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Physical Hydrodynamics, 2nd Edn$
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Etienne Guyon, Jean-Pierre Hulin, Luc Petit, and Catalin D. Mitescu

Print publication date: 2015

Print ISBN-13: 9780198702443

Published to Oxford Scholarship Online: March 2015

DOI: 10.1093/acprof:oso/9780198702443.001.0001

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Flows at Low Reynolds Number

Flows at Low Reynolds Number

Chapter:
(p.308) 9 Flows at Low Reynolds Number
Source:
Physical Hydrodynamics, 2nd Edn
Author(s):

Etienne Guyon

Jean-Pierre Hulin

Luc Petit

Catalin.D. Mitescu

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198702443.003.0009

Flows at low Reynolds numbers (Re) are characterized by the dominance of viscosity and are encountered in small channels, at low flow velocities and for very viscous fluids. The linear Stokes equation, which governs such flows, is valid because the non-linear convective term of the Navier–Stokes equation is negligible: several general properties of these flows (reversibility, additivity and minimum dissipation) result from this linearity. Unlike in Chapter 8, the geometry of these flows is arbitrary. Flows around small objects like in the suspensions of particles and in porous media (and the model Hele–Shaw cell) are important applications. Non-linear terms need to be taken into account at large distances and this leads to Oseen’s equation.

Keywords:   low Reynolds number, stokes equation, linear, suspensions, porous media, hele–Shaw cell, Oseen’s equation

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