Anomalous mass diffusion in a binary mixture and Rayleigh-Benard instability

TL;DR

This paper investigates how anomalous diffusion, characterized by non-linear mean squared displacement over time, affects the onset of Rayleigh-Benard instability in a binary fluid mixture, extending classical stability analysis.

Contribution

It introduces a stability analysis of Rayleigh-Benard convection considering anomalous diffusion effects in binary mixtures, a novel extension of traditional models.

Findings

Anomalous diffusion alters the critical conditions for instability.

Subdiffusion and superdiffusion influence the onset of convection differently.

Extended equations provide new insights into fluid stability with non-standard diffusion.

Abstract

The onset of the Rayleigh-Benard instability in a horizontal fluid layer is investigated by assuming the fluid as a binary mixture and the concentration buoyancy as the driving force. The focus of this study is on the anomalous diffusion phenomenology emerging when the mean squared displacement of molecules in the diffusive random walk is not proportional to time, as in the usual Fick's diffusion, but it is proportional to a power of time. The power-law model of anomalous diffusion identifies subdiffusion when the power-law index is smaller than unity, while it describes superdiffusion when the power-law index is larger than unity. This study reconsiders the stability analysis of the Rayleigh-Benard problem by extending the governing equations to include the anomalous diffusion.