There are many instances in everyday life where small particles can acquire an electrical charge of the same sign. Examples include aerosol and water droplets in clouds, dust particles in space, toner particles in ink-jet printers, and suspensions of colloidal particles. As the particles carry a charge of the same sign, either positive or negative, they are expected to repel one another; however, under certain circumstances (and very often!) their interaction can be strongly attractive. For conducting particles, this effect was identified by William Thomson (later Lord Kelvin) who in 1845 developed a theory showing that the attraction is due to differences in the magnitude of the image charge induced in pairs of particles where either their size or charge differs.
Until recently there was no stable solution to the fundamental problem of calculating the electrostatic interaction between charged particles of dielectric material, mainly due to significant mathematical complexity of the problem. To date a variety of solutions have been offered, many of which present mathematical derivations with limited applicability, numerical complications or poor convergence at short particle separations.
The authors developed a comprehensive theory [1,2] with universal relevance to the electrostatic properties of closely interacting dielectric particles each carrying an arbitrary amount of charge [3-5]. In this talk, the developed theory will be discussed and integrated across multiple disciplines.
Acknowledgments: ERC Consolidator grant is gratefully acknowledged.
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