Computing foaming flows across scales: from breaking waves to microfluidics (2103.01513v1)

Abstract: Crashing ocean waves, cappuccino froths and microfluidic bubble crystals are examples of foamy flows. Foamy flows are critical in numerous natural and industrial processes and remain notoriously difficult to compute as they involve coupled, multiscale physical processes. Computations need to resolve the interactions of the bubbles with the fluid and complex boundaries, while capturing the drainage and rupture of the microscopic liquid films at their interface. We present a novel multilayer simulation framework (Multi-VOF) that advances the state of the art in simulation capabilities of foamy flows. The framework introduces a novel scheme for the distinct handling of multiple neighboring bubbles and a new regularization method that produces sharp interfaces and removes spurious fragments. Multi-VOF is verified and validated with experimental results and complemented with open source, efficient scalable software. We demonstrate capturing of bubble crystalline structures in realistic microfluidics devices and foamy flows involving tens of thousands of bubbles in a waterfall. The present multilayer framework extends the classical volume-of-fluid methodology and allows for unprecedented large scale, predictive simulations of flows with multiple interfaces.

• The paper introduces the Multi-VOF methodology that uses a fixed number of scalar fields to efficiently simulate complex foamy flows regardless of bubble count.
• It employs a novel regularization approach to sharpen interfaces and minimize spurious fragments while integrating with established VOF and level-set methods.
• Validations against experimental data confirm its accuracy in simulating microfluidic crystals and bidisperse foam generation, highlighting broad industrial and natural applications.

Overview of Foamy Flows Across Scales, from Breaking Waves to Microfluidics

The paper "Computing foaming flows across scales: from breaking waves to microfluidics" by Petr Karnakov, Sergey Litvinov, and Petros Koumoutsakos introduces an advanced simulation framework termed Multi-VOF. This technique addresses the computational challenges associated with simulating foamy flows, characterized by the interaction of bubbles with surrounding fluids and surfaces, as well as the dynamic behavior of thin films separating the bubbles. The proposed method extends the classical volume-of-fluid (VOF) methodology by enabling the simulation of complex systems with multiple non-coalescing bubbles using a fixed number of scalar fields, regardless of the bubble count.

Key Contributions

1. Multi-VOF Methodology:
   • Efficiency: The method handles bubbles using a fixed number of scalar fields, significantly reducing computational costs associated with large-scale simulations. The cost remains invariant relative to the number of bubbles, an advantage over traditional methods.
   • Advection and Interface Regularization: The method includes a novel regularization approach that sharpens interfaces and minimizes spurious fragments, enhancing accuracy for complex simulations.
   • High Compatibility: It integrates seamlessly with existing VOF and level-set methodologies, enabling users to apply established stencil-based algorithms without requiring substantial modifications.
2. Applications and Results:
   • Microfluidic Crystals: The framework accurately simulates the formation and stability of microfluidic crystals, capturing their transitions influenced by varying gas pressure, as demonstrated in experimental studies.
   • Bidisperse Foam Generation: Numerical reproduction of bidisperse foam generation in microfluidic devices showed good congruence with experimental observations, underscoring the utility of the method for devising practical microfluidic applications.
   • Larger-Scale Phenomena: It extends its capacity to simulate broader scales, evident in the modeling of a foaming waterfall, capturing the foamy phenomena commonly seen in nature.
3. Verification and Validation: The methodology was rigorously validated against experimental data, demonstrating its reliability and accuracy across various scenarios involving complex bubble dynamics.

Implications and Future Directions

The Multi-VOF method remarkably extends the predictive simulation capabilities for systems involving large numbers of interacting bubbles and droplets without coalescence. It promises wide-ranging applications in industrial processes like foaming, coating, and manufacturing of advanced materials, as well as natural phenomena such as oceanographic studies and biophysical simulations. Furthermore, the method's efficiency identifies it as a viable tool for extensive studies concerning the control and optimization of bubbly flows.

Looking to the future, the Multi-VOF framework could support advancements in adaptive mesh refinement technologies, given its compatibility with standard computational fluid dynamics (CFD) practices. Enhanced accuracy and scalability will enable researchers to tackle even more challenging multiscale fluid problems. Additionally, integrating data-driven approaches with this framework could pave the way for real-time decision-making processes in engineering applications, particularly in microfluidics and materials science.

In conclusion, the Multi-VOF method exemplifies a crucial leap in simulating complex foamy flows, navigating the intricate balance between computational feasibility and physical fidelity. Researchers and practitioners in fluid dynamics and computational engineering are likely to find this method pivotal for both theoretical explorations and practical implementations.