to electrophoresis (see below). In fact, it describes the motion of a solution in contact with a charged surface or the motion of ions relative to a solution, both under the action of an electric held, in the case of electroosmosis and electrophoresis, respectively. 

Electrophoretic migrations are always superimposed on other displacements, which must either be eliminated or corrected to give accurate values for mobility. Examples of these other kinds of movement are Brownian motion, sedimentation, convection, and electroosmotic flow. Brownian motion, being random, is eliminated by averaging a series of individual observations. Sedimentation and convection, on the other hand, are systematic effects. Corrections for the former may be made by observing a particle with and without the electric field, and the latter may be minimized by effective thermostating and working at low current densities. 

Once the hydrocarbons have been solubilized in the formation water, they move with the water under the influence of elevation and pressure (fluid), thermal, electroosmotic and chemicoosmotic potentials. Of these, the fluid potential is the most important and the best known. The fluid potential is defined as the amount of work required to transport a unit mass of fluid from an arbitrary chosen datum (usually sea level) and state to the position and state of the point considered. The classic work of Hubbert (192) on the theory of groundwater motion was the first published account of the basinwide flow of fluids that considered the problem in exact mathematical terms as a steady-state phenomenon. His concept of formation fluid flow is shown in Figure 3A. However, incongruities in the relation between total hydraulic head and depth below surface in topographic low areas suggested that Hubbert s model was incomplete (193). Expanding on the work of Hubbert, Toth (194, 195) introduced a mathematical mfcdel in which exact flow patterns are... 

Capillary electrochromatography (CEC) — A special case of capillary liquid chromatography, in which the mobile phase motion is driven by -> electroosmotic volume flow through a capillary, filled, packed, or coated with a stationary phase, (which may be assisted by pressure). The retention time is determined by a combination of -> electrophoretic mobility and chromatographic retention. 

University, Krak6w [i]. He described Brownian molecular motion independently from Einstein considering the collisions explicitly between a particle and the surrounding solvent molecules [ii], worked on colloids [iv-v], and obtained an expression for the rate with which two particles diffuse together (-> Smoluchowski equation (b)) [iii-v]. He also derived an equation for the limiting velocity of electroosmotic flow through a capillary (-> Smoluchowski equation (a)). 

However, there is no corresponding increase in the average velocity with increased hydraulic diameter. This is because the nature of electroosmotic flow—the flow is generated by the motion of the net charge in the electrical double layer region driven by an applied electrical field. When the double layer thickness 1/k) is small, an analytical solution of the electroosmotic velocity can be derived from a one-dimensional channel system such as a cylindrical capillary with a circular cross section, given by... 

In most electroosmotic flows in microchannels, the flow rates are very small (e.g., 0.1 pL/min.) and the size of the microchannels is very small (e.g., 10 100 jm), it is extremely difficult to measure directly the flow rate or velocity of the electroosmotic flow in microchannels. To study liquid flow in microchannels, various microflow visualization methods have evolved. Micro particle image velocimetry (microPIV) is a method that was adapted from well-developed PIV techniques for flows in macro-sized systems [18-22]. In the microPIV technique, the fluid motion is inferred from the motion of sub-micron tracer particles. To eliminate the effect of Brownian motion, temporal or spatial averaging must be employed. Particle affinities for other particles, channel walls, and free surfaces must also be considered. In electrokinetic flows, the electrophoretic motion of the tracer particles (relative to the bulk flow) is an additional consideration that must be taken. These are the disadvantages of the microPIV technique. 

Fig. 3 Schematic representation of iontophoresis. Two electrode chambers, connected to a power source, are placed in contact with the skin. Upon application of the electric field, drug ions are repelled from the electrode of similar polarity (in this case, cations are repelled from the anode). This electrorepulsion (ER) also imposes inward motion on i) other cations present in the anode formulation, and ii) the outward transport of anions (e.g., CP) from within the skin. At the non-working electrode (in this case, the cathode), negative anions from the electrolyte are driven into and through the skin, while cations (e.g., Na ) are extracted from the tissue. The direction of the electroosmotic flow (EO) is also shown.

Figure 33-9 Velocities in the presence of electroosmotic flow. The length of the arrow next to an ion indicates the magnitude of its velocity the direction of the arrow indicates the direction of motion. The negative electrode would be to the right and the positive electrode to the left of this section of solution.

Electroosmosis causes a change in the level of the liquid in communicating vessels, i.e. in the anodic and cathodic parts of a U-shaped tube. This effect, referred to as the electroosmotic rise, turns out to be very strong for example an applied voltage of 100 V may result in a change in liquid levels of up to 20 cm. Electroosmosis and the electroosmotic rise are thus related to the motion of the liquid with respect to the immobilized disperse phase (porous diaphragm). In the case of electroosmotic rise, at equilibrium the electroosmotic transfer of the liquid is compensated by its back flow due to the change in hydrostatic pressures in different arms of the U-shaped tube. 

Electroosmosis is one of several electrokinetic effects that deal with phenomena associated with the relative motion of a charged solid and a solution. A related effect is the streaming potential that arises between two electrodes placed as in Figure 9.8.1 when a solution streams down the tube (essentially the inverse of the electroosmotic effect). Another is electrophoresis, where charged particles in a solution move in an electric field. These effects have been studied for a long time (37, 38). Electrophoresis is widely used for separations of proteins and DNA (gel electrophoresis) and many other substances (capillary electrophoresis). 

Electroosmosis The motion of liquid through a porous medium caused by an imposed electric field. The term replaces the older terms elec-trosmosis and electroendosmosis. The liquid moves with an electroos-motic velocity that depends on the electric surface potential in the stationary solid and on the electric field gradient. The electroosmotic volume flow is the volume flow rate through the porous plug and is usually expressed per unit electric field strength. The electroosmotic pressure is the pressure difference across the porous plug that is required to just stop electroosmotic flow. 

In analyzing the electrophoretic motion of a nonconducting particle where the Debye length is small compared with the characteristic particle dimension, say the radius, we may neglect curvature effects in the diffuse part of the double layer and treat the particle surface as locally plane. The electric field may therefore be considered to be applied parallel to the surface, and the analysis carried out in Section 6.5, in which electrical and viscous forces were balanced to determine the electroosmotic velocity for a fixed surface, applies here unchanged. Therefore in a reference frame in which the particle is stationary, from Eq. (6.5.5) we may write... 

Assume that the resistance to the cylinder motion is due to the shear stress associated with the electroosmotic flow that is generated, so that the Navier-Stokes equation reduces to a balance between viscous and electrical forces. Show that the solution for the electrophoretic velocity of the cylinder is the same as that for a sphere of the same zero potential with the Debye length small. 

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