# Transient Rayleigh-Benard-Marangoni Convection due to Evaporation : a Linear Non-normal Stability Analysis

## TL;DR

This paper develops a non-normal linear stability analysis method to predict the onset of transient Rayleigh-Benard-Marangoni convection driven by evaporation, providing theoretical and numerical insights aligned with experimental results.

## Contribution

It introduces a novel non-normal stability analysis approach for unsteady convection, applicable to evaporation-induced transient flows, with validation against experimental data.

## Key findings

- Critical parameters match experimental results
- Method accurately predicts instability onset
- Scaling laws for critical parameters derived

## Abstract

The convective instability in a plane liquid layer with time-dependent temperature profile is investigated by means of a general method suitable for linear stability analysis of an unsteady basic flow. The method is based on a non-normal approach, and predicts the onset of instability, critical wave number and time. The method is applied to transient Rayleigh-Benard-Marangoni convection due to cooling by evaporation. Numerical results as well as theoretical scalings for the critical parameters as function of the Biot number are presented for the limiting cases of purely buoyancy-driven and purely surface-tension-driven convection. Critical parameters from calculations are in good agreement with those from experiments on drying polymer solutions, where the surface cooling is induced by solvent evaporation.