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Comparison of the rheological behavior of particulate suspensions in power-law and Newtonian fluids by combined improved smoothed profile-lattice Boltzmann methods

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Abstract

In the present work, a numerical algorithm based on a combination of the lattice Boltzmann method (LBM) and the improved smoothed profile method (iSPM) has been proposed to study the motion of one, two and many circular particles in a non-Newtonian fluid. At first, the velocity profile of the non-Newtonian fluid at various power law indexes (n) was analyzed and the findings were compared with the numerical results of the previous works. Then, the motion of one circular cylinder and the hydrodynamic interactions between two particles in a shear flow were investigated. It was observed that Reshear, p had no important impact on the rotation of a single cylinder. In the two particles interaction, increasing the shear rate caused the particles to tumble on each other more closely and during a longer time. Therefore, the effective viscosity of a particulate suspension was considered for different Reynolds numbers and solid volume fractions, showing a satisfactory agreement with the previously published data. The results, therefore, showed that inertia increased the particles contribution to the effective viscosity of the suspension.

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Abbreviations

s αβ :

Strain rate tensor

∇:

Gradient operator

\({\partial \over {\partial t}}\) :

Partial time derivative

Π:

Stress tensor of the fluid

υ :

Kinematic viscosity

m :

Consistent factor

n :

Power-law index

\(\dot \gamma \) :

Shear rate

Re pl :

Reynolds number for power-law fluid

Re shear, p :

Particle-based shear Reynolds number

U c :

Characteristic velocity

D :

Characteristic length

f α :

Density distribution functions

τ :

Dimensionless relaxation time

f eq α :

Equilibrium density distribution functions

e α :

Discrete velocity vector

Δt :

Time step

x :

Coordinates of the grid points

c s :

Speed of sound

ω α :

Weight coefficient

σ αβ :

Stress tensor

´ αβ :

Kronecker delta

P :

Pressure

η :

Power-law viscosity

f neq α :

Non-equilibrium density distribution functions

Φ(x, t):

Particle concentration function

ζ i :

Interfacial thickness of the ith particle

N p :

Numbers of particles

u p(x, t):

Particle velocity

u(x, t):

Velocity field

p(x, t):

Density field

F H :

Solid-fluid hydrodynamic force

T H :

Solid-fluid hydrodynamic torque

M p :

Particle mass

F c :

Collision force

F ext :

External force

T est :

External torque

I p :

Particle moment of the inertia tensor

V n i :

Translational velocity

ω n i :

Angular velocity

u′ :

Fluctuating velocity

\({\boldsymbol{\bar u}}\) :

Average velocity

a :

Acceleration

α i :

Angular acceleration

∇u :

Volume average velocity gradient

F p ij :

Collision force between a particle and other particles

F wij :

Collision force between a particle and wall

R i :

Position of ith particle

R j :

Position of jth particle

R wj :

Wall positions

ε w,ε p :

Stiffness coefficients

c tj :

Force scale

Σij(p):

Particle stress

σ :

Local stress

Σ xy :

Bulk stress

μ eff :

Effective viscosity

U w :

Wall velocity

φ :

Solid volume fraction

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Authors and Affiliations

  1. Department of Chemical Engineering, Shahid Bahonar University of Kerman, Kerman, 7618868366, Iran

    Hamideh Rouhani Tazangi & Ataallah Soltani Goharrizi

  2. Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, 7618868366, Iran

    Ebrahim Jahanshahi Javaran

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  1. Hamideh Rouhani Tazangi
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  2. Ataallah Soltani Goharrizi
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  3. Ebrahim Jahanshahi Javaran
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Correspondence to Ebrahim Jahanshahi Javaran.

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Tazangi, H.R., Goharrizi, A.S. & Javaran, E.J. Comparison of the rheological behavior of particulate suspensions in power-law and Newtonian fluids by combined improved smoothed profile-lattice Boltzmann methods. Korea-Aust. Rheol. J. 33, 293–306 (2021). https://doi.org/10.1007/s13367-021-0023-z

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