Theory of tracer diffusion in concentrated hard-sphere suspensions

2019 ◽  
Vol 870 ◽  
pp. 1105-1126 ◽  
Author(s):  
S. S. L. Peppin
Keyword(s):  
Glass Transition ◽  
Hard Sphere ◽  
Volume Fraction ◽  
Pore Space ◽  
Particle Volume Fraction ◽  
Tracer Diffusion ◽  
Tracer Diffusivity ◽  
Particle Volume ◽  
Cross Diffusion ◽  
Sphere Suspensions

A phenomenological theory of diffusion and cross-diffusion of tracer particles in concentrated hard-sphere suspensions is developed. Expressions for the diffusion coefficients as functions of the host particle volume fraction are obtained up to the close-packing limit. In concentrated systems the tracer diffusivity decreases because of the reduced pore space available for diffusion. The tracer diffusivity can be modelled by a Stokes–Einstein equation with an effective viscosity that depends on the pore size. Tracer diffusion and segregation during sedimentation cease at a critical trapping volume fraction corresponding to a tracer glass transition. The tracer cross-diffusion coefficient, however, increases near the glass transition and diverges in the close-packed limit.

Static lengths in glass-forming monodisperse hard-sphere fluids from periodic array pinning

Soft Matter ◽  
2016 ◽  
Vol 12 (2) ◽  
pp. 402-407 ◽  
Author(s):  
Yuxing Zhou ◽  
Scott T. Milner
Keyword(s):  
Structural Relaxation ◽  
Hard Sphere ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Relaxation Times ◽  
Periodic Array ◽  
Length Scale ◽  
Master Curves ◽  
Particle Volume ◽  
Glass Forming

In glassy hard-sphere fluids, with varying particle volume fraction and distance between pinned particles, particle diffusivities and structural relaxation times both collapse to master curves, revealing a growing static length scale.

scholarly journals Anomalous tracer diffusion in hard-sphere suspensions

2021 ◽  
Author(s):  
Stephen Peppin
Keyword(s):  
Hard Sphere ◽  
Structural Heterogeneity ◽  
Tracer Diffusion ◽  
Host Matrix ◽  
Uphill Diffusion ◽  
Cross Diffusion ◽  
Coupled Equations ◽  
Tracer Particles ◽  
Sphere Suspensions ◽  
Matrix Concentration

Coupled equations describing diffusion and cross-diffusion of tracer particles in hard-sphere suspensions are derived and solved numerically. In concentrated systems with strong excluded volume and viscous interactions the tracer motion is subdiffusive. Cross diffusion generates transient perturbations to the host-particle matrix, which affect the motion of the tracer particles leading to nonlinear mean squared displacements. Above a critical host-matrix concentration the tracers experience clustering and uphill diffusion, moving in opposition to their own concentration gradient. A linear stability analysis indicates that cross diffusion can lead to unstable concentration fluctuations in the suspension. The instability is a potential mechanism for the appearance of dynamic and structural heterogeneity in suspensions near the glass transition.

scholarly journals Performance improvement of double-tube gas cooler in CO2 refrigeration system using nanofluids

2015 ◽  
Vol 19 (1) ◽  
pp. 109-118 ◽  
Author(s):  
Jahar Sarkar
Keyword(s):  
Performance Improvement ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Cooling Capacity ◽  
Inlet Temperature ◽  
Refrigeration Cycle ◽  
Particle Volume ◽  
Transcritical Carbon Dioxide ◽  
The Given ◽  
Theoretical Analyses

The theoretical analyses of the double-tube gas cooler in transcritical carbon dioxide refrigeration cycle have been performed to study the performance improvement of gas cooler as well as CO2 cycle using Al2O3, TiO2, CuO and Cu nanofluids as coolants. Effects of various operating parameters (nanofluid inlet temperature and mass flow rate, CO2 pressure and particle volume fraction) are studied as well. Use of nanofluid as coolant in double-tube gas cooler of CO2 cycle improves the gas cooler effectiveness, cooling capacity and COP without penalty of pumping power. The CO2 cycle yields best performance using Al2O3-H2O as a coolant in double-tube gas cooler followed by TiO2-H2O, CuO-H2O and Cu-H2O. The maximum cooling COP improvement of transcritical CO2 cycle for Al2O3-H2O is 25.4%, whereas that for TiO2-H2O is 23.8%, for CuO-H2O is 20.2% and for Cu-H2O is 16.2% for the given ranges of study. Study shows that the nanofluid may effectively use as coolant in double-tube gas cooler to improve the performance of transcritical CO2 refrigeration cycle.

