Microfluidics relies on the increasingly dominant role of phase interfaces at smaller scales, that allow tiny volumes of fluid to be manipulated. However, at smaller, nanofluidic scales new physics appears that simultaneously creates remarkable new counter-intuitive flow behaviour and also renders the classical Navier-Stokes-Fourier paradigm impotent.
Thermal fluctuations (which create Brownian motion) in fluids become prevalent at nanofluidic scales and can drive thermal capillary nanowaves on phase interfaces that render free surfaces ‘rough’. These waves can radically alter the generation of instabilities and the modify classical singularities in drop dynamics.
Our approach has been to use molecular dynamics (MD) as a nanoscale virtual experiment and then develop theory based on fluctuating hydrodynamics, which introduces thermal noise into the Navier-Stokes equations, to describe the observed behaviours. With this theory we are able to describe scales where MD is computational intractable, e.g. >10nm or >100ns.
In [Perumanath et al 2019], we have shown that drop coalescence becomes stochastic at the nanoscale, with a distribution of first-contact points (see below). This was understood by extending the well-known ‘capillary wave theory’ (valid in thermal equilibrium) for cylinders and spheres; current work is focussed on accounting for inertial effects.
Thin Film Dynamics
In [Zhang et al 2019], we showed linear stability analysis of a stochastic lubrication equation (SLE) derived from fluctuating hydrodynamics can capture data from molecular simulations. In [Zhang et al 2020], new SLEs were obtained that capture liquid-solid slip that is ubiquitous at the nanoscale for both planar and annular films. Recent work, to soon be published, has shown that the growth of a rough free surface falls into a universality class.
Liquid Thread Instability and Breakup
We have considered both sides of this problem, in [Zhao et al 2019] revisiting the Rayleigh-Plateau instability and incorporating noise to show that classically-stable cylinders can be ruptured by noise at the nanoscale. In [Zhao et al 2020], the breakup process is simulated using a computational approach and compared to similarity solutions proposed for the fluctuation-dominated regimes.
The problems we have considered are merely the tip of the iceberg – many open problems remain. In particular, assumptions of symmetry have been made which are not always justified (e.g. 2D flow), much remains to be understood about fluctuation-induced breakup/rupture and many other processes are ripe for analysis. Watch this space!