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Elastohydrodynamic wake and wave resistance

Published online by Cambridge University Press:  22 September 2017

Maxence Arutkin ,
René Ledesma-Alonso Open the ORCID record for René Ledesma-Alonso [Opens in a new window] ,
Thomas Salez  and
Élie Raphaël
Maxence Arutkin
Affiliation:
Laboratoire de Physico-Chimie Théorique, UMR CNRS 7083 Gulliver, ESPCI Paris, PSL Research University, 10 rue Vauquelin, 75005 Paris, France
René Ledesma-Alonso*
Affiliation:
CONACYT, Universidad de Quintana Roo, Boulevard Bahía s/n, Chetumal, 77019 Quintana Roo, México
Thomas Salez
Affiliation:
Laboratoire de Physico-Chimie Théorique, UMR CNRS 7083 Gulliver, ESPCI Paris, PSL Research University, 10 rue Vauquelin, 75005 Paris, France Global Station for Soft Matter, Global Institution for Collaborative Research and Education, Hokkaido University, Sapporo, Hokkaido 060-0808, Japan
Élie Raphaël
Affiliation:
Laboratoire de Physico-Chimie Théorique, UMR CNRS 7083 Gulliver, ESPCI Paris, PSL Research University, 10 rue Vauquelin, 75005 Paris, France
*
†Email address for correspondence: rene.ledesma@uqroo.edu.mx
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Abstract

The dynamics of a thin elastic sheet lubricated by a narrow layer of liquid is relevant to various situations and length scales. As a continuation of our previous work on viscous wakes (Ledesma-Alonso et al., J. Fluid Mech., vol. 792, 2016, pp. 829–849), we study theoretically the effects of an external pressure disturbance moving at constant speed along the surface of a thin lubricated elastic sheet. In the comoving frame, the imposed pressure field creates a stationary deformation of the free interface that spatially vanishes in the far-field region. The shape of the wake and the way it decays depend on the speed and size of the external disturbance, as well as the rheological properties of both the elastic and liquid layers. The wave resistance, namely the force that has to be externally furnished in order to maintain the wake, is analysed in detail.

JFM classification

Interfacial Flows (free surface): Thin films Non-Newtonian Flows: Viscoelasticity Wakes/Jets: Wakes

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Papers
Information
Journal of Fluid Mechanics , Volume 829 , 25 October 2017 , pp. 538 - 550
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© 2017 Cambridge University Press 

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