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Scaling relationships between viscosity and diffusivity in shear-thickening suspensions.

Abhinendra Singh¹, Kuniyasu Saitoh²

¹Department of Macromolecular Science and Engineering, Case Western Reserve University, Cleveland, Ohio 44106, USA. abhinendra.singh@case.edu.

|August 21, 2023

Summary

Particle viscosity and diffusion increase with shear stress due to lubrication to friction transitions. A universal relationship links viscosity and diffusivity via particle cluster size across different flow regimes.

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Area of Science:

Physics
Materials Science
Chemical Engineering

Background:

Dense suspensions exhibit complex behaviors under deformation.
These behaviors are linked to transitions between lubricated and frictional states.

Purpose of the Study:

Investigate flow behavior and shear-induced diffusion of frictional non-Brownian spheres.
Establish a relationship between viscosity and diffusivity.

Main Methods:

Numerical simulations of 2D simple shear flow.
Analysis of frictional non-Brownian spheres.

Main Results:

Viscosity (η) and diffusivity (D/τ) increase with characteristic shear stress, indicating a lubrication to frictional transition.
A one-to-one relationship between viscosity and diffusivity is proposed, governed by the length scale (ξ) of particle clusters.
This relationship shows a crossover from D/τ ∼ η in frictionless states to D/τ ∼ η^(1/3) in frictional states.

Conclusions:

The study reveals a universal relationship between viscosity and diffusivity in dense frictional suspensions.
This relationship is controlled by particle cluster size and is independent of interparticle friction and system size.