Reverse Marangoni surfing

Abstract

We theoretically study the surfing motion of chemically and thermally active particles located at a flat liquid–gas interface that sits above a liquid layer of finite depth. The particles’ activity creates and maintains a surface tension gradient resulting in the auto-surfing. It is intuitively perceived that Marangoni surfers propel towards the direction with a higher surface tension. Remarkably, we find that the surfers may propel in the lower surface tension direction depending on their geometry and proximity to the bottom of the liquid layer. In particular, our analytical calculations for Stokes flow and diffusion-dominated scalar fields (i.e. chemical concentration and temperature fields) indicate that spherical particles undergo reverse Marangoni propulsion under confinement whereas disk-shaped surfers always move in the expected direction. We extend our results by proposing an approximate formula for the propulsion speed of oblate spheroidal particles based on the speeds of spheres and disks.

From diffusive mass transfer in Stokes flow to low Reynolds number Marangoni boats

“…This is appropriate for water-soluble surfactants but, for example, the opposite limit of what has been considered in Refs. [ 29 , 31 ], where surfactant is strictly confined to the interface.…”

“… Because for , the total Marangoni force is always positive for concentration profiles with , which are increasing toward the rear side. Vandadi et al have shown that this can change in confinement, when the high of the fluid container becomes comparable to the sphere radius [ 31 ]. For constant concentration boundary conditions (B), this means that because there is no direct Marangoni force for these boundary conditions.…”

“…Because for , the total Marangoni force is always positive for concentration profiles with , which are increasing toward the rear side. Vandadi et al have shown that this can change in confinement, when the high of the fluid container becomes comparable to the sphere radius [ 31 ].…”

“…A full quantitative theory of Marangoni boats including hydrodynamics, surfactant advection, direct Marangoni forces and Marangoni flows is still elusive but numerical approaches exist [ 14 , 18 , 27 , 28 ]. Theoretical approaches ignore the advection of the surfactant concentration field [ 29 – 31 ] or even ignore hydrodynamic flow fields [ 16 , 17 , 24 , 32 ] or approximate it by uniform flow [ 20 ], which clearly oversimplifies the description of surfactant transport. Here, we focus on low Reynolds numbers as in Refs.…”

Effect of a surface tension imbalance on a partly submerged cylinder

“…According to Lauga & Davis (2012), Marangoni propulsion (Bush & Hu 2006;Masoud & Stone 2014) refers to 'the situation where a body, located at the surface of a fluid, generates an asymmetric distribution of surface active materials, thereby prompting a surface tension imbalance and a Marangoni flow, both of which lead to locomotion.' Examples of such bodies, which are sometimes called Marangoni surfers (Würger 2014;Vandadi et al 2017), include camphor scrapings (Van der Mensbrugghe 1870; Nakata et al 1997), organic solvent droplets (Oshima et al 2014;Janssens et al 2017), and water walking insects (Linsenmair & Jander 1963).…”