# ECS Intranet:

Higher-order forces and torques on dielectric particles

Dielectrophoresis (DEP), a phenomenon through which non-uniform electric field exerts force on a dielectric particle immersed in a dielectric medium, is one of the most widely-used techniques for manipulating and characterising biological particles in a lab-on-a-chip device. Inaccurate calculation of the DEP force would lead to incorrect modelling of the device or false determination of particle properties. Most, if not all, models in current literature are based on the so-called "dipolar approximation" for making calculation of the DEP force. This approximation accounts only for the first-order force term and ignores all higher-order terms. Theory predicts this approximation to work well only as long as particle dimensions are much smaller than those of the electrode geometry through which the electric field is applied. When the field magnitude varies significantly across the dimensions of the particle, which is a very likely occurrence as electrode geometries shrink in dimensions towards micro-electrode geometries, higher-order force terms are expected to gain increased significance. The same principle applies to torques of electric origin experienced by dielectric particles in lab-on-a-chip devices through the phenomena of electro-rotation (ROT) and electro-orientation (EO).

The preliminary aim of this project is to identify situations where higher-order forces are expected to contribute to a considerable extent to the total DEP force. To accomplish this goal, separate calculations have been made, numerically, of the first three terms of the DEP force, based on the "effective moment method", and of the total DEP force, based on an integration of the Maxwell stress tensor, for particles of different shapes and dimensions subjected to electric fields of varied extents of non-uniformity. Through a comparison of the two sets of results it has been verified that when particle dimensions, be the particles spherical or not, become comparable to a length scale of field non-uniformity, higher-order force terms become increasingly significant such that in some cases they exceed the first-order force term thereby proving the dipolar approximation wrong.

Once instances where higher-order force and torque terms become significant are discovered, the ultimate goal of this project comes into play: to realize an application where higher-order forces and/or torques could dictate particle behaviour in a way that cannot be achieved using a force/torque whose higher-order terms are negligible. One goal in mind is to achieve particle stabilisation through the exertion of higher-order electro-orientational (EO) torques.

**Type**: Postgraduate Research**Research Group**: Nano Research Group**Theme**: Microfluidics and Lab-on-a-chip**Dates**: 1st October 2007 to 30th September 2010

### Keywords

- dielectrophoresis
- electro-orientation
- Maxwell stress tensor
- multipoles
- Southampton Nanofabrication Centre

### Funding

- Department

### Principal Investigators

- hn07r
- Dr Nicolas G Green

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