Advanced CSF Model for Accurate Surface Tension and Wetting Simulation in Smoothed Particle Hydrodynamics


At the microscale and nanoscale, fluid flows are profoundly influenced by interfacial phenomena such as surface tension and wetting. These effects are critical in numerous technological applications, including oil recovery, two-phase heat transfer, and ink-jet printing. The behavior of liquid droplets interacting with solid substrates, driven by forces at the triple line, determines the equilibrium contact angles and overall flow dynamics. Accurate modeling of these phenomena is essential for predicting and controlling fluid behavior in various engineering and scientific processes. Smoothed Particle Hydrodynamics (SPH) is a powerful numerical method for simulating fluid flows, particularly advantageous for handling complex free-surface problems. However, traditional SPH models face significant challenges when dealing with surface tension and wetting at free surfaces. One primary challenge is the accurate computation of local curvature and normal vectors near the free surface, where kernel truncation can lead to substantial errors. Additionally, modeling the dynamics at the triple line, where the liquid, solid, and gas phases meet, requires precise handling of wetting forces to predict equilibrium contact angles accurately. The Continuum Surface Force (CSF) model has been widely used in Eulerian, mesh-based methods for simulating surface tension effects. However, its application to SPH, a Lagrangian method, presents unique difficulties. The truncation of the kernel near the free surface in SPH can result in unacceptable inaccuracies in local curvature estimation, limiting the scope of three-dimensional free-surface simulations to high Weber number flows. To address these challenges, new study published in Journal of Fluid Mechanics and led by Dr. Michael Blank, Dr. Prapanch Nair and Professor Thorsten Pöschel from the Friedrich-Alexander-Universität Erlangen-Nürnberg developed a more reliable and efficient CSF model tailored for SPH. Their goal was to enhance the accuracy and robustness of surface tension and wetting simulations at free surfaces, thereby expanding the applicability of SPH to a broader range of fluid dynamics problems.

The new CSF model incorporates an improved smoothed normal correction scheme to better handle the dynamics at the triple line and free surface. This approach ensures accurate computation of equilibrium contact angles and surface tension forces, even in three-dimensional simulations. By validating the model through a series of test cases, including plane Poiseuille flow, Laplace pressure jump, droplet oscillations, and interactions with solid substrates, the researchers demonstrated the model’s efficacy and reliability. The study’s significance lies in its potential to advance the field of fluid mechanics, particularly for applications requiring precise control over microscale and nanoscale fluid flows. The proposed model addresses the critical limitations of existing SPH methods, offering a robust solution for simulating interfacial phenomena with high fidelity. This advancement opens new avenues for research and technological innovation in areas where surface tension and wetting play a pivotal role.

The new CSF model improves the accuracy of simulating surface tension and wetting at free surfaces. Traditional SPH models struggled with kernel truncation errors near free surfaces, leading to inaccuracies in local curvature estimation. The improved smoothed normal correction scheme introduced in this study mitigates these errors, enabling precise computation of equilibrium contact angles and interfacial dynamics. This enhancement is particularly crucial for applications involving microscale and nanoscale fluid flows, where surface tension effects dominate. By addressing the limitations of existing SPH methods, the study broadens the applicability of SPH to a wider range of fluid dynamics problems. The ability to accurately model three-dimensional free-surface flows at various Weber numbers without the constraints of previous inaccuracies expands the potential use cases for SPH. This makes the method more versatile and applicable to a broader spectrum of engineering and scientific challenges. The study lays a solid foundation for further research into interfacial phenomena. The validated CSF model can serve as a benchmark for future studies aiming to explore more complex fluid behaviors, such as multiphase flows, phase transitions, and interactions between different fluid phases. Researchers can build upon this work to develop even more sophisticated models and simulation techniques.  The accurate simulation of surface tension and wetting phenomena is crucial for numerous technological processes. For instance, in ink-jet printing, precise control over droplet formation and deposition on substrates directly impacts print quality and resolution. The improved CSF model can enhance the design and optimization of ink-jet printers, leading to better performance and higher quality prints. In oil recovery, understanding the wetting behavior of fluids on rock surfaces is essential for optimizing extraction processes. The new model can help in designing more efficient recovery techniques by accurately predicting how fluids interact with porous media. Two-phase heat transfer applications, such as cooling systems in electronics, also benefit from accurate simulations of interfacial phenomena. The ability to predict droplet behavior on cooling surfaces can lead to more effective thermal management solutions.

