Dynamics of rear stagnant cap formation at the surface of rising bubbles in surfactant solutions at large Reynolds and Marangoni numbers and for slow sorption kinetics
Dynamics of rear stagnant cap formation at the surface of rising bubbles in surfactant solutions at large Reynolds and Marangoni numbers and for slow sorption kinetics
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在大雷诺数和马兰戈尼数以及慢速吸附动力学的表面活性剂溶液中上升气泡表面形成后停滞帽的动力学
DOI：
10.1016/j.colsurfa.2015.12.028
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Reinhard Miller
中科院分区：
文献类型：
--
作者：
S. Dukhin;M. Lotfi;V. Kovalchuk;Dariush Bastani;Reinhard Miller
尽管稳定后滞帽理论及其对稳定上升的影响已达到很高的水平，但由于吸附和解吸速率系数分别未知，其实际应用几乎是不可能的。分别确定ka和kd是整个吸附动力学的实际任务。虽然稳定RSC和稳定上升的表面活性剂的延迟在文献中有详细的描述，只有很少的文章致力于减速上升的建模。此外，稳定上升依赖于ka/kd比值，其研究对kd的测定没有帮助。相反，Zholkovskij等人（2000年）提出了通过测量减速上升来确定kd（或依赖于kd）的可能性。然而，由于Re < 1的条件，该理论的实验应用是困难的，这对应于即使在超净水中表面也被杂质固定的小气泡。由于Cuenot等人（1997）提出的结果，这个约束可以消除，其中减速上升的模拟是在Re = 100时用数值完成的。然而，对于一些表面活性剂，如本模拟工作中假设的Marangoni数Ma = 61，本研究的直接应用是可能的.本工作中，从Re = 200（气泡半径400 μm）的减速上升测量中，得到了一个在大Manbers范围内确定k的方程.该方程是根据Zholkovskij等人（2000年）推导的缓慢吸附动力学方程、准稳态近似和表面活性剂累积方程以及由于在该理论中纳入了Fdhila和Duineveld（1996年）在Re = 200时计算的涡度分布而获得的。为了确定kdit，kdit足以测量临界浓度以上的浓度（即最小上升速度开始所需的最小浓度）的最大表面延迟开始所需的时间。
In spite of the high level in the theory of steady rear stagnant caps (RSC) and its influence on steady rising, its practical application is mostly impossible because the coefficients for the adsorption and desorption rates are separately unknown. The determination ofkaandkdseparately is an actual task for the adsorption dynamics as whole. While steady RSC and steady rising retardation by surfactants are described in literature in details, only few papers are devoted to the modeling of the decelerated rising. Moreover, steady rising depends on the ratioka/kdand its investigation is not helpful for the determination ofkd. In contrast a possibility to determinekd(orkaindependently) from measurements of decelerated rising was shown by Zholkovskij et al. (2000).However, experimental applications of this theory is difficult because of the conditionRe< 1, that corresponds to small bubbles which surface is immobilized by impurities even in super clean water. This constraint may be eliminated due to the results presented by Cuenot et al. (1997), where the modeling of decelerated rising is accomplished numerically forRe= 100. However, direct application of this research is possible for a few surfactants, corresponding to the Marangoni numberMa= 61, as assumed in this simulation work.An equation is obtained for the determination ofkdin a broad range of largeManumbers from measurements of decelerated rising atRe= 200 (bubble radius 400 μm) in this work. This equation is obtained on the basis of an equation for slow adsorption kinetics, a quasi-steady approximation and an equation for surfactant accumulation derived by Zholkovskij et al. (2000) as well as due to incorporation in this theory the vorticity distribution, as calculated by Fdhila and Duineveld (1996) forRe= 200. For the determination ofkdit is sufficient to measure the time required for the onset of maximal surface retardation for the concentrations above the critical concentration, i.e. the minimum concentration required for the onset of the minimum rising velocity.