hard spheres
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2022 ◽  
Author(s):  
Mohsen Farshad

The energy and entropy, expressed in free energy, determine the behavior of a system. Therefore, infinite knowledge of these two quantities leads to precise prediction of the system's trajectories. Here, we study how the energy and entropy affect the distribution of a two-component system in a box. First, using a model, we intuitively show that large particles prefer to position at contact with the wall as it accompanies an increase of the system's entropy. We intuitively show that this is a consequence of maximizing the accessible states for fluctuating degrees of freedom as a portion of excluded volumes reside outside of the box when they locate near the wall. Then we employ molecular dynamics simulations to extract the effect of entropy and energy on the binary mixture distribution and how they compete with each other to determine the system's configuration. While particle-particle and particle-wall attraction energies affect the distribution of particles, we show that the emergent entropic forces --- quasi-gravitational --- have a significant contribution to the configuration of the system. This system is realized clearly for a binary mixture of hard spheres in a box with reflective walls.


2022 ◽  
Vol 13 (1) ◽  
Author(s):  
Liang Xu ◽  
Zhigang Wang ◽  
Jian Chen ◽  
Songyi Chen ◽  
Wenge Yang ◽  
...  

AbstractThe fundamental relationships between the structure and properties of liquids are far from being well understood. For instance, the structural origins of many liquid anomalies still remain unclear, but liquid-liquid transitions (LLT) are believed to hold a key. However, experimental demonstrations of LLTs have been rather challenging. Here, we report experimental and theoretical evidence of a second-order-like LLT in molten tin, one which favors a percolating covalent bond network at high temperatures. The observed structural transition originates from the fluctuating metallic/covalent behavior of atomic bonding, and consequently a new paradigm of liquid structure emerges. The liquid structure, described in the form of a folded network, bridges two well-established structural models for disordered systems, i.e., the random packing of hard-spheres and a continuous random network, offering a large structural midground for liquids and glasses. Our findings provide an unparalleled physical picture of the atomic arrangement for a plethora of liquids, shedding light on the thermodynamic and dynamic anomalies of liquids but also entailing far-reaching implications for studying liquid polyamorphism and dynamical transitions in liquids.


Author(s):  
Yue Chen ◽  
Wei Chen ◽  
Xiaosong Chen

Abstract In this article, we apply classical density functional theory to investigate the characteristics of depletion interaction in Lennard-Jones (LJ) binary fluid mixtures. First of all, in order to confirm the validity of our adopted density functional formalism, we calculate the radial distribution functions with theoretical approach and compare them with results obtained by molecular dynamics simu- lation. Then this approach is applied to the case of two colloids immersed in LJ solvent systems. We investigate the variation of depletion interaction with respect to the distance of two colloids in LJ binary systems. We find that depletion interaction may be attractive or repulsive, mostly depending on the bulk density of solvent and the temperature of binary system. For high bulk densities, the repulsive barrier of depletion force is remarkable when the total excluded volume of colloids touches each other and reaches a maximum. The height of repulsive barrier is related to the parameters of LJ potential and bulk density. Moreover, depletion force may exhibit attractive wells if the bulk density of solvent is low. The attractive well tends to appear when the surface-surface distance of colloids is half of the size of polymer and deepen with temperature lowering in a fixed bulk density. In contrast with the hard-spheres system, no oscillation of depletion potential around zero is observed.


Membranes ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 960
Author(s):  
Gun Woo Park ◽  
Gerhard Nägele

Cross-flow membrane ultrafiltration (UF) is used for the enrichment and purification of small colloidal particles and proteins. We explore the influence of different membrane geometries on the particle transport in, and the efficiency of, inside-out cross-flow UF. For this purpose, we generalize the accurate and numerically efficient modified boundary layer approximation (mBLA) method, developed in recent work by us for a hollow cylindrical membrane, to parallel flat sheet geometries with one or two solvent-permeable membrane sheets. Considering a reference dispersion of Brownian hard spheres where accurate expressions for its transport properties are available, the generalized mBLA method is used to analyze how particle transport and global UF process indicators are affected by varying operating parameters and the membrane geometry. We show that global process indicators including the mean permeate flux, the solvent recovery indicator, and the concentration factor are strongly dependent on the membrane geometry. A key finding is that irrespective of the many input parameters characterizing an UF experiment and its membrane geometry, the process indicators are determined by three independent dimensionless variables only. This finding can be very useful in the design, optimization, and scale-up of UF processes.


2021 ◽  
Vol 104 (6) ◽  
Author(s):  
Mahdi Zarif ◽  
Raymond J. Spiteri ◽  
Richard K. Bowles

2021 ◽  
Vol 104 (5) ◽  
Author(s):  
O. B. Eriçok ◽  
K. Ganesan ◽  
J. K. Mason

2021 ◽  
Vol 929 ◽  
Author(s):  
Xiaoyan Ye ◽  
Devaraj van der Meer

The impact of a hydrogel sphere onto a granular target results in both the deformation of the sphere and the formation of a prominent topographic feature known as an impact crater on the granular surface. We investigate the crater formation and scaling, together with the spreading diameter and post-impact dynamics of spheres by performing a series of experiments, varying the Young's modulus $Y$ and impact speed $U_{0}$ of the hydrogel spheres, and the packing fraction and grain size of the granular target. We determine how the crater diameter and depth depend on $Y$ and show the data to be consistent with those from earlier experiments using droplets and hard spheres. Most specifically, we find that the crater diameter data are consistent with a power law, where the power exponent changes more sharply when $Y$ becomes less than 200 Pa. Next, we introduce an estimate for the portion of the impact kinetic energy that is stored as elastic energy during impact, and thus correct the energy that remains available for crater formation. Subsequently, we determine the deformation of the hydrogel spheres and find that the normalized spreading diameter data are well collapsed introducing an equivalent velocity from an energy balance of the initial kinetic energy against surface and elastic energy. Finally, we observe that under certain intermediate values for the Young's modulus and impact velocities, the particles rebound from the impact crater. We determine the phase diagram and explain our findings from a comparison of the elastocapillary spreading time and the impact duration.


2021 ◽  
Vol 104 (4) ◽  
Author(s):  
Hideki Kobayashi ◽  
Paul B. Rohrbach ◽  
Robert Scheichl ◽  
Nigel B. Wilding ◽  
Robert L. Jack
Keyword(s):  

2021 ◽  
Vol 44 (9) ◽  
Author(s):  
Fergus J. Moore ◽  
C. Patrick Royall ◽  
Tanniemola B. Liverpool ◽  
John Russo

AbstractWe explore crystallisation and polymorph selection in active Brownian particles with numerical simulation. In agreement with previous work (Wysocki et al. in Europhys Lett 105:48004, 2014), we find that crystallisation is suppressed by activity and occurs at higher densities with increasing Péclet number ($${ Pe }$$ Pe ). While the nucleation rate decreases with increasing activity, the crystal growth rate increases due to the accelerated dynamics in the melt. As a result of this competition, we observe the transition from a nucleation and growth regime at high $${ Pe }$$ Pe to “spinodal nucleation” at low $${ Pe }$$ Pe . Unlike the case of passive hard spheres, where preference for FCC over HCP polymorphs is weak, activity causes the annealing of HCP stacking faults, thus strongly favouring the FCC symmetry at high $${ Pe }$$ Pe . When freezing occurs more slowly, in the nucleation and growth regime, this tendency is much reduced and we see a trend towards the passive case of little preference for either polymorph.


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