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.

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.

Tracer-diffusion in binary colloidal hard-sphere suspensions

2002 ◽  
Vol 117 (12) ◽  
pp. 5908-5920 ◽  
Author(s):  
Haiyan Zhang ◽  
Gerhard Nägele
Keyword(s):  
Hard Sphere ◽  
Tracer Diffusion ◽  
Sphere Suspensions

The first normal stress difference of non-Brownian hard-sphere suspensions in the oscillatory shear flow near the liquid and crystal coexistence region

Soft Matter ◽  
2020 ◽  
Vol 16 (43) ◽  
pp. 9864-9875
Author(s):  
Young Ki Lee ◽  
Kyu Hyun ◽  
Kyung Hyun Ahn
Keyword(s):  
Shear Flow ◽  
Normal Stress ◽  
Hard Sphere ◽  
Normal Stress Difference ◽  
Oscillatory Shear ◽  
Stress Difference ◽  
Large Amplitude Oscillatory Shear ◽  
First Normal Stress Difference ◽  
Oscillatory Shear Flow ◽  
Sphere Suspensions

The first normal stress difference (N1) as well as shear stress of non-Brownian hard-sphere suspensions in small to large amplitude oscillatory shear flow is investigated.

Three-particle contribution to sedimentation and collective diffusion in hard-sphere suspensions

2002 ◽  
Vol 117 (3) ◽  
pp. 1231-1241 ◽  
Author(s):  
B. Cichocki ◽  
M. L. Ekiel-Jeżewska ◽  
P. Szymczak ◽  
E. Wajnryb
Keyword(s):  
Hard Sphere ◽  
Sphere Suspensions

Viscosity of Hard-Sphere Suspensions:  Can We Go Lower?

2006 ◽  
Vol 45 (21) ◽  
pp. 6906-6914 ◽  
Author(s):  
Vijay Gopalakrishnan ◽  
Charles F. Zukoski
Keyword(s):  
Hard Sphere ◽  
Sphere Suspensions

scholarly journals Lévy fluctuations and mixing in dilute suspensions of algae and bacteria

2011 ◽  
Vol 8 (62) ◽  
pp. 1314-1331 ◽  
Author(s):  
Irwin M. Zaid ◽  
Jörn Dunkel ◽  
Julia M. Yeomans
Keyword(s):  
Graphics Processing Units ◽  
Interaction Model ◽  
Tracer Diffusion ◽  
Theoretical Description ◽  
Active Suspensions ◽  
Tracer Particles ◽  
Dilute Suspensions ◽  
Nutrient Influx ◽  
Non Gaussian ◽  
Micro Organisms

Swimming micro-organisms rely on effective mixing strategies to achieve efficient nutrient influx. Recent experiments, probing the mixing capability of unicellular biflagellates, revealed that passive tracer particles exhibit anomalous non-Gaussian diffusion when immersed in a dilute suspension of self-motile Chlamydomonas reinhardtii algae. Qualitatively, this observation can be explained by the fact that the algae induce a fluid flow that may occasionally accelerate the colloidal tracers to relatively large velocities. A satisfactory quantitative theory of enhanced mixing in dilute active suspensions, however, is lacking at present. In particular, it is unclear how non-Gaussian signatures in the tracers' position distribution are linked to the self-propulsion mechanism of a micro-organism. Here, we develop a systematic theoretical description of anomalous tracer diffusion in active suspensions, based on a simplified tracer-swimmer interaction model that captures the typical distance scaling of a microswimmer's flow field. We show that the experimentally observed non-Gaussian tails are generic and arise owing to a combination of truncated Lévy statistics for the velocity field and algebraically decaying time correlations in the fluid. Our analytical considerations are illustrated through extensive simulations, implemented on graphics processing units to achieve the large sample sizes required for analysing the tails of the tracer distributions.

Dynamic Simulations of Hard-Sphere Suspensions Under Steady Shear

1993 ◽  
Vol 21 (3) ◽  
pp. 363-368 ◽  
Author(s):  
J. M. V. A Koelman ◽  
P. J Hoogerbrugge
Keyword(s):  
Hard Sphere ◽  
Steady Shear ◽  
Dynamic Simulations ◽  
Sphere Suspensions
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