Elastohydrodynamics of a sliding, spinning and sedimenting cylinder near a soft wall

Abstract

We consider the motion of a fluid-immersed negatively buoyant particle in the vicinity of a thin compressible elastic wall, a situation that arises in a variety of technological and natural settings. We use scaling arguments to establish different regimes of sliding, and complement these estimates using thin-film lubrication dynamics to determine an asymptotic theory for the sedimentation, sliding, and spinning motions of a cylinder. The resulting theory takes the form of three coupled nonlinear singular-differential equations. Numerical integration of the resulting equations confirms our scaling relations and further yields a range of unexpected behaviours. Despite the low-Reynolds feature of the flow, we demonstrate that the particle can spontaneously oscillate when sliding, can generate lift via a Magnus-like effect, can undergo a spin-induced reversal effect, and also shows an unusual sedimentation singularity. Our description also allows us to address a sedimentation-sliding transition that can lead to the particle coasting over very long distances, similar to certain geophysical phenomena. Finally, we show that a small modification of our theory allows to generalize the results to account for additional effects such as wall poroelasticity.

Cited by in corpus (34)

• Self-sustained lift and low friction via soft lubrication
• Lubrication of soft viscoelastic solids
• Long-lived anomalous thermal diffusion induced by elastic cell membranes on nearby particles
• Direct Measurement of the Elastohydrodynamic Lift Force at the Nanoscale
• Regimes of Soft Lubrication
• Rotation of an immersed cylinder sliding near a thin elastic coating
• Validity of Winkler's mattress model for thin elastomeric layers: Beyond Poisson's ratio
• Soft-lubrication interactions between a rigid sphere and an elastic wall
• Lift at low Reynolds number
• Gradient-dynamics model for liquid drops on elastic substrates
• Particle mobility between two planar elastic membranes: Brownian motion and membrane deformation
• Mobility of an axisymmetric particle near an elastic interface
• Hydrodynamic interaction between particles near elastic interfaces
• A reciprocal theorem for the prediction of the normal force induced on a particle translating parallel to an elastic membrane
• Brownian motion near an elastic cell membrane: A theoretical study
• Hydrodynamic mobility of a solid particle nearby a spherical elastic membrane. I. Axisymmetric motion
• Frequency-dependent higher-order Stokes singularities near a planar elastic boundary: implications for the hydrodynamics of an active microswimmer near an elastic interface
• Hydrodynamic mobility of a sphere moving on the centerline of an elastic tube
• Elastocapillary Levelling of Thin Viscous Films on Soft Substrates
• Slow rotation of a spherical particle inside an elastic tube
• Hydrodynamic mobility of a solid particle nearby a spherical elastic membrane. II. Asymmetric motion
• Axisymmetric flow due to a Stokeslet near a finite-sized elastic membrane
• Morphology of soft and slippery contact via fluid drainage
• Elastohydrodynamic wake and wave resistance
• Creeping motion of a solid particle inside a spherical elastic cavity. II. Asymmetric motion
• Turbulent channel flow of finite-size spherical particles with viscous hyper-elastic walls
• Lift induced by slip inhomogeneities in lubricated contacts
• Steady azimuthal flow field induced by a rotating sphere near a rigid disk or inside a gap between two coaxially positioned rigid disks
• Similarity solutions in elastohydrodynamic bouncing
• Rivulet flow over a flexible beam
• Asymmetric Stokes flow induced by a transverse point-force acting near a finite-sized elastic membrane
• Capillary lubrication of a spherical particle near a fluid interface
• Friction through molecular adsorption at the sliding interface of hydrogels: Theory and experiments
• From fluttering to drifting in inertialess sedimentation of achiral particles