# Computation of the drag force on a sphere close to a wall

David Gérard-Varet; Matthieu Hillairet

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

- Volume: 46, Issue: 5, page 1201-1224
- ISSN: 0764-583X

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topGérard-Varet, David, and Hillairet, Matthieu. "Computation of the drag force on a sphere close to a wall." ESAIM: Mathematical Modelling and Numerical Analysis 46.5 (2012): 1201-1224. <http://eudml.org/doc/277845>.

@article{Gérard2012,

abstract = {We consider the effect of surface roughness on solid-solid contact in a Stokes flow.
Various models for the roughness are considered, and a unified methodology is given to
derive the corresponding asymptotics of the drag force in the close-contact limit. In this
way, we recover and clarify the various expressions that can be found in previous
studies.},

author = {Gérard-Varet, David, Hillairet, Matthieu},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Fluid mechanics; Stokes equations; drag; roughness; homogenization; Navier boundary condition; fluid mechanics},

language = {eng},

month = {3},

number = {5},

pages = {1201-1224},

publisher = {EDP Sciences},

title = {Computation of the drag force on a sphere close to a wall},

url = {http://eudml.org/doc/277845},

volume = {46},

year = {2012},

}

TY - JOUR

AU - Gérard-Varet, David

AU - Hillairet, Matthieu

TI - Computation of the drag force on a sphere close to a wall

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2012/3//

PB - EDP Sciences

VL - 46

IS - 5

SP - 1201

EP - 1224

AB - We consider the effect of surface roughness on solid-solid contact in a Stokes flow.
Various models for the roughness are considered, and a unified methodology is given to
derive the corresponding asymptotics of the drag force in the close-contact limit. In this
way, we recover and clarify the various expressions that can be found in previous
studies.

LA - eng

KW - Fluid mechanics; Stokes equations; drag; roughness; homogenization; Navier boundary condition; fluid mechanics

UR - http://eudml.org/doc/277845

ER -

## References

top- Y. Achdou, O. Pironneau and F. Valentin, Effective boundary conditions for laminar flows over periodic rough boundaries. J. Comput. Phys.147 (1998) 187–218. Zbl0917.76013
- G. Barnocky and R. H. Davis, The influence of pressure-dependent density and viscosity on the elastohydrodynamic collision and rebound of two spheres. J. Fluid Mech.209 (1989) 501–519.
- A. Basson and D. Gérard-Varet, Wall laws for fluid flows at a boundary with random roughness. Comm. Pure Appl. Math.61 (2008) 941–987. Zbl1179.35207
- L. Bocquet and J. Barrat, Flow boundary conditions from nano-to micro-scales. Soft Matt.3 (2007) 985–693.
- H. Brenner and R.G. Cox, The resistance to a particle of arbitrary shape in translational motion at small Reynolds numbers. J. Fluid Mech.17 (1963) 561–595. Zbl0116.18003
- D. Bresch, B. Desjardins and D. Gérard-Varet, On compressible Navier-Stokes equations with density dependent viscosities in bounded domains. J. Math. Pures Appl.87 (2007) 227–235. Zbl1121.35093
- M. Cooley and M. O’Neill, On the slow motion generated in a viscous fluid by the approach of a sphere to a plane wall or stationary sphere. Mathematika16 (1969) 37–49. Zbl0174.27703
- R.H. Davis, Y. Zhao, K.P. Galvin and H.J. Wilson, Solid-solid contacts due to surface roughness and their effects on suspension behaviour. Philos. Transat. Ser. A Math. Phys. Eng. Sci.361 (2003) 871–894. Zbl1134.76725
- R.H. Davis, J. Serayssol and E. Hinch, The elastohydrodynamic collision of two spheres. J. Fluid Mech.163 (2006) 045302.
- D. Gérard-Varet, The Navier wall law at a boundary with random roughness. Commun. Math. Phys.286 (2009) 81–110. Zbl1176.35127
- D. Gérard-Varet and M. Hillairet, Regularity issues in the problem of fluid structure interaction. Arch. Rational Mech. Anal.195 (2010) 375–407. Zbl1192.35131
- M. Hillairet, Lack of collision between solid bodies in a 2D incompressible viscous flow. Commun. Partial Differ. Equ.32 (2007) 1345–1371. Zbl1221.35279
- L. Hocking, The effect of slip on the motion of a sphere close to a wall and of two adjacent sheres. J. Eng. Mech.7 (1973) 207–221. Zbl0263.76066
- W. Jäger and A. Mikelić, Couette flows over a rough boundary and drag reduction. Commun. Math. Phys.232 (2003) 429–455. Zbl1062.76012
- K. Kamrin, M. Bazant and H. Stine, Effective slip boundary conditions for arbitrary periodic surfaces: the surface mobility tensor. Phys. Rev. Lett.102 (2009).
- C. Kunert, J. Harting and O. Vinogradova, Random roughness hydrodynamic boundary conditions. Phys. Rev. Lett.105 (2010) 016001.
- E. Lauga, M. Brenner and H. Stone, Microfluidics: The no-slip boundary condition (2007).
- N. Lecoq, R. Anthore, B. Cichocki, P. Szymczak and F. Feuillebois, Drag force on a sphere moving towards a corrugated wall. J. Fluid Mech.513 (2004) 247–264. Zbl1107.76319
- A. Lefebvre, Numerical simulation of gluey particles. ESAIM: M2AN43 (2009) 53–80. Zbl1163.76056
- P. Luchini, Asymptotic analysis of laminar boundary-layer flow over finely grooved surfaces. Eur. J. Mech. B, Fluids14 (1995) 169–195. Zbl0835.76024
- M. O’Neill, A slow motion of viscous liquid caused by a slowly moving solid sphere. Mathematika11 (1964) 67–74.
- M. O’Neill and K. Stewartson, On the slow motion of a sphere parallel to a nearby plane wall. J. Fluid Mech.27 (1967) 705–724. Zbl0147.45302
- J. Smart and D. Leighton, Measurement of the hydrodynamic surface roughness of noncolloidal spheres. Phys. Fluids1 (1989) 52–60.
- O. Vinogradova and G. Yakubov, Surface roughness and hydrodynamic boundary conditions. Phys. Rev. E73 (1986) 479–487.

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