A neutrally stable shell in a Stokes flow: a rotational Taylor's sheet. (26th July 2019)

• Record Type: Journal Article
• Authors: Corsi, G.; De Simone, A.; Maurini, C.; Vidoli, S.
• Is Part Of: Proceedings. Volume 475:Number 2227(2019)
• Publication Date: 2019-07-26
• Subjects: viscous flows -- micromotility -- morphing shells; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2019.0178
• Languages: English
• ISSNs: 1364-5021

Abstract

Abstract : In a seminal paper published in 1951, Taylor studied the interactions between a viscous fluid and an immersed flat sheet which is subjected to a travelling wave of transversal displacement. The net reaction of the fluid over the sheet turned out to be a force in the direction of the wave phase-speed. This effect is a key mechanism for the swimming of micro-organisms in viscous fluids. Here, we study the interaction between a viscous fluid and a special class of nonlinear morphing shells. We consider pre-stressed shells showing a one-dimensional set of neutrally stable equilibria with almost cylindrical configurations. Their shape can be effectively controlled through embedded active materials, generating a large-amplitude shape-wave associated with precession of the axis of maximal curvature. We show that this shape-wave constitutes the rotational analogue of a Taylor's sheet, where the translational swimming velocity is replaced by an angular velocity. Despite the net force acting on the shell vanishes, the resultant torque does not. A similar mechanism can be used to manoeuver in viscous fluids.