Moreover, in biomedical engineering, the interaction of fluids with biological tissues often involves complex wetting phenomena. Applications such as drug delivery systems, where microdroplets need to adhere to specific tissues, or wound healing treatments, where surface properties of dressings play a critical role, can be optimized using the insights provided by the new CSF model. Furthermore, environmental engineering applications, such as the design of materials for oil spill mitigation, rely on understanding how fluids spread on and interact with various surfaces. The improved model can aid in developing more effective materials and techniques for environmental cleanup efforts. Additionally, the manufacturing of advanced materials, particularly those involving coatings or thin films, requires precise control over wetting and surface tension effects. The ability to simulate these processes accurately can lead to better manufacturing techniques and higher-quality materials.

In conclusion, the study by Professor Thorsten Pöschel  and colleagues successfully developed an accurate and robust CSF model for SPH, addressing long-standing challenges in simulating surface tension and wetting phenomena at free surfaces. The practical implications span a wide range of industries, from printing and oil recovery to biomedical engineering and environmental cleanup. By enabling more precise simulations, this research opens the door to innovations in design, optimization, and application of fluid dynamics in numerous fields, demonstrating the broad and impactful potential of advanced SPH modeling techniques.

Advanced CSF Model for Accurate Surface Tension and Wetting Simulation in Smoothed Particle Hydrodynamics - Advances in Engineering

About the author

Prof. Dr. Thorsten Pöschel

Department of Chemical and Biological Engineering
Friedrich-Alexander-Universität Erlangen-Nürnberg,

The Institute for Multiscale Simulation of Particulate Systems was the first EAM funded institute to be appointed in December 2008. The institute headed by Thorsten Pöschel was created to strengthen the Cluster’s expertise in Modeling and Simulation.

In particular, the focus of his research is the relation between nanoscale and microscale particle properties on the one hand and macroscopic material characteristics on the other. In EAM, he studies this multi-scale problem by means of numerical simulations on the relevant length and time scales, using a variety of numerical approaches.

Thorsten Pöschel studied Physics at the University of Chemnitz and at the Electrotechnical Institute in St. Petersburg (Russia). He graduated from the Humboldt University in Berlin with a PhD in Theoretical Physics, and at the University of Dresden he obtained the degree of Doctor in Engineering in the field of Electronics. From 1990 to 2000 he worked as a research assistant at the Humboldt University in Berlin, from 2000 to 2007 as an assistant professor for Biophysics and Bioinformatics at the Charité in Berlin. During this period he assumed post doctorate positions at a number of academic institutions, including Saarland University, the University of Chicago, John von Neumann Institute for Computing in Jülich, ESPCI ParisTech in Paris, the University of Stuttgart, the University of California, Santa Barbara as well as a visiting professorship in Puebla, Mexico. Prior to his appointment at the University of Erlangen-Nürnberg and EAM, he had been Professor for Theoretical Physics at the University of Bayreuth.

About the author

Dr.-Ing. Michael Blank

Department of Chemical and Biological Engineering
Friedrich-Alexander-Universität Erlangen-Nürnberg,

I am a Physics Software Developer and Machine Learning Engineer with expertise in computational fluid mechanics and high-performance computing. My passion lies in solving complex multi-physics problems in fluid and solid mechanics, thermodynamics, and optics, utilizing my proficiency in C/C++, Python, and other related tools and libraries. I am skilled in the visualization of scientific simulation data using Blender and was recognized for winning the German Science Foundation Photo competition in 2022.


Blank M, Nair P, Pöschel T. Surface tension and wetting at free surfaces in smoothed particle hydrodynamics. Journal of Fluid Mechanics. 2024;987:A23. doi:10.1017/jfm.2024.410

Go to Journal of Fluid Mechanics.

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