# Electrokinetics

## Introduction

• Voltaic reports the creation of a source of steady electric power in 1800 (now called the Voltaic pile.)
• Napoleon acknowledges Volta's important contributions in 1801.
• In 1809 Reuss reports this experiment - electrophoresis and electro-osmosis.

Applying an electric field produces both particle motion and liquid motion.

The converse is true: having particle motion or liquid motion produces an electric field. These effects are called: the sedimentation potential and the streaming potential.

## Electrophoresis

The usual experiment is to place the dispersion in a narrow tube (to allow for temperature control); to apply a constant electric field; and measure the velocity of the particles.

Because electro-osmosis causes liquid motion in the opposite direction of the particle motion, a correction needs to be applied. The usual procedure is to measure particle motion only at those positions across the cell corresponding to no liquid flow (which is circulating).

A common improvement is to use a laser to illuminate the dispersion and measure particle velocities with laser velocimetry.

One of the most common uses of electrophoresis is the process of agarose gel electrophoresis in biology, used to separate DNA fragments according to size. DNA is negatively charged so it will travel towards to the positive terminal. Since the gel is semi-porous, the smaller fragments of DNA will travel faster and hence further than the larger fragments, resulting in separation based on size (number of base pairs in the DNA). By staining the DNA with a dye like ethidium bromide, the DNA fragments can be seen when the gel is illuminated with UV light.

An example of gel electrophoresis (of caviar): http://www.amnh.org/learn/pd/genetics/case_study/alter.html

## Dielectrophoresis

Dielectrophoresis is the motion of a dielectric object in a nonuniform electric field. A non-uniform electric field creates an induced electric dipole in a dielectric that feels a force in the non-uniform field. By applying an appropriate local electric field pattern, any particle with a dielectric constant different to that of the surrounding medium can be manipulated with DEP. Nowadays, dielectrophoresis are widely used to manipulate, transport, separate and sort different types of particles.

Force on a dielectric particle in a non-uniform Electric Field

Consider a dielectric particle suspended in a spatially non-uniform electric field such as that shown in figure 1. The applied field induces a dipole in the particle; the interaction of the induced dipole with the electric field generates a force. Due to the presence of a field gradient, these forces are not equal and there is a net movement. If the particle is more conductive than the medium around it (as shown in the figure below), the dipole aligns with the field and the force acts up the field gradient towards the region of highest electric field. If the particle is less polarisable than the medium, the dipole aligns against the field and the particle is repelled from regions of high electric field. The force is dependent on the induced dipole, and is unaffected by the direction of the electric field, responding only to the field gradient. Since the alignment of the field is irrelevant, this force can also be generated in AC fields which has the advantage of reducing any electrophoretic force (due to any net particle charge) to zero.

A schematic of a polarisable particle suspended within a point-plane electrode system. When the particle polarises, the interaction between the dipolar charges with the local electric field produces a force. Due to the inhomogeneous nature of the electric field, the force is greater in the side facing the point than that on the side facing the plane, and there is net motion towards the point electrode. This effect is called positive dielectrophoresis. If the particle is less polarisable than the surrounding medium, the dipole will align counter to the field and the particle will be repelled from the high field regions, called negative dielectrophoresis.

[[1]]

DEP Electrode Array (Westervelt Group)
Yeast Cells trapped in place to spell "Lab on a Chip" - made the cover of said magazine in 2008

## Electro-osmosis

Electro-osmosis is particularly useful for large particles or fibers. These materials are held stationary in a cell with electrodes on the outside to create an electric field.

The volume of liquid motion is small, so a trick is needed to detect it: See the diagram. The liquid motion causes a bubble in a fine tube to move. Its velocity is easy to detect.

Morrison Fig. 17.15

"In electrochemistry, physics and vascular plant biology, electro-osmosis, also called electroendosmosis, is the motion of polar liquid through a membrane or other porous structure (generally, along charged surfaces of any shape and also through non-macroporous materials which have ionic sites and allow for water uptake, the latter sometimes referred to as "chemical porosity" ) under the influence of an applied electric field. Electro-osmosis was first described by F.F. Reuss in 1809, and has growing applications in microfluidics." [[2]]

"The cause of electroosmotic flow is an electrical double layer that forms at the stationary/solution interface. In capillary electrophoresis, the narrow channels are made up of silica, and silanol groups form the inner surface of the capillary column. These silanol groups are ionized above pH3. Thus, the inner surface of the channel is negatively charged. In solutions containing ions, the cations will migrate to the negatively charged wall. This forms an electrical double layer. When an electrical potential is applied to the column, with an anode at one end of the column and a cathode at another, the cations will migrate towards the cathode. Since these cations are solvated and clustered at the walls of the channel, they drag the rest of the solution with them, even the anions." [[3]]

## Sedimentation potential

A easy method to make particles move is to let them sediment. The sedimentation potential is measured (in principle) with electrodes attached to the cylinder walls. In practice, this is a difficult experiment because the falling particles create an upward liquid flow complicating the analysis.

