(171p) Insights into Bubble Coalescence Phenomena: Utilizing the Navier-Stokes-Korteweg Approach

In a variety of technical processes, such as fermentation or rectification, the presence of dispersed phases is of importance for the design and performance of these operations. For example, Foaming is one of the major causes of failure in distillation columns [1]. The state of the art approach to describe foam is known as population balancing. It includes several unknown parameters, such as coalescence rate and breakup rate, which are difficult to obtain and significantly affect the model. Approaches are needed that can determine parameters without oversimplifying thermophysical properties such as phase equilibria and interfacial tension. General knowledge about two phase phenomena like coalescence is scarce, therefore a detailed perspective is needed to help get a better understanding.

The use of modeling compared to experiments has a significant advantage, for example, by incorporating information about the velocity field and more detailed transient analysis. Recently Perumanath et. al. showed an undiscovered regime of droplet coalescence with molecular dynamic (MD) simulations, where the initial regime is induced by thermal motion of the molecules [2]. However, many modeling methods face the challenge of fully resolving the interfacial regions and often rely on auxiliary models for various thermophysical properties such as interfacial tension (Volume of Fluid) or are very expensive regarding to computational resources (MD-Simulation). This situation makes it difficult to predict the behavior of disperse systems, especially when they are kinetically stabilized.

A recently developed alternative approach is the Navier-Stokes-Korteweg (NSK) method [3], which is based on density gradient theory [4] and an equation of state (EoS) [5], here for a simplified model fluid (Perturbed, Truncated, and Shifted EoS). This approach incorporates a square gradient energy term to represent the interfacial free energy. The key advantage of this approach is that it inherently incorporates properties such as phase equilibria and interfacial tensions due to the utilization of an EoS and density gradient theory. The results of this approach demonstrate outstanding agreement when compared to MD simulations [6]. Due to the large number of molecules involved in analyzing bubbles rather than droplets in MD simulations, obtaining high-resolution molecular-level data for bubbles at larger scales is uncommon. This is where the NSK method comes in handy. However, it currently faces limitations in terms of spatial and temporal scales, as a sub-nanometer resolution is needed to resolve interfacial regions. This usually leads to an s³-dependence of the number of discretization elements in space (if s is the spatial size of the simulation volume), if standard methods are used, leading to computational times equaling that of molecular simulations.

In this work, the NSK method is combined with a local grid refinement approach to overcome these limitations. Using the new approach together with a cylindrical coordinate system, the s³ dependence can be lowered to roughly a s dependence. Pre-factors of the computational scaling are reduced further using symmetry arguments. After a brief validation of this method, simple coalescence phenomena of bubbles of the same size at different distances are investigated (cf. Fig. 1). This includes a discussion of the initial thermal coalescence range of bubbles, which is currently known only for droplets. Furthermore, simulations of the coalescence of dissimilar bubbles are examined (cf. Fig. 2), including the interplay of Ostwald ripening with coalescence, taking the method a step further towards the description of many-bubble systems. A cross-over regime between coalescence and Ostwald ripening is identified.

The detailed understanding of competing processes in complex situations gives new insights into the ripening behavior of heterogeneous media. In future work, it planned to extend the approach to mixtures. While this is straight-forward in terms of the NSK approach, inclusion of diffusion processes is mandatory for this situation.

Literature:

[1] H.Z. Kister, Distillation Operation.

[2] S. Perumanath, M. K. Borg, M. V. Chubynsky, J. E. Sprittles, J. M. Reese

Phys. Rev. Lett. 122, 104501 (2019).

[3] F. Diewald, M. P. Lautenschläger, S. Stephan, K. Langenbach, C. Kuhn, S. Seckler, H.-J. Bungartz, H. Hasse, R. Müller; Comp. Meth. Appl. Mech. Eng. 361 (2020).

[4] J W. Cahn; J. E. Hillard; J. Chem. Phys. 28, 258–267 (1958).

[5] M. Heier, S. Stephan, J. Liu, W. G. Chapman, H. Hasse, K. Langenbach; Mol. Phys. 116 (2018) 2083-2094.

[6] M. Heinen; M. Hoffmann; F Diewald; S. Seckler; K. Langenbach; J. Vrabec; Physics of Fluids 34, 042006 (2022).