Describing capillary wave dynamics through renormalization of liquid properties

• Applicant: Professor Dr. Steffen Hardt
• Subject Area: Fluid Mechanics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 560549432

This proposal addresses fundamental questions related to the fluid dynamics of interfacial (gas-liquid and liquid-liquid) flows. The proposed work addresses the following question: Can the degrees of freedom of a physical system on small scales be captured by averaging (integrating) over these scales and the renormalization of model parameters? Specifically, we will explore how far the dynamics of capillary waves (CWs) at a fluid interface can be captured via replacing the system by a steady-state substitute system with renormalized model parameters, such as surface tension. Preliminary work indicates that an effective surface tension can be assigned to a surface with chaotic CWs. This suggests that gradients in the wave energy produce effective Marangoni stresses, and that a bubble or droplet with chaotic CWs on its surface exhibits an effective Laplace pressure. These two hypotheses will be tested using dedicated experimental setups. Furthermore, based on the relationship between surface tension and vapor pressure, it is anticipated that a liquid surface with chaotic CWs is characterized by an effective vapor pressure that is higher than the vapor pressure at a steady-state surface. Also, it can be expected that CWs at a liquid-liquid interface induce an effective miscibility of the two phases if the effective interfacial tension is reduced by a sufficient degree. The latter two hypotheses will be tested as well, if time allows.

• DFG Programme: Research Grants
• International Connection: USA
• Cooperation Partner: Professor Dr. Lou Kondic