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, \(\varDelta T\), 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.

在狭窄的通道上施加温度梯度会引发声学不稳定，从而驱动流体的自持振荡。当通道壁被可发生相变的挥发性液体薄膜覆盖时，触发不稳定性所需的温度梯度会显着降低。在目前的工作中，我们考虑了一种施加了温度梯度的挥发性液滴气溶胶，并从理论上研究了液滴和气体之间的热量和质量传递是否会引发声学不稳定性。气溶胶结构分为两个不同的尺度：液滴集合，建模为气体流动通过的周期性通道网格，以及“微尺度”，其中围绕单个液滴的流动作为基本单元周期性结构。这种尺度分离导致了一个新函数的推导，该函数解释了由于液滴-气体相互作用引起的粘性、热和扩散弛豫过程造成的损失。然后进行稳定性分析，利用导出的“损失”函数，计算最小温差，\(\varDelta T\)，触发不稳定。我们的分析表明，气溶胶中不均匀的温度分布可能会导致声学不稳定性，这随后会增强气溶胶内液滴的聚结和聚集。这种现象可用于触发或增强热声发动机的运行，并且可能由于太阳辐照不均而在大气云中自然发生。