Elastohydrodynamics of contact in adherent sheets

Carlson, Andreas; Mandre, Shreyas; Mahadevan, L.

doi:10.48550/arxiv.1508.06234

Cited by 2 publications

(2 citation statements)

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“…Trinh et al (2014a) and Trinh et al (2014b) studied rigid and elastic plates, either pinned or free floating, moving over a viscous film laying on a flat rigid surface. Carlson et al (2015) studied the deformation and flow-field created by a propagating adhesion front attaching an elastic sheet to a rigid surface, where the gap between the elastic sheet and rigid surface is filled with a viscous fluid.…”

Section: Introductionmentioning

confidence: 99%

Axial creeping flow in the gap between a rigid cylinder and a concentric elastic tube

Elbaz

Gat

2016

J. Fluid Mech.

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We examine transient axial creeping flow in the annular gap between a rigid cylinder and a concentric elastic tube. The gap is initially filled with a thin fluid layer. The study focuses on viscous-elastic time-scales for which the rate of solid deformation is of the same order-of-magnitude as the velocity of the fluid. We employ an elastic shell model and the lubrication approximation to obtain a forced nonlinear diffusion equation governing the viscous-elastic interaction. In the case of an advancing liquid front into a configuration with a negligible film layer (compared with the radial deformation of the elastic tube), the governing equation degenerates into a forced porous medium equation, for which several closed-form solutions are presented. In the case where the initial film layer is nonnegligible, self-similarity is used to devise propagation laws for a pressure driven liquid front. When advancing external forces are applied on the tube, the formation of dipole structures is shown to dominate the initial stages of the induced flow and deformation regimes. These are variants of the dipole solution of the porous medium equation. Finally, since the rate of pressure propagation decreases with the height of the liquid film, we show that isolated moving deformation patterns can be created and superimposed to generate a moving wave-like deformation field. The presented interaction between viscosity and elasticity may be applied to fields such as soft-robotics and micro-scale or larger swimmers by allowing for the time-dependent control of an axisymmetric compliant boundary.

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Section: Introductionmentioning

confidence: 99%

Axial creeping flow in the gap between a rigid cylinder and a concentric elastic tube

Elbaz

Gat

2016

J. Fluid Mech.

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“…Besides, an emergent lift force exerted on a moving object near a brush ( [29]), a soft ( [30,31,27]) or viscoelastic ( [20]) boundary was predicted and confirmed experimentally ( [26]). Adhesive contact between a wet elastic sheet and a substrate also appears in a lot of physical and biological applications, and was shown to lead to patterns reminiscent of classical dewetting ( [5,4]). Measurements on small-scale systems using surface-force apparatus revealed striking substrate deformations ( [33]), with obvious implications on the accuracy of nanorheological experiments.…”

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Elastohydrodynamic wake and wave resistance

et al. 2017

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The dynamics of a thin elastic sheet lubricated by a narrow layer of liquid is relevant to various situations and length scales. In the continuity of our previous work on viscous wakes ([18]), 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 analyzed in detail.Interfacial phenomena lead to qualitatively different behaviours from those encountered in bulk materials. In fluid mechanics and soft matter, this includes in particular the existence of surface waves. As an example, water waves have fascinated a large number of physicists and mathematicians for many decades. Among them, Lagrange derived the equation of water waves ([8]), and Kelvin described the wake behind a ship ([16]) -characterized by the universal angle of 19.7 • . This observation continues to trigger fundamental questions ([24, 7]). Moreover, in the context of atomic-force microscopy and thin viscous films, the surface wake might directly be used as a new kind of nanorheological probe ([2, 34, 18]). It may as well play a crucial role in biolocomotion, as demonstrated by the case of water striders that propel 1 arXiv:1607.07816v1 [physics.flu-dyn]

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Elastohydrodynamics of contact in adherent sheets

Cited by 2 publications

References 29 publications

Axial creeping flow in the gap between a rigid cylinder and a concentric elastic tube

Axial creeping flow in the gap between a rigid cylinder and a concentric elastic tube

Elastohydrodynamic wake and wave resistance

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