The slow motion of a sphere through a viscous fluid towards a plane surface
TL;DR: In this paper, bipolar co-ordinates are employed to obtain exact solutions of the equations of slow viscous flow for the steady motion of a solid sphere towards or away from a plane surface of infinite extent.
About: This article is published in Chemical Engineering Science.The article was published on 1961-12-01. It has received 1507 citations till now. The article focuses on the topics: Plane (geometry) & Free surface.
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TL;DR: The atomic force microscope (AFM) is not only used to image the topography of solid surfaces at high resolution but also to measure force-versus-distance curves as discussed by the authors, which provide valuable information on local material properties such as elasticity, hardness, Hamaker constant, adhesion and surface charge densities.
3,281 citations
TL;DR: In this paper, a review of applications of the lattice-Boltzmann method to simulations of particle-fluid suspensions is presented, together with some of the important applications of these methods.
Abstract: This paper reviews applications of the lattice-Boltzmann method to simulations of particle-fluid suspensions. We first summarize the available simulation methods for colloidal suspensions together with some of the important applications of these methods, and then describe results from lattice-gas and lattice-Boltzmann simulations in more detail. The remainder of the paper is an update of previously published work,(69, 70) taking into account recent research by ourselves and other groups. We describe a lattice-Boltzmann model that can take proper account of density fluctuations in the fluid, which may be important in describing the short-time dynamics of colloidal particles. We then derive macro-dynamical equations for a collision operator with separate shear and bulk viscosities, via the usual multi-time-scale expansion. A careful examination of the second-order equations shows that inclusion of an external force, such as a pressure gradient, requires terms that depend on the eigenvalues of the collision operator. Alternatively, the momentum density must be redefined to include a contribution from the external force. Next, we summarize recent innovations and give a few numerical examples to illustrate critical issues. Finally, we derive the equations for a lattice-Boltzmann model that includes transverse and longitudinal fluctuations in momentum. The model leads to a discrete version of the Green–Kubo relations for the shear and bulk viscosity, which agree with the viscosities obtained from the macro-dynamical analysis. We believe that inclusion of longitudinal fluctuations will improve the equipartition of energy in lattice-Boltzmann simulations of colloidal suspensions.
1,117 citations
TL;DR: The physico-chemical mechanisms underlying the adhesive interactions are described and a critical review is given of currently employed methods to study microbial adhesive interactions, with an emphasis on the use of the parallel plate flow chamber.
Abstract: In this review, initial microbial adhesive interactions are divided into adhesion to substratum surfaces, coaggregation between microbial pairs and co-adhesion between sessile and planktonic microorganisms of different strains or species. The physico-chemical mechanisms underlying the adhesive interactions are described and a critical review is given of currently employed methods to study microbial adhesive interactions, with an emphasis on the use of the parallel plate flow chamber. Subsequently, for each of the three microbial adhesive interactions distinguished, the role of Lifshitz-van der Waals, acid-base and electrostatic interactions is described based on existing literature.
1,071 citations
Cites background from "The slow motion of a sphere through..."
...In the Smoluchowski-Levich approximation, the attractive Lifshitz-van der Waals forces between a particle and a substratum surface are thought to be counterbalanced by the hydrodynamic drag which a particle experiences when approaching a substratum surface [141], while electrostatic interactions are neglected....
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TL;DR: Using bipolar co-ordinates, an exact solution of Stokes equations was obtained for the translational and rotational velocities of a neutrally buoyant sphere moving in proximity to a single plane wall under the influence of a simple shearing flow as mentioned in this paper.
1,011 citations
TL;DR: In this paper, it is shown that the particle flux in probability space due to Brownian motion is the same as that which would be produced by the application of a certain "thermodynamic" force to each particle.
Abstract: The classical theory of Brownian motion applies to suspensions which are so dilute that each particle is effectively alone in infinite fluid. We consider here the modifications to the theory that are needed when rigid spherical particles are close enough to interact hydrodynamically. It is first shown that Brownian motion is a diffusion process of the conventional kind provided that the particle configuration does not change significantly during a viscous relaxation time. The original argument due to Einstein, which invokes an equilibrium situation, is generalized to show that the particle flux in probability space due to Brownian motion is the same as that which would be produced by the application of a certain ‘thermodynamic’ force to each particle. We then use this prescription to deduce the Brownian diffusivities in two -different types of situation. The first concerns a dilute homogeneous suspension which is being deformed, and the relative translational diffusivity of two rigid spherical particles with a given separation is calculated from the properties of the low-Reynolds-number flow due to two spheres moving under equal and opposite forces. The second concerns a suspension in which there is a gradient of concentration of particles. The thermodynamic force on each particle in this case is shown to be equal to the gradient of the chemical potential of the particles, which brings considerations of the multi-particle excluded volume into the problem. Determination of the particle flux due to the action of this force is equivalent to determination of the sedimentation velocity of particles falling through fluid under gravity, for which a theoretical result correct to the first order in volume fraction of the particles is available, The diffusivity of the particles is found to increase slowly as the concentration rises from zero. These results are generalized to the case of a (dilute) inhomogeneous suspension of several different species of spherical particle, and expressions are obtained for the diagonal and off-diagonal elements of the diffusivity matrix. Numerical values of all the relevant hydrodynamic functions are given for the case of spheres of uniform size.
1,007 citations