1. THEORY

An electrode geometry and applied voltage arrangement where the interplay between dielectrophoretic and electrorotation effects produces interesting particle electrokinetics is shown in Figure 1.

Figure 1 An electric "wave" travelling from left to right is produced by electrodes of this design if energised by cosine voltages of the indicated phase relationships. (a) Motion expected for a viable cell (f1 in Figure 2). (b) A cell trapped by positive dielectrophoresis. (c) Motion of a non-viable cell (f2 in Figure 2).

The time-averaged force acting on a particle in the centre of the channel formed between the electrode arrangement of Figure 1 is given by [1]:

(1)

where E is the field strength across the channel and is the wavelength of the travelling field of value equal to the repetitive distance between electrodes of the same phase. Away from the centre of the channel and near to the electrode tips, the electrokinetic behaviour of a particle is more complicated than that described by equation (1).

Figure 2 Frequency variations of the real and imaginary components of the induced dipole moment for model cases of (a) a viable cell with an intact membrane, and (b) a cell with a porous membrane. Translational motion under the influence of travelling fields can occur in frequency ranges f1 and f2.

The potential applications of travelling field effects for the selective manipulation and separation of bioparticles can be appreciated by referring to the frequency variations of the real and imaginary components of the induced dipole moment shown in Figure 2. The ideal situation depicted in Figure 2(a) is for a viable cell suspended in a weakly conducting aqueous medium. At low frequencies (typically below 10 kHz) the cytoplasmic lipid membrane represents a resistive barrier to the applied field, and the situation shown in Figure 2(b) occurs where the particle appears to be less polarisable than the surrounding medium and thus exhibits negative dielectrophoresis. The equivalent electrical circuit of a lipid membrane can be represented [2] as a parallel combination of a resistance (c.a. 1~10 k.cm² ) and a capacitance (c.a. 1F/cm² ). Thus, with increasing frequency and at around 100 kHz the capacitive reactance [1/(C )] of the membrane will begin to "short-out" the membrane resistance and the field will penetrate into the conducting cytoplasmic electrolyte, so that the particle appears more polarisable than the surrounding medium and positive dielectrophoresis occurs. Since dielectrophoresis is determined by the real component of the induced dipole moment this means that Re{m} increases with increasing frequency and because of the underlying dielectric processes involved it follows [3] that Im{m} is positive over this frequency range. Referring to the travelling wave electrode geometry of Figure 1, cells will only be "pushed" into the inter-electrode channel if they experience a negative dielectrophoretic force, otherwise they will be trapped at the electrodes by positive dielectrophoresis (as for particle b in Figure 1). Also, from equation (1) the rate at which the particle is propelled along the channel is proportional to the value of Im{m}. From consideration of this, as well as equation (1) and Figure 2(a), the viable cell will be propelled against the direction of the travelling wave over the frequency "window" f1, otherwise it will be levitated above the plane of the electrodes (for f < f1) or trapped at the electrodes (for f > f1).

For the case of non-viable cells the lipid membrane will usually have become physically damaged and be porous to ions, so that it no longer represents a resistive barrier to the applied electric field and at low frequencies the cell will exhibit positive dielectrophoresis. Ions will also have leaked from the cytoplasm into the surrounding medium, and at high frequencies (above around 1 MHz) the lipid and protein structures of the cell appear in dielectric terms as "dead spaces". The volume occupied by the cell then appears to be less polarisable than the weakly conducting suspending medium and a frequency will be reached where the cell exhibits negative dielectrophoresis. The parameter Re{m} thus falls with increasing frequency, and from theoretical considerations [3] it follows that Im{m} is negative over this range and motion in the same direction as the travelling wave will occur in the frequency window f2 (figure 2b). The behaviour of cells and micro-organisms is rather more complicated than the idealised description presented here, but selective bioparticle manipulation using travelling field effects has been demonstrated in our laboratories [1]. Our present efforts are directed towards investigating the use of different electrode geometries and applied voltage schemes for the separation of cancer cells from biological fluids, for example, and to progress towards the electrokinetic characterisation and manipulation of sub-cellular bioparticles such as chromosomes and proteins.

2. REFERENCES

1. Huang, Y., Wang, X.-B., Tame, J. A. and Pethig, R. (1993) J. Phys. D: Appl. Phys. 26, 1528-153
2. Pethig, R. (1979) Dielectric and Electronic Properties of Biological Materials, John Wiley & Sons, Chichester
3. Wang, X.-B., Huang, Y., Hölzel, R., Burt, J. P. H. and Pethig, R. (1993) J. Phys. D: Appl. Phys. 26, 312-322