Mixing structures in bubble wakes of single bubbles and bubble swarms and their influence on gas-liquid mass transfer and chemical reactions

本提案的主要目的是揭示如何将自由上升的单个气泡尾迹和气泡群中的混合结构纳入过程工程的紧凑传质关联中。这样，尾迹对化学反应的影响就可以更容易地估计出来。关于详细的传质过程的知识对于生产日常生活中使用的大量大宗化学品至关重要，这些化学品是通过气液反应合成的，如氢化、氧化或氯化反应。此外，气泡尾迹中含有的高浓度气体也可能对充气反应器中的微生物和酶有害，导致底物抑制。为了预测有多少气体从气泡转移到周围的液体中，必须确定传质系数（或无量纲化的舍伍德数）。目前的传质模型（Sherwood关联）要么建立在双膜理论，要么建立在穿透理论，要么建立在表面更新理论上，这些理论的参数取决于气泡相对于周围液体的相对速度和层流或湍流的周围流动条件。现有的适应模型可以解释表面活性剂对传质过程的影响。然而，所有的理论都假设，一旦气体溶解在液相中，它就会立即得到很好的混合，并且所有通过气泡界面的流体包在离开气泡表面后，在气泡尾流中都会经历相同的条件。根据Levenspiel的说法，这幅图忽略了非均质浓度尾流的影响，它可能会影响在气泡界面附近和气泡尾流中发生的小到中等Hatta数的反应。到目前为止，气泡尾迹中混合结构的细节还没有考虑到传质相关性。在本研究计划中，将使用源于动力系统理论的最新开发的数学工具，通过评估4D-PTV测量结果，分析停滞液体中三维自由上升气泡和气泡群的气泡尾迹中的拉格朗日相干结构（LCS）。此外，将使用时间分辨激光诱导荧光（TRS-LIF）对溶解气体的浓度进行定量评估。LCS将与浓度尾迹进行比较，这两种测量都为新的舍伍德关联的发展提供了输入，舍伍德关联包含了气泡尾迹中相干流结构的影响。

The main objective of this proposal is to unveil how mixing structures in the wakes of freely rising single bubbles and in bubble swarms can be incorporated into compact mass transfer correlations for process engineering. In this way the impact of the wakes on chemical reactions can be estimated more easily. The knowledge about the detailed mass transfer is crucial to produce a vast proportion of bulk chemicals used in everyday life that are synthesized in gas-liquid reactions like hydrogenation, oxidation, or chlorination. Furthermore, contained high gas concentrations in bubble wakes can also be potentially harmful to microorganisms and enzymes in gassed reactors leading to a substrate inhibition. To predict how much gas is transferred from a bubble to a surrounding liquid the mass transfer coefficient (or the nondimensionalized Sherwood number )has to be determined. Todays mass transfer models (Sherwood correlations) either build on the two-film theory, on the penetration theory, or on the surface-renewal theory with varying parameters in dependence on bubble relative velocity to the surrounding liquid and laminar or turbulent surrounding flow conditions. Adapted models exist to account for the effect of surfactants onto the mass transfer. All theories assume, however, that once the gas is dissolved in the liquid phase it gets immediately well mixed and that all fluid parcels passing the bubble interface experience the same conditions in the bubble wake once they leave the bubble surface. This picture neglects effects of a heterogeneous concentration wake that will likely influence a reaction taking place close to the bubble interface and in the bubble wake for small to intermediate Hatta numbers as according to Levenspiel. So far, the details of the structure of the mixing in the bubble wake are not considered for mass transfer correlations. In this research proposal, the Lagrangian coherent structures (LCS) in the bubble wake of 3D freely rising bubbles and bubble swarms in stagnant liquid will be analyzed by evaluating 4D-PTV measurements using recently developed mathematical tools stemming from dynamical systems theory. Additionally, a quantitative evaluation of the concentration of the dissolved gas will be obtained using Time Resolved Laser Induced Fluorescence (TRS-LIF). The LCS will be compared to the concentration wakes and both measurements supply input for the development of new Sherwood correlations that incorporate the effect of coherent flow structures in bubble wakes.