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Low Reynolds number hydrodynamics

TL;DR: Low Reynolds number flow theory finds wide application in such diverse fields as sedimentation, fluidization, particle-size classification, dust and mist collection, filtration, centrifugation, polymer and suspension rheology, and a host of other disciplines.
Abstract: Low Reynolds number flow theory finds wide application in such diverse fields as sedimentation, fluidization, particle-size classification, dust and mist collection, filtration, centrifugation, polymer and suspension rheology, flow through porous media, colloid science, aerosol and hydrosal technology, lubrication theory, blood flow, Brownian motion, geophysics, meteorology, and a host of other disciplines. This text provides a comprehensive and detailed account of the physical and mathematical principles underlying such phenomena, heretofore available only in the original literature.

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Journal ArticleDOI
TL;DR: An overview of flows in microdevices with focus on electrokinetics, mixing and dispersion, and multiphase flows is provided, highlighting topics important for the description of the fluid dynamics: driving forces, geometry, and the chemical characteristics of surfaces.
Abstract: Microfluidic devices for manipulating fluids are widespread and finding uses in many scientific and industrial contexts. Their design often requires unusual geometries and the interplay of multiple physical effects such as pressure gradients, electrokinetics, and capillarity. These circumstances lead to interesting variants of well-studied fluid dynamical problems and some new fluid responses. We provide an overview of flows in microdevices with focus on electrokinetics, mixing and dispersion, and multiphase flows. We highlight topics important for the description of the fluid dynamics: driving forces, geometry, and the chemical characteristics of surfaces.

3,307 citations


Cites background from "Low Reynolds number hydrodynamics"

  • ...When the drop radius is small compared to the channel dimensions, the drop moves nearly with the local fluid velocity, and corrections for boundary effects and “Faxen” effects based on the pressure-drop across the particle have been studied frequently (e.g., Happel & Brenner 1965)....

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  • ...Studies of such fluid-related phenomena have long been part of the fluid mechanical component of colloid science (e.g., Russel et al. 1989) and plant biology (Canny 1977) and draw on many classical features of the dynamics of viscous flows (e.g., Happel & Brenner 1965, Batchelor 1977)....

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Journal ArticleDOI
TL;DR: In this paper, the forces on a small rigid sphere in a nonuniform flow are considered from first prinicples in order to resolve the errors in Tchen's equation and the subsequent modified versions that have since appeared.
Abstract: The forces on a small rigid sphere in a nonuniform flow are considered from first prinicples in order to resolve the errors in Tchen’s equation and the subsequent modified versions that have since appeared. Forces from the undisturbed flow and the disturbance flow created by the presence of the sphere are treated separately. Proper account is taken of the effect of spatial variations of the undisturbed flow on both forces. In particular the appropriate Faxen correction for unsteady Stokes flow is derived and included as part of the consistent approximation for the equation of motion.

3,130 citations

Journal ArticleDOI
TL;DR: The biophysical and mechanical principles of locomotion at the small scales relevant to cell swimming, tens of micrometers and below are reviewed, with emphasis on the simple physical picture and fundamental flow physics phenomena in this regime.
Abstract: Cell motility in viscous fluids is ubiquitous and affects many biological processes, including reproduction, infection and the marine life ecosystem. Here we review the biophysical and mechanical principles of locomotion at the small scales relevant to cell swimming, tens of micrometers and below. At this scale, inertia is unimportant and the Reynolds number is small. Our emphasis is on the simple physical picture and fundamental flow physics phenomena in this regime. We first give a brief overview of the mechanisms for swimming motility, and of the basic properties of flows at low Reynolds number, paying special attention to aspects most relevant for swimming such as resistance matrices for solid bodies, flow singularities and kinematic requirements for net translation. Then we review classical theoretical work on cell motility, in particular early calculations of swimming kinematics with prescribed stroke and the application of resistive force theory and slender-body theory to flagellar locomotion. After examining the physical means by which flagella are actuated, we outline areas of active research, including hydrodynamic interactions, biological locomotion in complex fluids, the design of small-scale artificial swimmers and the optimization of locomotion strategies. (Some figures in this article are in colour only in the electronic version) This article was invited by Christoph Schmidt.

2,274 citations


Cites background or methods from "Low Reynolds number hydrodynamics"

  • ...The reciprocal theorem (4) forces these matrices to be symmetric [59]....

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  • ...For more detail we refer to the classic monographs by Happel and Brenner [60], Kim and Karrila [61] and Leal [62]; an introduction is also offered by Hinch [63] and Pozrikidis [64]....

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  • ...These properties lead to kinematic reversibility, an important and wellknown symmetry property associated with the motion of any body at zero Reynolds number [59, 61]....

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  • ...For more detail we refer to the classic monographs by Happel and Brenner [59], Kim and Karilla [60], and Leal [61]; a nice introduction is also offered by Hinch [62], as well as a more formal treatment by Pozrikidis [63]....

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Journal ArticleDOI
Peter Reimann1
TL;DR: In this paper, the main emphasis is put on directed transport in so-called Brownian motors (ratchets), i.e. a dissipative dynamics in the presence of thermal noise and some prototypical perturbation that drives the system out of equilibrium without introducing a priori an obvious bias into one or the other direction of motion.

2,098 citations

Journal ArticleDOI
TL;DR: In this article, a general technique for simulating solid-fluid suspensions is described, which combines Newtonian dynamics of the solid particles with a discretized Boltzmann equation for the fluid phase; the many-body hydrodynamic interactions are fully accounted for, both in the creeping flow regime and at higher Reynolds numbers.
Abstract: A new and very general technique for simulating solid–fluid suspensions is described; its most important feature is that the computational cost scales linearly with the number of particles. The method combines Newtonian dynamics of the solid particles with a discretized Boltzmann equation for the fluid phase; the many-body hydrodynamic interactions are fully accounted for, both in the creeping-flow regime and at higher Reynolds numbers. Brownian motion of the solid particles arises spontaneously from stochastic fluctuations in the fluid stress tensor, rather than from random forces or displacements applied directly to the particles. In this paper, the theoretical foundations of the technique are laid out, illustrated by simple analytical and numerical examples; in a companion paper (Part 2), extensive numerical tests of the method, for stationary flows, time-dependent flows, and finite-Reynolds-number flows, are reported.

2,073 citations


Cites background from "Low Reynolds number hydrodynamics"

  • ...suspended solid particles (Ladd (1993)); this was demonstrated in our earlier lattice-gas simulations (Ladd & Frenkel (1990); Ladd (1991); van der Hoef et al. (1991))....

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