scholarly journals Tagged-particle motion of Percus–Yevick hard spheres from first principles

2021 ◽  
Vol 155 (3) ◽  
pp. 034502
Author(s):  
Chengjie Luo ◽  
Vincent E. Debets ◽  
Liesbeth M. C. Janssen
Keyword(s):  
Particle Motion ◽  
First Principles ◽  
Hard Spheres ◽  
Tagged Particle

scholarly journals Tagged-particle motion in quasi-confined colloidal hard-sphere liquids

2021 ◽  
Vol 2021 (4) ◽  
pp. 043301
Author(s):  
Lukas Schrack ◽  
Charlotte F Petersen ◽  
Michele Caraglio ◽  
Gerhard Jung ◽  
Thomas Franosch
Keyword(s):  
Particle Motion ◽  
Hard Sphere ◽  
Tagged Particle ◽  
Hard Sphere Liquids

scholarly journals First-principles design of nanomachines

2009 ◽  
Vol 106 (17) ◽  
pp. 6900-6903 ◽  
Author(s):  
Jayanth R. Banavar ◽  
Marek Cieplak ◽  
Trinh Xuan Hoang ◽  
Amos Maritan
Keyword(s):  
First Principles ◽  
Reference Frames ◽  
Hard Spheres ◽  
Molecular Machines ◽  
Thermal Fluctuations ◽  
Chain Molecule ◽  
Inherent Anisotropy ◽  
Predictive Design ◽  
Simple Chain ◽  
A Chain

Learning from nature's amazing molecular machines, globular proteins, we present a framework for the predictive design of nanomachines. We show that the crucial ingredients for a chain molecule to behave as a machine are its inherent anisotropy and the coupling between the local Frenet coordinate reference frames of nearby monomers. We demonstrate that, even in the absence of heterogeneity, protein-like behavior is obtained for a simple chain molecule made up of just 30 hard spheres. This chain spontaneously switches between 2 distinct geometries, a single helix and a dual helix, merely because of thermal fluctuations.

Self-diffusion in sheared suspensions

1996 ◽  
Vol 312 ◽  
pp. 223-252 ◽  
Author(s):  
Jeffrey F. Morris ◽  
John F. Brady
Keyword(s):  
Volume Fraction ◽  
Diffusion Tensor ◽  
Hard Spheres ◽  
Strain Tensor ◽  
The Self ◽  
Hydrodynamic Interactions ◽  
Spherical Particles ◽  
Tagged Particle ◽  
Self Diffusion ◽  
Long Time

Self-diffusion in a suspension of spherical particles in steady linear shear flow is investigated by following the time evolution of the correlation of number density fluctuations. Expressions are presented for the evaluation of the self-diffusivity in a suspension which is either raacroscopically quiescent or in linear flow at arbitrary Peclet number $Pe = \dot{\gamma}a^2/2D$, where $\dot{\gamma}$ is the shear rate, a is the particle radius, and D = kBT/6πa is the diffusion coefficient of an isolated particle. Here, kB is Boltzmann's constant, T is the absolute temperature, and η is the viscosity of the suspending fluid. The short-time self-diffusion tensor is given by kBT times the microstructural average of the hydrodynamic mobility of a particle, and depends on the volume fraction $\phi = \frac{4}{3}\pi a^3n$ and Pe only when hydrodynamic interactions are considered. As a tagged particle moves through the suspension, it perturbs the average microstructure, and the long-time self-diffusion tensor, D∞s, is given by the sum of D0s and the correlation of the flux of a tagged particle with this perturbation. In a flowing suspension both D0s and D∞ are anisotropic, in general, with the anisotropy of D0s due solely to that of the steady microstructure. The influence of flow upon D∞s is more involved, having three parts: the first is due to the non-equilibrium microstructure, the second is due to the perturbation to the microstructure caused by the motion of a tagged particle, and the third is by providing a mechanism for diffusion that is absent in a quiescent suspension through correlation of hydrodynamic velocity fluctuations.The self-diffusivity in a simply sheared suspension of identical hard spheres is determined to O(øPe3/2) for Pe ≤ 1 and ø ≤ 1, both with and without hydro-dynamic interactions between the particles. The leading dependence upon flow of D0s is 0.22DøPeÊ, where Ê is the rate-of-strain tensor made dimensionless with $\dot{\gamma}$. Regardless of whether or not the particles interact hydrodynamically, flow influences D∞s at O(øPe) and O(øPe3/2). In the absence of hydrodynamics, the leading correction is proportional to øPeDÊ. The correction of O(øPe3/2), which results from a singular advection-diffusion problem, is proportional, in the absence of hydrodynamic interactions, to øPe3/2DI; when hydrodynamics are included, the correction is given by two terms, one proportional to Ê, and the second a non-isotropic tensor.At high ø a scaling theory based on the approach of Brady (1994) is used to approximate D∞s. For weak flows the long-time self-diffusivity factors into the product of the long-time self-diffusivity in the absence of flow and a non-dimensional function of $\bar{P}e = \dot{\gamma}a^2/2D^s_0(\phi)$. At small $\bar{P}e$ the dependence on $\bar{P}e$ is the same as at low ø.

Dependence of tagged-particle motion on size and mass

1983 ◽  
Vol 27 (5) ◽  
pp. 2603-2615 ◽  
Author(s):  
A. J. Masters ◽  
T. Keyes
Keyword(s):  
Particle Motion ◽  
Tagged Particle

scholarly journals Asymptotic laws for tagged-particle motion in glassy systems

1998 ◽  
Vol 58 (3) ◽  
pp. 3384-3399 ◽  
Author(s):  
M. Fuchs ◽  
W. Götze ◽  
M. R. Mayr
Keyword(s):  
Particle Motion ◽  
Tagged Particle ◽  
Glassy Systems
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