Elastohydrodynamic wake and wave resistance

Abstract

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]

Asymptotic regimes in elastohydrodynamic and stochastic leveling on a viscous film

“…magmatic intrusion in the Earth's crust [1,2], to fracturing and crack formation in glaciers [3], to pumping in the digestive and arterial systems [4][5][6], or the construction of 2D crystals for electronic engineering [7]. Elastohydrodynamic flows have been studied in model geometries in order to understand their generic features and the inherent coupling between the driving force from the elastic deformations of the material and the viscous friction force resisting motion [8][9][10][11][12][13][14][15][16].…”

Elastohydrodynamics of a pre-stretched finite elastic sheet lubricated by a thin viscous film with application to microfluidic soft actuators

“…Elastohydrodynamic interaction between an elastic substrate and a thin liquid film is of interest in the study of various natural processes, such as passage of air flow in the lungs (Grotberg & Jensen 2004) and geological formation of laccoliths (Michaut 2011), as well as in the dynamic control of elastic structures for applications in soft robotics, adaptive optics and reconfigurable microfluidics (Thorsen et al 2002;Chronis et al 2003;Kim et al 2013). In particular, the case of a viscous fluid confined between an elastic sheet and a rigid surface has been extensively studied in the context of viscous peeling (Hosoi & Mahadevan 2004;Lister et al 2013;Hewitt et al 2015), suppression of viscous fingering instabilities (Pihler-Puzović et al 2012Al-Housseiny et al 2013;Pihler-Puzović et al 2014), impact mitigation (Tulchinsky & Gat 2016), elastohydrodynamic wakes (Arutkin et al 2017), and dynamics of wrinkling of a lubricated elastic sheet (Kodio et al 2017). The configuration consists of a 12 µm thick low-density polyethylene sheet stretched over a rigid frame that is supported by 100 µm tall pillars from a rigid glass substrate, forming a Hele-Shaw chamber.…”

Hydroelastic wake on a thin elastic sheet floating on water

“…Interestingly, the propagation of such waves can be finely controlled in an optical-like fashion by using model thin sheets with heterogeneous elastic properties [29]. Different properties of these waves, such as the wave resistance or non-linear effects, have been further studied theoretically [30,31], including the overdamped limit of lubrication settings where viscosity dominates over fluid inertia [32][33][34][35][36][37][38]. The dispersion relation in the inertial case was analytically derived and found to depend on three components: gravity, bending and stretching [39].…”