Single Contaminated Drops Falling through Stagnant Liquid at Low Reynolds Numbers
Single Contaminated Drops Falling through Stagnant Liquid at Low Reynolds Numbers
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DOI：
10.3390/fluids7020055
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发表时间：
2022-02-01
期刊：
影响因子：
1.9
通讯作者：
Tomiyama, Akio
中科院分区：
文献类型：
--
作者：
Hayashi, Kosuke;Motoki, Yuya;Tomiyama, Akio
采用有限差分法对低雷诺数下球形污染液滴在静止液体中的下落过程进行了数值模拟。数值结果被用来描述的行为的表面活性剂的浓度，并了解表面活性剂对流体运动的详细影响。预测的界面表面活性剂浓度，γ，几乎为零的角度，θ，低于一定的值（滞流帽角，θ（帽）），而它急剧增加，并达到一个大的值θ> θ（帽）（滞流帽区）。液滴中初始表面活性剂浓度C-0的增加增强了从液滴到界面的吸附，这导致Gamma的增加和theta（cap）的减小。峰值出现在预测的Marangoni应力theta（帽）附近，这导致压力分布中出现类似的峰值。高压点阻碍了流体沿着界面的运动，导致了滞帽区的形成和连续相切向速度的衰减。从本体到界面的表面活性剂通量降低了界面附近的C（对于θ <θ（cap）），并且弱扩散不能补偿通过吸附的C的减少，这导致界面处的C小于C-0。低C区的模式是由平流决定的，并且不会因为小的扩散通量而被涂抹。
Numerical simulations of contaminated spherical drops falling through a stagnant liquid at low Reynolds numbers are carried out using the finite difference method. The numerical results are used to describe the behavior of the surfactant concentrations and to understand the surfactant effects on the fluid motions in detail. The predicted interfacial surfactant concentration, Gamma, is almost zero for angles, theta, below a certain value (the stagnant-cap angle, theta(cap)), whereas it steeply increases and reaches a large value for theta > theta(cap) (the stagnant-cap region). The increase in the initial surfactant concentration, C-0, in the drop enhances the adsorption from the drop to the interface, which results in the increase in Gamma and the decrease in theta(cap). Peaks appear in the predicted Marangoni stresses around theta(cap), which causes similar peaks in the pressure distribution. The high-pressure spots prevent the fluid motion along the interface, which results in the formation of the stagnant-cap region and the attenuation of the tangential velocity in the continuous phase. The surfactant flux from the bulk to the interface decreases C in the vicinity of the interface for theta < theta(cap) and the weak diffusion cannot compensate for the reduction in C by adsorption, which results in C at the interface smaller than C-0. The pattern of the low C region is determined by the advection and does not smear out because of a small diffusive flux.