Studied Shear-induced particle migration and size segregation for Mono-disperse and Bi-disperse with the help of the OpenFOAM toolbox. Geometry: Lid driven cavity

1. References:
1. Leighton, D., Acrivos, A., 1987a. Measurement of shear-induced self diffusion in concentrated suspensions of spheres. J. Fluid Mech. 177, 19-131.
2. Leighton, D., Acrivos, A., 1987b. The shear induced migration of particles in concentrated suspensions. J. Fluid Mech. 181, 415-439.
3. P Kanehl and H. Stark, 2015. Hydrodynamic segregation in a bidisperse colloidal suspension in micro channel flow : A theoretical study. J. Chem. Phys. 142, 214901
Reflux 7.0 , 2019. Annual Symposium of Chemical Engineering Venue: Indian Institute of Technology, Guwahati, Guwahati, Assam, Pin: 781039, India
Reflux 7.0
Size segregation of bidisperse suspension in a Lid driven cavity
Palleti Vishnu raja Reddy, M Mallikarjuna Reddy and Anugrah Singh
Department of chemical Engineering, Indian Institute of Technology Guwahati, India
Email: palleti@iitg.ac.in
Conclusions:
 Effect of particle size ratio and individual species concentrations are investigated.
 Smaller particles were thrown to the channel and the larger particles migrate towards the center.
 Size segregation of particles strongly depends upon particle size ratio and concentration.
Results and Discussion
0.0 0.2 0.4 0.6 0.8 1.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8 



max
y/h
0.0 0.2 0.4 0.6 0.8 1.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7








max
x/h
Varying Species concentration Varying Species concentration
Mono-disperse
0.0 0.2 0.4 0.6 0.8 1.0
0.58
0.59
0.60
0.61
0.62
ai
-40m, aj
-20m
ai
-40m, aj
-30m
m-bi
y/h
0.0 0.2 0.4 0.6 0.8 1.0
0.30
0.35
0.40
0.45
0.50
0.55
0.60
1
- 0.25 2
- 0
1
- 0.25 2
- 0.1
1
- 0.25 2
- 0.15
1
- 0.25 2
- 0.2
1
- 0.25 2
- 0.25
m-bi
x/h
Varying species concentrationVarying radii of the particles
Bi-disperse
Abstract
Introduction
 Shear-induced particle migration:
 Problem description:
Mathematical Models
 Diffusive Flux Model (Mono disperse)
Diffusive Flux Model (Bi disperse) Solution Method
• We utilized OpenFOAM environment to solve governing equations.
• OpenFOAM – Open source Field Operation And Manipulation
• It’s an enclosure of C++ libraries.
Open source Field Operation And Manipulation (OpenFOAM)
Pre
processing
Solving
Post
processing
Kanehl and Stark extended the DFM to bidisperse suspension flow by
considering the shear induced drift velocity resulting from collisions between
similar types as well as different types of particles.
2 . .
ij
t,i i ij c j j c j
j 1
N A k k D

     

   
        
   

 
d
i
2
i j j
ij d
i
j
a
1
a a a
A
2 a
1
a
 
    
 
   
 
 
ij ii 1
c c 2
2
D D
1




m,bi2.5
0
m,bi
1


 


 
   
 
3
23 ji2
m,bi m
3
1 b
2

 
 
   
     
     
1 2   
i j
i j
a a
b
a a



 
2
1
S
1 1

 


 
2
2
j j
j 1
2
2
j j
j 1
c a
c a



 
 
 


Total migration flux
Coupling matrix
Collective diffusion matrix
Krieger’s correlation
Maximum packing volume fraction
Static structure factor
where,
where,
Ref: Kanehl and Stark 2015
• This work mainly emphasis the importance of shear induced particle
migration and size segregation of particles in a bidisperse suspension in
a two dimensional Lid driven cavity.
• The model of Kanehl and Stark was used to investigate the shear
induced particle migration in bidisperse suspension.
• Suspension refers to the dispersion of solid particles in liquid media.
• The migration of solid
particles from higher shear
rate region to lower shear
rate region is called SIPM.
• It’s one of the important
properties in explaining the
demixing mechanism of
concentrated suspensions.
• The macroscopic approaches assume suspension as a continuous media
and its behavior is governed by conservation equations.
• To overcome the high computational requirement, continuum models
came into existence.
DFM assumes whole suspension as a generalized Newtonian fluid with
effective viscosity as a function of particle volume fraction(φ).
Total migration flux:
Flux due to spatially varying collision frequency
Flux due to spatially varying Viscosity
Flux due to spatially varying Brownian diffusion
Flux due to spatially varying Radius of curvature
The effective viscosity of suspension (Krieger, 1972)
2 ( )   E  1
2
t
where    E U U
1.82
0( ) 1
m

  


 
  
 
0 Suspending fluid viscosity
Max packing fractionm
where




. 0U = . . 0P      
. . tN
t



   

U
Continuity Equation Momentum Equation Particle Transport Equation
.
2
c cN k a    
    
 
.
2 2
nN k a

 


 
b bN D   
.
2
r rN k n a  
0.41
0.62
cwhere K
K


tN
cN
N
bN
rN
Ref: Phillips et al. 1992
Migration from higher to
lower shear rate zones
(Towards the centerline)
The Flow
Incompressible and
Viscous
Flow direction
Migration
U = 0.0063m/s
d = 0.002m
Lid driven cavity
Simulation Parameters
Height of the cavity (H)
Particle volume fraction(φ)
Medium Viscosity(η)
Fluid density(ρ)
Particle radii(a)
Inlet velocity(U)
Parameters Values
3
1
2
S.No
4
5
6
0.002 m
0.001 m/s
20 – 50 μm
4e-04 Pa.S
0 – 0.25
1190 kg.m-3
Velocity Contours (U)Concentration Contours (φ) Velocity Contours (U)Concentration Contours (φ2)Concentration Contours (φ1)
Utilities Meshing
tools
User
Application
Standard
Application
ParaView Others
Eg. Ensight
• Lid driven cavity: It’s a square/rectangular domain in which the top
wall is moving while the other 3 are stationary.