# Warwick researchers rewrite classical theory for nanoscale

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Often in the sciences, much of the classical theory has remained the same for centuries, with current students learning the same content as students from decades past. However, cross-disciplinary research at the University of Warwick has adapted the theory for how the disintegration of a jet of fluid into droplets can be modelled, specifically for jets of around 1 nanometre; 10,000 times smaller than the diameter of a strand of human hair. They have, in effect, found a difference between how droplets appear from a tap, and how nano-droplets appear from a much smaller aperture. The classical theory, for jets much larger than this, is taught to third year undergraduates in the Mathematics Department.

This new research has amended the work of Rayleigh and Plateau from the nineteenth century, which accurately describes instability in the flow of cylinders of fluid on large scales. In considering a cylinder of fluid falling under gravity, Rayleigh and Plateau found at a critical length the fluid becomes unstable and deforms, at just over three times the wavelength of the fluid. Firstly, the jet has varying circumference along its length such that at lengths greater than the critical value, there are areas of positive or negative curvature. The sections of the fluid where the circumference is smaller has higher pressure than the sections of fluid with larger circumference. These pressure differences cause the pinched areas to rupture, forming droplets of fluid – a more favourable, lower energy state as surface area is reduced due to surface tension.

The classical theory, for jets much larger than this, is taught to third year undergraduates in the Mathematics Department

However, academics from the University of Warwick have found a difference in the stability criterion for a nano-jet of fluid flow. They accounted for the presence of thermal fluctuation effects, where molecules interacting with each other produce waves on the boundary of the liquid. By including this, they found that nano-flows became unstable and uncouple into droplets below the classical critical length, in a finite length of time. Hence, nanoscale droplets are easier to produce than droplets from a larger jet of fluid. These results were verified in a simulation, which again showed the loss of a critical length beneath which the jet flow was stable.

In being able to accurately describe fluid flows at this scale, it is a crucial step in enabling a number of emerging nano-technologies. By creating a smaller nozzle for ink jet printing, we could see droplets of ink form and hence have two- or three-dimensional printers produce work with increased resolution. Moreover, this discovery could have medical applications, improving techniques for needle-free liquid jet injection of drugs, or for the production of drugs which are on the nanoscale. The number of these applications highlight the fundamental nature of this research, and we could soon see the impact of this work in the latest feats of engineering.

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