A simulation and experimental study on particle volume fraction of PMMA suspension in centrifugal fields

2021 ◽  
Author(s):  
Yosephus Ardean Kurnianto Prayitno ◽  
Tong Zhao ◽  
Yoshiyuki Iso ◽  
Masahiro Takei
Keyword(s):  
Experimental Study ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Particle Volume

Solidification Processing of Functionally Graded Materials by Sedimentation

1999 ◽  
Author(s):  
J. W. Gao ◽  
S. J. White ◽  
C. Y. Wang
Keyword(s):  
Functionally Graded Materials ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Computer Code ◽  
Functionally Graded ◽  
Particle Volume ◽  
Particle Sedimentation ◽  
Graded Materials ◽  
Free Zone ◽  
Free Region

Abstract A combined experimental and numerical investigation of the solidification process during gravity casting of functionally graded materials (FGMs) is conducted. Focus is placed on the interplay between the freezing front propagation and particle sedimentation. Experiments were performed in a rectangular ingot using pure substances as the matrix and glass beads as the particle phase. The time evolutions of local particle volume fractions were measured by bifurcated fiber optical probes working in the reflection mode. The effects of various processing parameters were explored. It is found that there exists a particle-free zone in the top portion of the solidified ingot, followed by a graded particle distribution region towards the bottom. Higher superheat results in slower solidification and hence a thicker particle-free zone and a higher particle concentration near the bottom. The higher initial particle volume fraction leads to a thinner particle-free region. Lower cooling temperatures suppress particle settling. A one-dimensional solidification model was also developed, and the model equations were solved numerically using a fixed-grid, finite-volume method. The model was then validated against the experimental results, and the validated computer code was used as a tool for efficient computational prototyping of an Al/SiC FGM.

Shock-Induced Multiphase Instability in a High Volume Fraction Finite-Thickness Particle Layer

2021 ◽  
Author(s):  
Bertrand Rollin ◽  
Frederick Ouellet ◽  
Bradford Durant ◽  
Rahul Babu Koneru ◽  
S. Balachandar
Keyword(s):  
Shock Tube ◽  
Volume Fraction ◽  
Solid Phase ◽  
Particle Volume Fraction ◽  
Finite Thickness ◽  
Spherical Particles ◽  
Shock Strength ◽  
Particle Volume ◽  
Particle Cloud ◽  
Particle Layer

Abstract We study the interaction of a planar air shock with a perturbed, monodispersed, particle curtain using point-particle simulations. In this Eulerian-Lagrangian approach, equations of motion are solved to track the position, momentum, and energy of the computational particles while the carrier fluid flow is computed in the Eulerian frame of reference. In contrast with many Shock-Driven Multiphase Instability (SDMI) studies, we investigate a configuration with an initially high particle volume fraction, which produces a strongly two-way coupled flow in the early moments following the shock-solid phase interaction. In the present study, the curtain is about 4 mm in thickness and has a peak volume fraction of about 26%. It is composed of spherical particles of d = 115μm in diameter and a density of 2500 kg.m−3, thus replicating glass particles commonly used in multiphase shock tube experiments or multiphase explosive experiments. We characterize both the evolution of the perturbed particle curtain and the gas initially trapped inside the particle curtain in our planar three-dimensional numerical shock tube. Control parameters such as the shock strength, the particle curtain perturbation wavelength and particle volume fraction peak-to-trough amplitude are varied to quantify their influence on the evolution of the particle cloud and the initially trapped gas. We also analyze the vortical motion in the flow field. Our results indicate that the shock strength is the primary contributor to the cloud particle width. Also, a classic Richtmyer-Meshkov instability mixes the gas initially trapped in the particle curtain and the surrounding gas. Finally, we observe that the particle cloud contribute to the formation of longitudinal vortices in the downstream flow.

Alignment of Nanoplates in Lamellar Diblock Copolymer Domains and the Effect of Particle Volume Fraction on Phase Behavior

2018 ◽  
Vol 7 (12) ◽  
pp. 1400-1407 ◽  
Author(s):  
Nadia M. Krook ◽  
Jamie Ford ◽  
Manuel Maréchal ◽  
Patrice Rannou ◽  
Jeffrey S. Meth ◽  
...  
Keyword(s):  
Phase Behavior ◽  
Diblock Copolymer ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Particle Volume

scholarly journals Steady electrodiffusion in hydrogel-colloid composites: macroscale properties from microscale electrokinetics

2010 ◽  
Vol 82 (1) ◽  
pp. 69-86
Author(s):  
Reghan J. Hill
Keyword(s):  
Membrane Potential ◽  
Electrostatic Potential ◽  
Colloidal Particles ◽  
Electrolyte Concentration ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Solid Volume Fraction ◽  
Electrical Current ◽  
Inclusion Size ◽  
Particle Volume

A rigorous microscale electrokinetic model for hydrogel-colloid composites is adopted to compute macroscale profiles of electrolyte concentration, electrostatic potential, and hydrostatic pressure across membranes that separate electrolytes with different concentrations. The membranes are uncharged polymeric hydrogels in which charged spherical colloidal particles are immobilized and randomly dispersed with a low solid volume fraction. Bulk membrane characteristics and performance are calculated from a continuum microscale electrokinetic model (Hill 2006b, c). The computations undertaken in this paper quantify the streaming and membrane potentials. For the membrane potential, increasing the volume fraction of negatively charged inclusions decreases the differential electrostatic potential across the membrane under conditions where there is zero convective flow and zero electrical current. With low electrolyte concentration and highly charged nanoparticles, the membrane potential is very sensitive to the particle volume fraction. Accordingly, the membrane potential - and changes brought about by the inclusion size, charge and concentration - could be a useful experimental diagnostic to complement more recent applications of the microscale electrokinetic model for electrical microrheology and electroacoustics (Hill and Ostoja-Starzewski 2008, Wang and Hill 2008).

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