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Dielectrophoresis (often abbreviated DEP) was first observed early in the 20th century, but described fully (and named) Herbert Pohl in 1950. It is an electrostatic phenomenon, distantly related to electrophoresis, and describes the motion of suspended particles resulting from polarisation forces produced by an inhomogeneous electric field.

In order to understand DEP, we begin with its more famous cousin, Electrophoresis (EP).  This is the physical manifestation of Coulomb's law:

                                                                              F= QE

Where F is the electrophoretic force, Q is charge and E is the electric field.at the charge.  The electric field is itself due to another charge; consider figure 1 with two charges Q1 and Q2.  Q1 induced a force in Q2 dependent on its magnitude, distance from Q2, and sign (as well as the physical properties of the space between them). The "electric field" of Q1 is merely the influence the charge has on any other charge throughput space, with a value which will vary with position.

Hence, any charge in an electric field will experience a force in the direction of the field; whether the charge moves towards the positive or negative potential creating the field will depend on the sign of Q.  Electrophoresis is commonly used in chemistry to separate molecules by capillary electrophoresis, or in fields from genetics to forensics to identify specific genes in DNA via gel electrophoresis (AKA the "DNA barcode").

As its name suggests, dielectrophoresis is related to electrophoresis, but the "di-" suffix (Greek for "two") comes from the fact that this is not the force arising from a single charge (or "monopole"), but from a dipole - something with both positive an negative charges that do not share the same position.   If an object consists or positive and negative charges, but the average positions of those charges do not lie in the same place, the object is a dipole. You can get permanent dipoles (e.g. water) and induced dipoles (e.g. a capacitor); particles are polarised when the average positions of positive and negative charge are moved apart by an electric field.

Coulomb's law states that a force acts on free charges, so our dipole in an electric field will experience  forces applied to both charges moving in opposite directions.  If the electric field is equal everywhere, then the forces on the dipole are equal and opposite, and the particle will not move (though it may align with the field).  However, if the electric field is non-uniform - that is, there is a gradient - then the force on the charge at the higher electric field will be greater than the force on the dipole in the lower electric field.  The particle will then move in the direction governed by the charge in the highest field, along the direction of the field gradient. The force can be in the direction of increasing or decreasing electric field - these are termed "positive dielectrophoresis" and "negative dielectrophoresis" respectively. Positive dielectrophoresis is shown in figure 2.

What governs whether the particle experiences positive or negative DEP? In reality, all materials have capacitance and resistance.  We can treat this as a resistor and capacitor in parallel. Any charged capacitor will accumulate charges at its surfaces. Where two different materials meet, the net charge on the dipole depends on the charges on both sides of the interface. The effect can be to change the direction of a net dipole on a particle without actually changing the sign of the dipole on the particle. This is called the Maxwell-Wagner interfacial polarisation (see figure, left). Where two such materials – say, a cell and water – meet, there will be different amounts of charge on either side of the interface, depending on which material is mostly conductive and which is mostly capacitive. As the ratios of charge either side of the interface changes, the cumulative effect is that the dipole can change in both magnitude and direction.  

 

This effect depends on the impedance and reactance of the materials and is therefore frequency dependent, producing different behaviours at different frequencies.  If we determine the DEP behaviour as a function of frequency, we can then use mathematical techniques to determine the electrical properties of the particle.