Erratum: “Finite amplitude vibrations of a sharp-edged beam immersed in a viscous fluid near a solid surface” [J. Appl. Phys. 112, 104907 (2012)]

2013 ◽  
Vol 113 (2) ◽  
pp. 029901
Author(s):  
Emma Grimaldi ◽  
Maurizio Porfiri ◽  
Leonardo Soria
Keyword(s):  
Viscous Fluid ◽  
Solid Surface ◽  
Finite Amplitude

Finite amplitude vibrations of a sharp-edged beam immersed in a viscous fluid near a solid surface

2012 ◽  
Vol 112 (10) ◽  
pp. 104907 ◽  
Author(s):  
Emma Grimaldi ◽  
Maurizio Porfiri ◽  
Leonardo Soria
Keyword(s):  
Viscous Fluid ◽  
Solid Surface ◽  
Finite Amplitude

Small amplitude oscillations of a thin beam immersed in a viscous fluid near a solid surface

2005 ◽  
Vol 17 (7) ◽  
pp. 073102 ◽  
Author(s):  
Christopher P. Green ◽  
John E. Sader
Keyword(s):  
Viscous Fluid ◽  
Solid Surface ◽  
Small Amplitude ◽  
Thin Beam

Distortion and necking of a viscous inclusion in Stokes flow

1989 ◽  
Vol 422 (1862) ◽  
pp. 173-192 ◽  
Keyword(s):  
Viscous Fluid ◽  
Stokes Flow ◽  
Numerical Solutions ◽  
Finite Amplitude ◽  
Elliptic Solution ◽  
Small Perturbations ◽  
All Solutions ◽  
Elliptic Profile ◽  
The Stability ◽  
Small Disturbances

Spence & Wilmott (1988) considered the deformation of a slender inclusion of highly-viscous fluid in a Stokes flow of less viscous fluid, and derived a coupled pair of equations to describe its evolution. The equations possess self-preserving solutions for elliptical inclusions, previously known from the work of Bilby et al . (1975, 1976) and Bilby & Kolbuszewski (1977). In the present paper numerical solutions are presented for non-elliptic shapes. These have been obtained on a CRAY XMP-22 by use of an eigenfunction expansion suggested by the elliptic solution, leading to an initial value problem for the coefficients. The solutions show that large deformations can develop in finite time from small perturbations of the ellipse, particularly at large viscosity ratios. Special attention is directed to the phenomenon of boudinage, whereby alternate swelling and necking develops as the inclusion is stretched by the Stokes flow. This appears to characterize all solutions that depart significantly from pure elliptic shape. In the Appendix the stability of the elliptic profile to small disturbances is examined. It is found that all subharmonics of a given disturbance are excited to a finite amplitude that increases with the viscosity ratio, but that higher harmonics are not excited in linear theory, although nonlinear coupling leads to the eventual excitation of all modes.

SLIDING FRICTION IN VISCOUS HYDRODYNAMICS: THE ROUGH SURFACE AS VORTICITY SOURCE

1989 ◽  
Vol 03 (05) ◽  
pp. 393-397
Author(s):  
H. DEKKER
Keyword(s):  
Friction Coefficient ◽  
Viscous Fluid ◽  
Rough Surface ◽  
Solid Surface ◽  
Sliding Friction ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Vorticity Source ◽  
Viscous Hydrodynamics

Basset’s collective friction coefficient for a viscous fluid flowing past a rough solid surface is obtained — analytically — as an intrinsic consequence of the Navier-Stokes equations by treating the surface as a source of vorticity.

Instabilities of the upstream meniscus in directional viscous fingering

1996 ◽  
Vol 312 ◽  
pp. 125-148 ◽  
Author(s):  
Sylvain Michalland ◽  
Marc Rabaud ◽  
Yves Couder
Keyword(s):  
Viscous Fluid ◽  
Viscous Fingering ◽  
Finite Amplitude ◽  
Dynamical Behaviour ◽  
Solid Surfaces ◽  
Time Dependent ◽  
Narrow Gap ◽  
Propagating Waves ◽  
Spatio Temporal ◽  
Set Up

New instabilities affecting the meniscus of a viscous fluid are presented. They occur in an experimental set-up introduced previously by Rabaud et al. (1990) in which a small quantity of a viscous fluid is placed in the narrow gap between two rotating cylinders. In this geometry the downstream meniscus located in the region where the two solid surfaces move away from each other is known to be unstable and to exhibit directional viscous fingering. In the present article it is shown that the upstream meniscus can also be unstable. Two types of instabilities are observed. In the first supercritical transition the front becomes time-dependent with either standing or propagating waves. In a second transition, which is subcritical, parallel fingers of finite amplitude are formed. The various types of spatio-temporal dynamical behaviour are discussed.

The elastohydrodynamic collision of two spheres

1986 ◽  
Vol 163 ◽  
pp. 479-497 ◽  
Author(s):  
Robert H. Davis ◽  
Jean-Marc Serayssol ◽  
E. J. Hinch
Keyword(s):  
Viscous Fluid ◽  
Solid Particle ◽  
Solid Surface ◽  
Dynamic Deformation ◽  
Fluid Layer ◽  
Pressure Profile ◽  
Solid Surfaces ◽  
Elastic Sphere ◽  
Numerical Techniques ◽  
Viscous Forces

The dynamic deformation of a solid elastic sphere which is immersed in a viscous fluid and in close motion toward another sphere or a plane solid surface is presented. The deformed shape of the solid surfaces and the pressure profile in the fluid layer separating these surfaces are determined simultaneously via asymptotic and numerical techniques. This research provides the first steps in establishing rational criteria for predicting whether a solid particle will stick or rebound subsequent to impact during filtration or coagulation when viscous forces are important.

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