scholarly journals Soft-lubrication interactions between a rigid sphere and an elastic wall

2021 ◽  
Vol 933 ◽  
Author(s):  
Vincent Bertin ◽  
Yacine Amarouchene ◽  
Elie Raphaël ◽  
Thomas Salez
Keyword(s):  
Stress Field ◽  
Viscous Fluid ◽  
Thin Layers ◽  
Reciprocal Theorem ◽  
Rigid Sphere ◽  
Hydrodynamic Stress ◽  
Soft Surface ◽  
Elastic Wall ◽  
Elastic Substrates ◽  
Small Deformations

The motion of an object within a viscous fluid and in the vicinity of a soft surface induces a hydrodynamic stress field that deforms the latter, thus modifying the boundary conditions of the flow. This results in elastohydrodynamic interactions experienced by the particle. Here, we derive a soft-lubrication model, in order to compute all the forces and torque applied on a rigid sphere that is free to translate and rotate near an elastic wall. We focus on the limit of small deformations of the surface with respect to the fluid-gap thickness, and perform a perturbation analysis in dimensionless compliance. The response is computed in the framework of linear elasticity, for planar elastic substrates in the limiting cases of thick and thin layers. The EHD forces are also obtained analytically using the Lorentz reciprocal theorem.

Brownian dynamics simulation of the motion of a rigid sphere in a viscous fluid very near a wall

2000 ◽  
Vol 113 (20) ◽  
pp. 9268-9278 ◽  
Author(s):  
David S. Sholl ◽  
Michael K. Fenwick ◽  
Edward Atman ◽  
Dennis C. Prieve
Keyword(s):  
Viscous Fluid ◽  
Brownian Dynamics ◽  
Dynamics Simulation ◽  
Rigid Sphere ◽  
Brownian Dynamics Simulation

Lubricated steady sliding of a rigid sphere on a soft elastic substrate: hydrodynamic friction in the Hertz limit

Soft Matter ◽  
2020 ◽  
Vol 16 (11) ◽  
pp. 2760-2773 ◽  
Author(s):  
Haibin Wu ◽  
Nichole Moyle ◽  
Anand Jagota ◽  
Chung-Yuen Hui
Keyword(s):  
Rigid Sphere ◽  
Elastic Substrate ◽  
Hydrodynamic Friction ◽  
Elastic Substrates ◽  
Lubricated Sliding

Lubricated sliding on soft elastic substrates occurs in a variety of natural and technological settings.

Asymptotic analysis of a viscous fluid–thin plate interaction: Periodic flow

2014 ◽  
Vol 24 (09) ◽  
pp. 1781-1822 ◽  
Author(s):  
G. P. Panasenko ◽  
R. Stavre
Keyword(s):  
Viscous Fluid ◽  
Asymptotic Analysis ◽  
Coupled System ◽  
Thin Elastic Plate ◽  
Periodic Flow ◽  
Complete Asymptotic Expansion ◽  
Thin Channel ◽  
Elastic Wall ◽  
Leading Term ◽  
2D Elasticity

The first goal of this paper is to provide an asymptotic derivation and justification of the model studied in [Asymptotic analysis of a periodic flow in a thin channel with visco-elastic wall, J. Math. Pures Appl.85 (2006) 558–579]. We consider the coupled system "viscous fluid flow–thin elastic plate" when the thickness of the plate, ε, tends to zero, while the density and the Young's modulus of the plate material are of order ε-1and ε-3, respectively. The plate lies on the fluid which occupies a thick domain. The complete asymptotic expansion is constructed when ε tends to zero and it is proved that the leading term of the expansion satisfies the equations of [Asymptotic analysis of a periodic flow in a thin channel with visco-elastic wall, J. Math. Pures Appl.85 (2006) 558–579]. The second goal is the partial asymptotic decomposition formulation of the original problem when a part of the plate is described by a one-dimensional (1D) model while the other part is simulated by the two-dimensional (2D) elasticity equations. The appropriate junction conditions based on the previous asymptotic analysis are proposed at the interface point between the 1D and 2D equations. The error of the method is evaluated.

The Calculation of Residual Stresses in Worn Surfaces

1994 ◽  
Vol 208 (2) ◽  
pp. 113-119 ◽  
Author(s):  
A A Torrance
Keyword(s):  
Stress Field ◽  
Residual Stresses ◽  
Crack Propagation ◽  
Elastoplastic Model ◽  
Soft Surface ◽  
Worn Surfaces

An elastoplastic model for calculating the residual stresses caused by the indentation of a semi-infinite solid by aflat punch is developed to allow calculation of the residual stresses left in a soft surface after it has been rubbed by a hard wedge. Despite the simplifications used, the model predicts to within 20 per cent the magnitude of the residual stresses produced by the gentle grinding of metals. It also predicts the essential features of the stress field and direction of crack propagation in some recent experiments on the sliding of steel wedges on aluminium.

scholarly journals On the dynamics of thin layers of viscous flows inside another viscous fluid

2021 ◽  
Vol 300 ◽  
pp. 252-311
Author(s):  
Tania Pernas Castaño ◽  
Juan J.L. Velázquez
Keyword(s):  
Viscous Fluid ◽  
Viscous Flows ◽  
Thin Layers

Galerkin representations and fundamental solutions for an axisymmetric microstretch fluid flow

2009 ◽  
Vol 619 ◽  
pp. 277-293 ◽  
Author(s):  
H. H. SHERIEF ◽  
M. S. FALTAS ◽  
E. A. ASHMAWY
Keyword(s):  
Fluid Flow ◽  
Rigid Body ◽  
Fundamental Solutions ◽  
Reciprocal Theorem ◽  
Rigid Sphere ◽  
Microstretch Fluid ◽  
Point Body

The method of associated matrices is used to obtain Galerkin type representations. Fundamental solutions are then obtained for the cases of a point body couple and a point microstretch force. A formula for calculating the total couple acting on a rigid body rotating axi-symmetrically in a microstretch fluid is deduced. A generalized reciprocal theorem is deduced. An application for a rigid sphere rotating in a microstretch fluid is discussed. The results of the application are represented graphically.

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