Non-local stresses in highly non-uniformly flowing suspensions: The shear-curvature viscosity

H. Jin, K. Kang, K.H. Ahn, W.J. Briels (Corresponding Author), J.K.G. Dhont (Corresponding Author)

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)
9 Downloads (Pure)

Abstract

For highly non-uniformly flowing fluids, there are contributions to the stress related to spatial variations of the shear rate, which are commonly referred to as non-local stresses. The standard expression for the shear stress, which states that the shear stress is proportional to the shear rate, is based on a formal expansion of the stress tensor with respect to spatial gradients in the flow velocity up to leading order. Such a leading order expansion is not able to describe fluids with very rapid spatial variations of the shear rate, like in micro-fluidics devices and in shear-banding suspensions. Spatial derivatives of the shear rate then significantly contribute to the stress. Such non-local stresses have so far been introduced on a phenomenological level. In particular, a formal gradient expansion of the stress tensor beyond the above mentioned leading order contribution leads to a phenomenological formulation of non-local stresses in terms of the so-called "shear-curvature viscosity". We derive an expression for the shear-curvature viscosity for dilute suspensions of spherical colloids and propose an effective-medium approach to extend this result to concentrated suspensions. The validity of the effective-medium prediction is confirmed by Brownian dynamics simulations on highly non-uniformly flowing fluids.

Original languageEnglish
Article number014903
JournalJournal of chemical physics
Volume149
Issue number1
DOIs
Publication statusPublished - 7 Jul 2018

Fingerprint

Shear viscosity
Suspensions
curvature
viscosity
shear
Shear deformation
stress tensors
Tensors
Fluids
Shear stress
shear stress
expansion
fluids
Fluidic devices
Colloids
gradients
microfluidic devices
Flow velocity
colloids
Derivatives

Cite this

Jin, H. ; Kang, K. ; Ahn, K.H. ; Briels, W.J. ; Dhont, J.K.G. / Non-local stresses in highly non-uniformly flowing suspensions : The shear-curvature viscosity. In: Journal of chemical physics. 2018 ; Vol. 149, No. 1.
@article{bcd7225c7a994089beaf01e8d753ccec,
title = "Non-local stresses in highly non-uniformly flowing suspensions: The shear-curvature viscosity",
abstract = "For highly non-uniformly flowing fluids, there are contributions to the stress related to spatial variations of the shear rate, which are commonly referred to as non-local stresses. The standard expression for the shear stress, which states that the shear stress is proportional to the shear rate, is based on a formal expansion of the stress tensor with respect to spatial gradients in the flow velocity up to leading order. Such a leading order expansion is not able to describe fluids with very rapid spatial variations of the shear rate, like in micro-fluidics devices and in shear-banding suspensions. Spatial derivatives of the shear rate then significantly contribute to the stress. Such non-local stresses have so far been introduced on a phenomenological level. In particular, a formal gradient expansion of the stress tensor beyond the above mentioned leading order contribution leads to a phenomenological formulation of non-local stresses in terms of the so-called {"}shear-curvature viscosity{"}. We derive an expression for the shear-curvature viscosity for dilute suspensions of spherical colloids and propose an effective-medium approach to extend this result to concentrated suspensions. The validity of the effective-medium prediction is confirmed by Brownian dynamics simulations on highly non-uniformly flowing fluids.",
author = "H. Jin and K. Kang and K.H. Ahn and W.J. Briels and J.K.G. Dhont",
year = "2018",
month = "7",
day = "7",
doi = "10.1063/1.5035268",
language = "English",
volume = "149",
journal = "Journal of chemical physics",
issn = "0021-9606",
publisher = "American Institute of Physics",
number = "1",

}

Non-local stresses in highly non-uniformly flowing suspensions : The shear-curvature viscosity. / Jin, H.; Kang, K.; Ahn, K.H.; Briels, W.J. (Corresponding Author); Dhont, J.K.G. (Corresponding Author).

In: Journal of chemical physics, Vol. 149, No. 1, 014903, 07.07.2018.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Non-local stresses in highly non-uniformly flowing suspensions

T2 - The shear-curvature viscosity

AU - Jin, H.

AU - Kang, K.

AU - Ahn, K.H.

AU - Briels, W.J.

AU - Dhont, J.K.G.

PY - 2018/7/7

Y1 - 2018/7/7

N2 - For highly non-uniformly flowing fluids, there are contributions to the stress related to spatial variations of the shear rate, which are commonly referred to as non-local stresses. The standard expression for the shear stress, which states that the shear stress is proportional to the shear rate, is based on a formal expansion of the stress tensor with respect to spatial gradients in the flow velocity up to leading order. Such a leading order expansion is not able to describe fluids with very rapid spatial variations of the shear rate, like in micro-fluidics devices and in shear-banding suspensions. Spatial derivatives of the shear rate then significantly contribute to the stress. Such non-local stresses have so far been introduced on a phenomenological level. In particular, a formal gradient expansion of the stress tensor beyond the above mentioned leading order contribution leads to a phenomenological formulation of non-local stresses in terms of the so-called "shear-curvature viscosity". We derive an expression for the shear-curvature viscosity for dilute suspensions of spherical colloids and propose an effective-medium approach to extend this result to concentrated suspensions. The validity of the effective-medium prediction is confirmed by Brownian dynamics simulations on highly non-uniformly flowing fluids.

AB - For highly non-uniformly flowing fluids, there are contributions to the stress related to spatial variations of the shear rate, which are commonly referred to as non-local stresses. The standard expression for the shear stress, which states that the shear stress is proportional to the shear rate, is based on a formal expansion of the stress tensor with respect to spatial gradients in the flow velocity up to leading order. Such a leading order expansion is not able to describe fluids with very rapid spatial variations of the shear rate, like in micro-fluidics devices and in shear-banding suspensions. Spatial derivatives of the shear rate then significantly contribute to the stress. Such non-local stresses have so far been introduced on a phenomenological level. In particular, a formal gradient expansion of the stress tensor beyond the above mentioned leading order contribution leads to a phenomenological formulation of non-local stresses in terms of the so-called "shear-curvature viscosity". We derive an expression for the shear-curvature viscosity for dilute suspensions of spherical colloids and propose an effective-medium approach to extend this result to concentrated suspensions. The validity of the effective-medium prediction is confirmed by Brownian dynamics simulations on highly non-uniformly flowing fluids.

UR - http://www.scopus.com/inward/record.url?scp=85049654999&partnerID=8YFLogxK

U2 - 10.1063/1.5035268

DO - 10.1063/1.5035268

M3 - Article

VL - 149

JO - Journal of chemical physics

JF - Journal of chemical physics

SN - 0021-9606

IS - 1

M1 - 014903

ER -