Velocity relaxation of a particle in a confined compressible fluid

Abstract

The velocity relaxation of an impulsively forced spherical particle in a fluid confined by two parallel plane walls is studied using a direct numerical simulation approach. During the relaxation process, the momentum of the particle is transmitted in the ambient fluid by viscous diffusion and sound wave propagation, and the fluid flow accompanied by each mechanism has a different character and affects the particle motion differently. Because of the bounding walls, viscous diffusion is hampered, and the accompanying shear flow is gradually diminished. However, the sound wave is repeatedly reflected and spreads diffusely. As a result, the particle motion is governed by the sound wave and backtracks differently in a bulk fluid. The time when the backtracking of the particle occurs changes non-monotonically with respect to the compressibility factor ε = ν/ac and is minimized at the characteristic compressibility factor. This factor depends on the wall spacing, and the dependence is different at small and large wall spacing regions based on the different mechanisms causing the backtracking.

Nanoparticle stochastic motion in the inertial regime and hydrodynamic interactions close to a cylindrical wall

“…It is shown that, for no slip boundary conditions, the long-time VACFs for both parallel and perpendicular motions obey an exponential decay with a friction coefficient ξ ∝ π 2 ψ/ H 2 , where H is the separation between two walls. Tatsumi and Yamamoto [22] have studied the velocity relaxation of a spherical particle subject to an impulse and confined between two parallel planar walls. Their results show that the long-time decay of the velocity parallel to the walls is proportional to t −5/2 exp(− ψπ 2 t / H 2 ), which is attributed to a continuous spectrum of viscous modes with wave vector components perpendicular to the walls with a magnitude of π / H .…”

Composite generalized Langevin equation for Brownian motion in different hydrodynamic and adhesion regimes

“…Moreover, as τ ν ~ τ w , the fluid momentum diffusion is curtailed by confinement, which would result in a faster (exponential) decay in C v than the algebraic correlation for the near-wall case, making the fluid memory effect negligible over a wide span of t . While theoretical investigations of the VACF in the lubrication regime have not been reported, it has been shown that C v decays exponentially when a particle is placed between parallel plates where the strong confinement influences the fluid momentum diffusion [38,39]. Therefore, we assume quasisteady state and apply classical lubrication theory, which yields F drag = −[6 πηa 2 / ( h − a )] dh/dt [40], and arrive at the following approximate equation of motion for the particle:…”

The Raspberry model for hydrodynamic interactions revisited. II. The effect of confinement

“…Other works include: semi-analytic calculations, [12][13][14][15] numerical simulations that exploit analytic approximations to capture hydrodynamic behavior, [16][17][18][19][20][21] and simulations that employ coarse-grained hydrodynamic solvers to fully resolve hydrodynamic interactions. [22][23][24][25] In addition, numerous experimental studies into the diffusive behavior of spheres under confinement, [26][27][28][29][30] as well as other shapes, [31][32][33] have been undertaken. However, it goes beyond the confines of this introduction to fully list and do justice to all these investigations.…”