Kelvin–Helmholtz instability of a confined nano-liquid sheet in planar channels is investigated by utilizing the viscous potential theory. The present theoretical model considers the effects of heat and mass transfer, Marangoni effects, and boundary conditions at walls. The dispersion relation of the gas-liquid interface is obtained numerically as a solution to a nonlinear algebraic equation. Results show that there is a non-monotonic correlation of the instability growth rate with the Reynolds numbers in gas and liquid phases. The perturbed gas-liquid interface tends to be stable with the increase of the Prandtl number and the Lewis number in both gas and liquid phases. On the contrary, the gas thermal conduction and the Brownian diffusion enhance the instability of the gas-liquid interface. The temperature andmass gradient coefficients of surface tension show a promoting impact on the destabilization of the interface. In addition, it is demonstrated that the increase of gas layer thickness noticeably decreases the instability of the interface.

中文翻译：

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受热传质和马兰戈尼对流影响的受限纳米液体片的开尔文-亥姆霍兹不稳定性

利用粘性势理论研究了平面通道中受限纳米液体片的开尔文-亥姆霍兹不稳定性。目前的理论模型考虑了传热和传质、Marangoni 效应和壁面边界条件的影响。气液界面的色散关系作为非线性代数方程的解在数值上获得。结果表明，在气相和液相中，不稳定性增长率与雷诺数之间存在非单调相关性。随着气相和液相中普朗特数和路易斯数的增加，扰动的气液界面趋于稳定。相反，气体热传导和布朗扩散增强了气液界面的不稳定性。表面张力的温度和质量梯度系数对界面的失稳有促进作用。此外，还证明了气层厚度的增加显着降低了界面的不稳定性。