scholarly journals Unsteady Stokes flow near boundaries: the point-particle approximation and the method of reflections

2018 ◽  
Vol 841 ◽  
pp. 883-924 ◽  
Author(s):  
A. Simha ◽  
J. Mo ◽  
P. J. Morrison
Keyword(s):  
Brownian Motion ◽  
Slip Plane ◽  
Metallic Nanoparticles ◽  
Particle Density ◽  
Point Particle ◽  
Plane Boundary ◽  
Short Time Scale ◽  
Approximation Techniques ◽  
Numerical Predictions ◽  
Particle Approximation

Problems of particle dynamics involving unsteady Stokes flows in confined geometries are typically harder to solve than their steady counterparts. Approximation techniques are often the only resort. Felderhof (see e.g. J. Phys. Chem. B, vol. 109 (45), 2005, pp. 21406–21412; J. Fluid Mech., vol. 637, 2009, pp. 285–303) has developed a point-particle approximation framework to solve such problems, especially in the context of Brownian motion. Despite excellent agreement with past experiments, this framework produces unsteady drag coefficients that depend on particle density. This is inconsistent, since the problem can be formulated mathematically without any reference to the particle’s density. We address this inconsistency in our work. Upon implementing our modifications, the framework passes consistency checks that it previously failed. Further, it is not obvious that such an approximation should work for short-time-scale motion. We investigate its validity by deriving it from a general formalism based on integral equations through a series of systematic approximations. We also compare results from the point-particle framework against a calculation performed using the method of reflections, for the specific case of a sphere near a full-slip plane boundary. We find from our analysis that the reasons for the success of the point-particle approximation are subtle and have to do with the nature of the unsteady Oseen tensor. Finally, we provide numerical predictions for Brownian motion near a full-slip and a no-slip plane wall based on the point-particle approximation as used by Felderhof, our modified point-particle approximation and the method of reflections. We show that our modifications to Felderhof’s framework would become significant for systems of metallic nanoparticles in liquids.

A Simple Model for Anomalous Relaxation in Porous Media

1995 ◽  
Vol 407 ◽  
Author(s):  
Mariela Araujo ◽  
Orlando Gonzalez
Keyword(s):  
Porous Media ◽  
Simple Model ◽  
Disordered Systems ◽  
Particle Density ◽  
Numerical Data ◽  
Random Variable ◽  
Porous Rocks ◽  
Power Law Distribution ◽  
Numerical Predictions ◽  
Anomalous Relaxation

ABSTRACTWe present a simple model to explain anomalous relaxation in random porous media. The model, based on the properties of random walks on a disordered structure, is able to describe essential features of the relaxation process in terms of a one body picture, in which the many body effects are approximated by geometrical restrictions on the particles diffusion. Disorder is considered as a random variable (quenched and annealed) taken from a power-law distribution |μ|ξμ−1. Quantities relevant to relaxation phenomena, such as the characteristic function and the particle density are calculated. Different regimes are observed as a function of the disorder parameter μ. For μ > 1 the relaxation is of exponential or Debye type, and turns into a stretched exponential as μ decreases. We compare numerical predictions (based on Monte Carlo simulations) with experimental data from porous rocks obtained by Nuclear Magnetic Resonance, and numerical data from other disordered systems.

Flow Field Inside a Sessile Droplet on a Hydrophobic Surface in Relation to Self Cleaning Applications of Dust Particles

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Abdullah Al-Sharafi ◽  
Bekir S. Yilbas ◽  
Ahmet Z. Sahin ◽  
H. Ali
Keyword(s):  
Flow Field ◽  
Particle Density ◽  
Early Period ◽  
Hydrophobic Surface ◽  
Contact Angles ◽  
Dust Particles ◽  
Sessile Droplet ◽  
Experimental Conditions ◽  
Particle Tracking Method ◽  
Numerical Predictions

Internal fluidity of a sessile droplet on a hydrophobic surface and dynamics of fine size dust particles in the droplet interior are examined for various droplet contact angles. The geometric features of the droplet incorporated in the simulations resemble the actual droplet geometry of the experiments, and simulation conditions are set in line with the experimental conditions. The dust particles are analyzed, and the surface tension of the fluid, which composes of the dust particles and water, is measured and incorporated in the analysis. Particle tracking method is adopted experimentally to validate the numerical predictions of the flow field. It is found that heat transfer from the hydrophobic surface to the droplet gives rise to the formation of two counter rotating cells inside the droplet. The Nusselt and the Bond numbers increase with increasing droplet contact angle. The number of dust particles crossing over the horizontal rake, which corresponds to the top surface of the dust particles settled in the droplet bottom, toward the droplet interior increases as the particle density reduces, which is more pronounced in the early period. Experimental findings of flow velocity well agree with its counterparts obtained from the simulations.

