Imposing a temperature gradient on a narrow channel can trigger an acoustic instability, driving self-sustained oscillations of the fluid. The temperature gradient required to trigger the instability is dramatically decreased when the channel wall is covered by a thin film of volatile liquid that can undergo phase change. In the present work, we consider a volatile-droplet aerosol on which a temperature gradient is imposed, and theoretically examine whether the heat and mass transfer between the droplets and gas can trigger the acoustic instability. The aerosol structure is separated into two disparate scales: the droplet ensemble, modelled as a periodic grid of channels through which the gas flows, and the ‘micro-scale’, in which the flow around a single droplet serves as an elementary unit in the periodic structure. This scale separation led to the derivation of a new function that accounts for losses caused by viscous, thermal and diffusive relaxation processes due to droplet–gas interactions. A stability analysis is then performed, utilising the derived ‘loss’ function, calculating the minimum temperature difference, ΔT\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\varDelta T$$\end{document}, that triggers the instability. Our analysis suggests that a non-uniform temperature distribution across aerosols may lead to an acoustic instability, which can subsequently enhance coalescence and agglomeration of droplets within an aerosol. Such phenomenon may be utilised to trigger or enhance the operation of thermoacoustic engines, and may possibly occur naturally in atmospheric clouds due to uneven solar irradiation.
