Discovery of a new convective instability in complex fluids, 140 years after Lord Rayleigh

A completely new convective instability has been predicted and experimentally discovered, 140 years after Lord Rayleigh. Convective instabilities are of fundamental importance for our daily lives as well as for ecology and climate in atmospheric and oceanic sciences.

A well-known example is the Rayleigh-Taylor instability which occurs whenever a lighter fluid moves vertically upwards into a denser fluid, such as volcanic eruptions and nuclear mushroom clouds following nuclear explosions.

The mechanism of convective instabilities was clarified by Lord Rayleigh in a series of papers about 140 years ago (the dimensionless Rayleigh number used to quantify the onset of the instability is named after him) and is still intensively studied as a physical and natural phenomenon by which self-organizing spatial patterns arise as a consequence of dynamical instability.

In close collaboration with our experimental colleagues at the University of Milan, we have discovered and mathematically predicted a new convective instability, 140 years after Lord Rayleigh’s work. In the Rayleigh-Taylor instability, the lighter fluid is initially at the bottom and the heavier fluid at the top, so the fluid mixture is gravitationally unstable in its initial condition. Our paper is published in The Journal of Physical Chemistry Letters.

In our experiment, however, we considered the opposite case: a heavier liquid (glycerol) is initially at the bottom, while a lighter liquid (water) is above the heavier one. The system is therefore gravitationally stable and no one would expect an instability to occur. At this point, we add silica nanoparticles to the system.

Silica nanoparticles tend to move upwards to minimize their interfacial energy, that is, they move from lower regions richer in glycerol to upper regions richer in water: this is called the process of diffusiophoresis.

Due to this upward diffusion of colloidal nanoparticles, locally denser regions form in the water-rich layers, which are then pushed back by gravity. This marks the onset of a hydrodynamic instability. The latter is manifested by a peak in the structure factor obtained by irradiating the sample with light and is accompanied by the formation of patterns.

In practice, cells in locally colloid-poor regions are surrounded by “arms” rich in colloidal nanoparticles. In our optical experiment, the arms of the formed network appear as bright fluorescent, in contrast to the dark blue regions devoid of colloids. Eventually, the pattern formation ends with a phase separation at long times.

This is a new physical effect (different from the Rayleigh-Taylor and Rayleigh-Benard instabilities), which we have modeled mathematically with coupled diffusion equations for nanoparticles and the solute (glycerol), from which we can predict the onset of the instability in terms of Rayleigh number.

This discovery may have a wide range of potential applications, both for technology and environmental protection. For example, this convective instability can be used to realize new materials with microscopic structure by inducing the coagulation of nanoparticles in the arms of the network, which could be a new avenue for sol-gel processes and to fabricate new materials with controlled internal microstructure.

This new convective instability could also be used as a method for separating fluid mixtures in various industrial, pharmaceutical and natural systems, as well as for separating colloidal contaminants, such as microplastics, from fluids. Finally, it could shed light on the formation of colorful patterns and stripes on the skin of animals, from zebras to tropical fish.

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