Roll and square convection in binary liquids: a few--mode Galerkin model

TL;DR

This paper introduces a simplified few-mode Galerkin model to study convection patterns like rolls and squares in binary fluids, showing good agreement with experiments and detailed simulations.

Contribution

The paper presents a novel few-mode Galerkin model that captures convection patterns in binary fluids with realistic boundary conditions, bridging simplified theory and complex simulations.

Findings

Stable square patterns at onset transition to rolls at higher thermal driving.

A crossroll regime exists between squares and rolls.

Model results align well with experimental and multi-mode simulation data.

Abstract

We present a few--mode Galerkin model for convection in binary fluid layers subject to an approximation to realistic horizontal boundary conditions at positive separation ratios. The model exhibits convection patterns in form of rolls and squares. The stable squares at onset develop into stable rolls at higher thermal driving. In between, a regime of a so-called crossroll structure is found. The results of our few--mode model are in good agreement with both experiments and numerical multi--mode simulations.