In nonaqueous dispersions sedimentation of particles or creaming of emulsions can lead to quite large and dangerous electric potentials.

## Streaming potential

Forcing liquid motion while holding particles stationary is easier than forcing particle motion as in measuring sedimentation potential.

The particle or fibers are packed in a cell. On the outside of the cell are electrodes to measure the electric potential generated from the flow of the liquid.

Georg Hermann Quincke first observed streaming current in 1859.

The instrument is commercially available from companies such as Micometrix (http://www.micrometrix.com/) and Chemtrac (http://www.chemtrac.com/products/scm/detail.htm).

Recently, scientists have also studied streaming currents in nanofluidic channels. The measured streaming current increases proportionally with the pressure gradient, increases with channel height, and decreases above a critical salt concentration of ~10 mM. The data fits well to nonlinear Poisson-Boltzmann theory.

(Sources: http://en.wikipedia.org/wiki/Streaming_current, F.H.J. van der Heyden et al., Phys. Rev. Lett. 95, 116104 (2005))

Brookhaven Instruments Corporation

## Electroacoustic measurements

Petrus (Peter) Josephus Wilhelmus Debye was born March 24, 1884, at Maastricht, the Netherlands. He won the Nobel Prize in Chemistry in 1936.

He was asked to contribute to the first issue of The Journal of Chemical Physics; a journal established as a recognition of the fertile interaction of these sciences. (J. Chem. Phys., 1, 13-16, 1933). The title of that article was "A method for the determination of the mass of electrolyte ions."

"The question how many molecules of solvent are intimately connected with the different ions in a solution is far from being solved. It occurred to me that we could perform some improvement if a method could be found enabling us to determine directly the masses of ions."

Debye showed that how oscillating pressure waves produce oscillating electric fields. At greater frequencies the inertia of large ions prevent them from remaining in phase with the sound wave and the magnitude of the oscillation electric field drops.

The idea is directly extended to charged particle dispersions since the difference in masses of the charged species is large.

Its great practical advantage is its use at high particle concentrations and/or opaque dispersions.

 One technique uses an ultrasonic pressure wave to perturb the equilibrium double layer. This polarization generates an alternating electric field called the Colloid Vibration Potential: $CVP=\frac{2p}{\lambda _{0}}\Phi \frac{\Delta \rho }{\rho }\frac{\varepsilon \zeta }{\eta }\,\!$ Another technique uses an high frequency AC electric field to perturb the equilibrium double layer. This motion generates an alternating pressure wave called the Electrokinetic Sonic Amplitude. $ESA=A\left( \omega \right)\Phi \frac{\Delta \rho }{\rho }\frac{\varepsilon \zeta }{\eta }\,\!$

## Diffusiphoresis and capillary osmosis

Diffusiphoresis is a motion of dispersed particles in a fluid induced by a diffusion gradient of molecular substances that are dissolved in the fluid. This gradient affects structure of the particles Double Layer (interfacial) and causes sliding motion of the fluid relative to the particle surface. Capillary osmosis is effect that is reverse to diffusiophoresis, like electro-osmosis is reverse to electrophoresis.

## Colloid vibration current

Colloid vibration current is an electroacoustic phenomenon that arises when ultrasound propagates through a fluid that contain ions and either solid particles or emulsion droplets. The pressure gradient in ultrasound wave moves particles relative to the fluid. This motion disturbes double layer that exist on the particle-fluid interface.

This picture illustrates mechanism of this distortion. Practically all particles in fluids cary surface charge. This surface charge is screened with equally charged duffuse layer. This structure is called double layer. Ions of the diffuse layer are located in the fluid. They can move with the fluid. Fluid motion relative to the particles drag this ions to one of the particles poles. On the picture it is the left hand side pole. As a result, there is an excess of negative ions in the vicinity of the left pole and excessive positive surface charge at the right pole. Particle gain dipole moment. These dipole moments generate electric field that in turn generates electric current. This current is measurable. This phenomenon is widely used for measuring zeta potential in concentrated colloids.