Elastohydrodynamics of a soft coating under fluid-mediated loading by a spherical probe

Abstract

Motion of an object near a soft wall with intervening fluid is a canonical problem in elastohydrodynamics, finding presence in subjects spanning biology to tribology. Particularly, motion of a sphere towards a soft substrate with intervening fluid is often encountered in the context of scanning probe microscopy. While there have been fundamental theoretical studies on this setup, they have focussed on specific applications and thus enforced suitable simplifications. Here we present a versatile semi-analytical framework for studying the elastohydrodynamics of axisymmetric loading of a rigid sphere near a soft elastic substrate coated on a rigid platform mediated by an aqueous electrolytic solution. Three loading modes are considered - approach, recession and oscillatory. The framework incorporates - large oscillation frequency and amplitude, two-way coupling between pressure and substrate deformation, and presence of DLVO forces. From computations using the framework, we gain insights on the effects of DLVO forces, substrate thickness, substrate material compressibility (quantified by Poisson's ratio) and high oscillation frequency for different physical setups encountered in SPM and the likes. We list some key observations. A substrate that is thicker and more compressible allows for larger deformation, i.e. is effectively softer. Presence of DLVO forces lead to magnification in force of upto two orders of magnitude and in substrate deformation of upto an order of magnitude for oscillatory loading at low frequencies and approach/recession loading at low speed. For oscillatory loading at high frequencies, DLVO forces do not appreciably affect the force and deflection behaviour of the system. Having demonstrated the versatility and utility of our framework, we expect it to evolve into a diverse and useful tool for solving problems of soft-lubrication.

References in corpus (11)

• Flow rate--pressure drop relation for deformable shallow microfluidic channels
• Soft swimming: Exploiting deformable interfaces for low-Reynolds number locomotion
• Non-Newtonian fluid--structure interactions: Static response of a microchannel due to internal flow of a power-law fluid
• Direct Measurement of the Elastohydrodynamic Lift Force at the Nanoscale
• 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
• Theory of the flow-induced deformation of shallow compliant microchannels with thick walls
• Non-uniform electro-osmotic flow drives fluid-structure instability
• Elastic deformations driven by non-uniform lubrication flows
• Influence of non-hydrodynamic forces on the elastic response of an ultra-thin soft coating under fluid-mediated dynamic loading
• Profiling a soft solid layer to passively control the conduit shape in a compliant microchannel during flow

Cited by in corpus (1)

• Viscoelasticity characterization of compressible soft matter via fluid-mediated dynamic interactions