Year: 2025
Type: article
Abstract: Surface tension gradients of air–liquid–air films play a key role in governing the dynamics of systems such as bubble caps, foams, bubble coalescence and soap films. Furthermore, for common fluids such as water, the flow due to surface tension gradients, i.e. Marangoni flow, is often inertial, due to the low viscosity and high velocities. In this paper, we consider the localised deposition of insoluble surfactants onto a thin air–liquid–air film, where the resulting flow is inertial. As observed by Chomaz (2001 J. Fluid Mech . 442 , 387–409), the resulting governing equations with only inertia and Marangoni stress are similar to the compressible gas equations. Thus, shocks are expected to form. We derive similarity solutions associated with the development of such shocks, where the mathematical structure is closely related to the Burgers equation. It is shown that the nonlinearity of the surface tension isotherm has an effect on the strength of the shock. When regularisation mechanisms are included, the shock front can propagate and late-time similarity solutions are derived. The late-time similarity solution due to regularisation by capillary pressure alone was found by Eshima et al. (2025 Phys. Rev. Lett. 134 , 214002). Here, the regularisation mechanism is generalised to include viscous extensional stress.
Source: Journal of Fluid Mechanics
Authors: Jun Eshima, Luc Deike, Howard A. Stone
Institutions: Princeton University, High Meadows Environmental Institute
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
Awards: G1453181110, Direct numerical simulations of droplet break-up in turbulence in inertial and viscous regimes, Track 4: Advanced CI Coordination Ecosystem: Monitoring and Measurement Services, CAREER: Bubble fragmentation in turbulent flows, G3562386289, Track 1: ACCESS Resource Allocations Marketplace and Platform Services (RAMPS), G4010157413, ACO: An Open CI Ecosystem to Advance Scientific Discovery (OpenCI), Track 3: COre National Ecosystem for CyberinfrasTructure (CONECT), G5367127336, G5464919783, Track 2: Customized Multi-tier Assistance, Training, and Computational Help (MATCH) for End User ACCESS to CI, Chemical Reactions and Chemically-driven Transport in Channels and Porous Media
OpenAlex ID: W4416234294