From Stokes to Maxwell: a new perspective on Marangoni flows

Abstract: When a drop of dishwashing liquid is deposited on the surface of water previously sprinkled with pepper, one observes a rapid outward flow that drives the peppercorns towards the edges of the bowl. This simple yet captivating kitchen experiment is a classic demonstration of the Marangoni effect — fluid motion driven by surface tension gradients. Beyond this everyday observation, the Marangoni effect plays a crucial role in a wide range of phenomena, from stabilizing soap films to enabling the self-propulsion of active particles at the water-air interface.
From a theoretical viewpoint, Marangoni flows are governed by the Navier-Stokes equation, which describes fluid motion, and the advection-diffusion equation, which characterizes the transport of surfactants. The problem happens to be highly nonlinear due to the dominance of advection over diffusion, making analytical progress particularly challenging. In this talk, I will show that Marangoni flows in a deep liquid layer and in the viscous regime (Re=0) can be mapped onto an electrostatic problem. This mathematical equivalence provides a simple way to establish novel analytical solutions to the spreading dynamics. More intriguingly, the electrostatic analogy can be extended further down the molecular scale. Indeed, surfactant spreading can be formally described as a set of N particles interacting via an effective Coulomb potential. The spreading dynamics then emerges from Newton’s equations of motions, entirely bypassing hydrodynamic considerations. This unconventional analogy therefore offers a fresh and effective perspective on Marangoni flows.

Bio: PhD in 2001 (University of Strasbourg, under the supervision of C. Marques) on the statistical physics of polymers and membranes. Then postdoc at UCLA with R. Bruinsma to work on biophysics problems. Assistant professor (2003) then full professor (2021) of physics at University of Bordeaux, working on hydrodynamics of soft matter (nonequilibrium fluctuations of colloids and interfaces, actuation of active particles, Marangoni flows).