Work

Hydrodynamic efficiency limit on a Marangoni surfer

Year: 2024

Type: article

Abstract: A Marangoni surfer is an object embedded in a gas–liquid interface, propelled by gradients in surface tension. We derive an analytical theorem for the lower bound on the viscous dissipation by a Marangoni surfer in the limit of small Reynolds and capillary numbers. The minimum dissipation can be expressed with the reciprocal difference between drag coefficients of two passive bodies of the same shape as the Marangoni surfer, one in a force-free interface and the other in an interface with surface incompressibility. The distribution of surface tension that gives the optimal propulsion is given by the surface tension of the solution for the incompressible surface and the flow is a superposition of both solutions. For a surfer taking the form of a thin circular disk, the minimum dissipation is $16\mu a V^2$ , giving a Lighthill efficiency of $1/3$ . This places the Marangoni surfers among the hydrodynamically most efficient microswimmers.

Source: Journal of Fluid Mechanics

DOI: 10.1017/jfm.2024.363

Authors: Abdallah Daddi-Moussa-Ider, Ramin Golestanian, Andrej Vilfan

Institutions: The Open University, Max Planck Institute for Dynamics and Self-Organization, University of Oxford, Jožef Stefan Institute

Language: English

Topic: Micro and Nano Robotics

Subfield: Condensed Matter Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,450

Funders: Max-Planck-Gesellschaft, Javna Agencija za Raziskovalno Dejavnost RS