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波纹基底上含不溶性活性剂液滴的铺展稳定性*
Stability of liquid droplet containing insoluble surfactant spreading over corrugated topography
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摘要: 针对波纹基底上含不溶性活性剂液滴的铺展历程，采用润滑理论建立了液滴铺展数理模型，推导出基态和扰动态下液膜厚度和活性剂浓度的演化方程组，基于非模态稳定性理论分析了液滴铺展的稳定性及参数的影响规律。研究表明：扰动量在液滴中心及铺展前沿处很小，在液膜最薄处达到最大值且活性剂浓度的负扰动现象比较明显；扰动波数可增强液滴铺展稳定性，但随扰动波数增加，该稳定性逐渐下降甚至转变为不稳定。增加Marangoni数将导致液滴铺展不稳定性加剧；增大基底高度具有增强液滴铺展稳定的作用， Peclet数和基底波数取适中值时有利于液滴铺展的稳定性。Abstract: For the spreading of an insoluble surfactant-laden droplet over the corrugated topography, the lubrication theory is used to establish the physical and mathematical models of the spreading of droplet and to derive the base state and disturbance evolution equations for thin liquid film thickness and surfactant concentration. The stability of droplet spreading on topography surfaces, as well as the effects of several parameters are investigated based on the non-model stability theory. Results show that disturbance quantities reach minimum at the droplet center and spreading fronts, and achieve the maximum in thinning regions, and the negative disturbance of surfactant concentration is quite obvious. Disturbance wave number can enhance the stability of the droplet spreading, but with increasing wave number, the stability tends to be weak and even transform into instability. The spreading stability is distinctly promoted with decreasing Marangoni number or increasing corrugated topography height. The droplet evolution displays a much stable spreading for moderate values of Peclet number and topography wave number.
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