# Morphology Formation in Binary Mixtures upon Gradual Destabilisation

## TL;DR

This paper demonstrates that in slowly destabilized binary mixtures near the critical point, the characteristic length scale of phase separation depends on the quench rate with a critical exponent different from mean-field predictions, revealing more sensitive dynamics.

## Contribution

The study shows that the length scale of phase separation in near-critical binary mixtures scales with the quench rate according to a non-mean-field critical exponent, challenging traditional theories.

## Key findings

- Length scale decreases with quench rate following a 4/15 power law.
- Dynamics are more sensitive to destabilization rate than mean-field theory predicts.
- Implications for 3D systems with liquid crystals and active/passive particles.

## Abstract

Spontaneous liquid-liquid phase separation is commonly understood in terms of phenomenological mean-field theories. These theories correctly predict the structural features of the fluid at sufficiently long time scales and wavelengths. However, these conditions are not met in various examples in biology and materials science where the mixture is slowly destabilised, and phase separation takes place close to the critical point. Using kinetic Monte Carlo and molecular dynamics simulations of a binary surface fluid under these conditions, we show that the characteristic length scale of the emerging structure decreases, in 2D, with the 4/15 dynamic critical exponent of the quench rate rather than the mean-field 1/6th power. Hence, the dynamics of cluster formation governed by thermodynamically undriven Brownian motion is much more sensitive on the rate of destabilisation than expected from mean-field theory. We discuss the expected implications of this finding to 3D systems with ordering liquid crystals, as well as phase-separating passive or active particles.