Direct numerical simulation of multi-physics reactive mass transfer at single and multiple bubbles

气泡上升的反应传质是许多重要工业化学过程的基础。必要的工艺强化导致更快的工艺步骤和高度集中的系统。在这样的两相流中，在传质、输运和化学反应之间存在复杂的局部相互作用，额外的多物理场变得相关。这包括：溶解气泡的体积效应；由于污染或添加剂而部分固定的气泡表面；具有扩散通量与本征电场强耦合的离子种，通常导致混合物的局部电中性远离界面；交叉扩散效应以及高浓度系统中的非理想性。这些复杂性增加了反应质传递的多尺度性质，由于对流主导的输运，具有极薄的浓度边界层。除了实验研究，深入了解基本子过程的局部相互作用需要基于严格的数学建模的数值模拟。我们的方法采用基于质量、动量和物质质量的两相平衡的连续介质物理。基于流体体积法（VOF），建立了气泡传质的二维直接数值模拟方法。该方法采用了一种亚电网规模模型，该模型在第一个资助期得到了极大的改进，以允许实际的施密特数字。在第二个资助期内，将该方法扩展并应用于若干气泡组，在具有周期性边界条件的计算盒中上升，从而模拟无限气泡群。此外，考虑污染效应的现有方法将得到改进，包括一个可变的吉布斯弹性来模拟部分固定的气泡界面。详细的数值模拟将深入了解反应传质过程和在蜂群条件下气泡周围的散装混合。在优先项目的网络中，这些技术允许用不同的化学模型模拟气泡流动中的传质，这些模型是在其他项目中开发的。特别是，铁配合物在甲醇中的氧化和铁配合物在水中的硝化将被考虑。除了局部Sherwood数和增强外，还将研究系统参数对收率和选择性的影响。除了研究自由上升的气泡群/链外，该项目还将通过模拟气泡收缩和共轭传质，为Taylor气泡/流动的指导性措施做出贡献。最后，分析了固有电场对离子迁移的影响。所有实验装置的模拟结果将与合作的同事讨论。将在SPP内部合作开发缩小比例模型的改进相关性。

Reactive mass transfer from rising gas bubbles is the basis for many chemical processes of industrial importance. The necessary process intensification leads to faster process steps and highly concentrated systems. In such two-phase flows with complex local interaction between mass transfer, transport and chemical reactions, additional multi-physics becomes relevant. This includes: volume effects for dissolving bubbles; partly immobilized bubble surfaces due to contamination or additives; ionic species with strong coupling of diffusive fluxes by the intrinsic electrical field, typically leading to local electro-neutrality of the mixture away from the interface; cross-diffusion effects as well as non-idealities in systems of higher concentrations. These complexities add to the multi-scale nature of reactive mass transfer with extremely thin concentration boundary layers due to convection-dominated transport. Besides experimental investigations, a thorough understanding of the local interplay of elementary sub-processes requires numerical simulations based on rigorous mathematical modeling. Our approach employs continuum physics based on the two-phase balances of mass, momentum and species mass. Based on the Volume of Fluid (VOF)-method, we built on our two-scalar approach for 3D Direct Numerical Simulations of mass transfer at gas bubbles. The approach employs a subgrid-scale model which has been strongly improved in the first funding period to allow for realistic Schmidt numbers. In the second funding period, the method will be extended and applied to groups of several bubbles, rising in a computational box with periodic boundary conditions, thus simulation an infinite bubble swarm. Moreover, the existing approach to account for contamination effects will be improved by including a variable Gibbs elasticity to model a partly immobilized bubble interface. Detailed numerical simulations will yield deep insights into reactive mass transfer processes and bulk mixing around bubbles under swarm-like conditions. Within the network of the priority program, these techniques allow to simulate the mass transfer in bubbly flows with different model chemistry, developed in other projects. In particular, the oxidation of iron complexes in methanol and the nitration of iron complexes in water will be considered. In addition to local Sherwood numbers and enhancement, the influence of system parameters on yield and selectivity will be studied. Besides the investigation of freely rising bubble groups/chains, the project will contribute to the guiding measure of Taylor bubbles/flow with simulations including bubble shrinkage and conjugate mass transfer. Finally, the influence of electro-migration of ionic species due to the inherent electrical field will be analyzed. All simulation results for experimental setups will be discussed with the cooperating colleagues. Improved correlations for a scale-reduced modeling will be developed in cooperation within the SPP.