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- W2075573034 abstract "We report a hydrodynamic analysis of the long-time behavior of the linear and angular velocity autocorrelation functions of an isolated colloid particle constrained to have quasi-two-dimensional motion, and compare the predicted behavior with the results of lattice-Boltzmann simulations. Our analysis uses the singularity method to characterize unsteady linear motion of an incompressible fluid. For bounded fluids we construct an image system with a discrete set of fundamental solutions of the Stokes equation from which we extract the long-time decay of the velocity. For the case that there are free slip boundary conditions at walls separated by $H$ particle diameters, the time evolution of the parallel linear velocity and the perpendicular rotational velocity following impulsive excitation both correspond to the time evolution of a two-dimensional (2D) fluid with effective density ${ensuremath{rho}}_{2D}=ensuremath{rho}H$. For the case that there are no slip boundary conditions at the walls, the same types of motion correspond to 2D fluid motions with a coefficient of friction $ensuremath{xi}={ensuremath{pi}}^{2}ensuremath{nu}/{H}^{2}$ modulo a prefactor of order 1, with $ensuremath{nu}$ the kinematic viscosity. The linear particle motion perpendicular to the walls also experiences an effective frictional force, but the time dependence is proportional to ${t}^{ensuremath{-}2}$, which cannot be related to either pure 3D or pure 2D fluid motion. Our incompressible fluid model predicts correct self-diffusion constants but it does not capture all of the effects of the fluid confinement on the particle motion. In particular, the linear motion of a particle perpendicular to the walls is influenced by coupling between the density flux and the velocity field, which leads to damped velocity oscillations whose frequency is proportional to ${c}_{s}/H$, with ${c}_{s}$ the velocity of sound. For particle motion parallel to no slip walls there is a slowing down of a density flux that spreads diffusively, which generates a long-time decay proportional to ${t}^{ensuremath{-}1}$." @default.
- W2075573034 created "2016-06-24" @default.
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- W2075573034 date "2007-12-28" @default.
- W2075573034 modified "2023-09-26" @default.
- W2075573034 title "Hydrodynamic description of the long-time tails of the linear and rotational velocity autocorrelation functions of a particle in a confined geometry" @default.
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- W2075573034 doi "https://doi.org/10.1103/physreve.76.061404" @default.
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