Fluid-Elastic Interactions Near Contact at Low Reynolds Number

Abstract

Interactions between fluid flow and elastic structures are important in many naturally occurring and engineered systems. This review collects and organizes recent theoretical and experimental developments in understanding fluid-structure interactions at low Reynolds numbers. Particular attention is given to the motion of objects moving in close proximity to deformable soft materials and the ensuing interplay between fluid flow and elastic deformation. We discuss how this interplay can be understood in terms of forces and torques, and harnessed in applications such as microrheometry, tribology, and soft robotics. We then discuss the interaction of soft and wet objects close to contact, where intermolecular forces and surface roughness effects become important and are sources of complexity and opportunity. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 56 is January 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Similarity solutions in elastohydrodynamic bouncing

“…Within the lubrication approximation, the contribution of the outer region of the contact to the hydrodynamic viscous force is negligible, and the hydrodynamic viscous force comes mainly from the contact region and follows the lubrication force as . Additionally, the sphere being very close to the surface, the undeformed spherical particle can be modelled with a parabolic approximation such that the liquid gap can be written as (Rallabandi 2024) where represents the elastic deformations (see figure 1 a ). These deformations are modelled by using the linear elasticity theory, and are related to the pressure field with a convolution integral involving the elastic Green's function.…”

“…where p(r, t) is the pressure field. Within the lubrication approximation, the contribution of the outer region of the contact to the hydrodynamic viscous force is negligible, and the hydrodynamic viscous force comes mainly from the contact region and follows the lubrication force as F(t) = ∞ 0 p(r, t) 2πr dr. Additionally, the sphere being very close to the surface, the undeformed spherical particle can be modelled with a parabolic approximation such that the liquid gap can be written as (Rallabandi 2024)…”