scholarly journals Entanglement Dynamics of Second Quantized Quantum Fields

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Mikhail Erementchouk ◽  
Michael N. Leuenberger
Keyword(s):  
Particle Density ◽  
Short Time Scale ◽  
Multiple Quantum ◽  
Entanglement Dynamics ◽  
Graph States ◽  
Cavity Modes ◽  
Boson Fields ◽  
The One ◽  
Short Time ◽  
Number Of Particles

We study the entanglement dynamics in the system of coupled boson fields. We demonstrate that there are different natural notions of locality in this context leading to inequivalent notions of entanglement. We concentrate on the particle picture, when entanglement of one particle is determined by one-particle density matrix. We study, in detail, the effect of interaction preserving populations of individual one-particle states. We show that if the system is initially in a disentangled state with the definite total number of particles and the dimension of the one-particle Hilbert space is more than two, then only potentials of the special form admit complete entanglement, which is shown to be reached at NOON states. If the system is initially in Glauber’s coherent state, complete entanglement is not reached despite the presence of two entangling channels in this case. We conclude with studying the time evolution of entanglement of photons in a cavity with multiple quantum dots in the limit of large number of photons. We show that in a relatively short time scale the completely entangled states belong to the class of graph states and are formed due to the interaction with dots in resonance with the cavity modes.

scholarly journals Modelling bacterial behaviour close to a no-slip plane boundary: the influence of bacterial geometry

2010 ◽  
Vol 466 (2118) ◽  
pp. 1725-1748 ◽  
Author(s):  
H. Shum ◽  
E. A. Gaffney ◽  
D. J. Smith
Keyword(s):  
Slip Plane ◽  
Power Efficiency ◽  
Electrostatic Interactions ◽  
Plane Boundary ◽  
Geometrical Parameters ◽  
The Novel ◽  
Stable Orbit ◽  
Stable Circular Orbit ◽  
Micro Organisms ◽  
Unbounded Fluid

We describe a boundary-element method used to model the hydrodynamics of a bacterium propelled by a single helical flagellum. Using this model, we optimize the power efficiency of swimming with respect to cell body and flagellum geometrical parameters, and find that optima for swimming in unbounded fluid and near a no-slip plane boundary are nearly indistinguishable. We also consider the novel optimization objective of torque efficiency and find a very different optimal shape. Excluding effects such as Brownian motion and electrostatic interactions, it is demonstrated that hydrodynamic forces may trap the bacterium in a stable, circular orbit near the boundary, leading to the empirically observable surface accumulation of bacteria. Furthermore, the details and even the existence of this stable orbit depend on geometrical parameters of the bacterium, as described in this article. These results shed some light on the phenomenon of surface accumulation of micro-organisms and offer hydrodynamic explanations as to why some bacteria may accumulate more readily than others based on morphology.

scholarly journals Talbot-Lau effect beyond the point-particle approximation

2019 ◽  
Vol 100 (3) ◽  
Author(s):  
Alessio Belenchia ◽  
Giulio Gasbarri ◽  
Rainer Kaltenbaek ◽  
Hendrik Ulbricht ◽  
Mauro Paternostro
Keyword(s):  
Point Particle ◽  
Particle Approximation

scholarly journals The Anomalous Distributions and Soret Coefficient in a Nonequilibrium Colloidal System

2016 ◽  
Vol 15 (01) ◽  
pp. 1650001 ◽  
Author(s):  
Yanjun Zhou ◽  
Jiulin Du
Keyword(s):  
Brownian Motion ◽  
Temperature Gradient ◽  
Potential Energy ◽  
Colloidal Particle ◽  
Particle Density ◽  
Soret Coefficient ◽  
Colloidal System ◽  
Nonextensive Statistics ◽  
Tsallis Distribution ◽  
New Formula

We study the density distribution and Soret coefficient in a nonequilibrium colloidal system by using the overdamped Langevin equation for Brownian motion in an inhomogeneous strong friction medium. Based on the relation between the temperature gradient, the interaction potential and the [Formula: see text]-parameter in nonextensive statistics, we show that the colloidal particle density can be a function of the temperature and anomalously follows the noted [Formula: see text]-distribution, or equivalently it can also be a function of the potential energy following Tsallis distribution. With the [Formula: see text]-parameter we can establish a new formula of Soret coefficient and thus, bridge the gap between the ideally theoretical Soret coefficient and available experiments.

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