- The document summarizes a numerical simulation of blood cell focusing in a microchannel flow. Spheres and ellipsoids were used to model blood cells. The simulation showed that particles refocused from four initial positions to two locations downstream, with a lower particle concentration increasing the focusing rate. Ellipsoids qualitatively reproduced experimental observations of blood cell focusing but with some blurring, which could be improved in future work.
Call Girls in Netaji Nagar, Delhi 💯 Call Us 🔝9953056974 🔝 Escort Service
Master Thesis Poster: Numerical Simulation of Modelled Blood Cells in a Viscous Flow Through a Duct
1. -The particles re-focus from 4 to 2 (lateral or vertical)
locations further downstream from measurements[1]:
-A lower particle concentration
increases the rate of particle
focusing and vice-versa:
0 , 0 0 , 1 0 , 2 0 , 3 0 , 4 0 , 5 0 , 6 0 , 7 0 , 8 0 , 9 1 , 0
0 , 0
0 , 1
0 , 2
0 , 3
0 , 4
0 , 5
0 , 6
0 , 7
0 , 8
0 , 9
1 , 0
y/Ly
z / L z
• 3 2 p a r t ic le s
Ellipsoids
Institute of Fluid Mechanics
Jesus Alvarez Sarro (j.alvarez-sarro-08@student.lboro.ac.uk)
The project was conducted at the TU Dresden, Germany
Motivation & Goals
• Numerical simulation of experiments performed by Di
Carlo et al. (2007) [1]: spheres and ellipsoids
• Investigation of physical parameters involved in particle
focusing, suggestions on possible improvements
• Statistical analysis of particle and flow behaviour
Method
• DNS, staggered Cartesian grid 2nd order in space
• Immersed Boundary Method (IBM) [3]
• 1) spherical particles 2) Red Blood Cells (RBC) modelled
as ellipsoids in a square duct
• Collision: repulsive potential particle-particle/wall
Spheres:
- Experiments by [1] show that spheres
concentrate at locations in a square duct
when the wall, Saffman (shear) and
Magnus (rotation) effects are in balance.
Conclusions and outlook
• particle concentration affects rate of focusing
• spheres focus further from four to two locations
• there is a recirculation pattern happenning in the duct
• future simulations with ellipsoids should incorporate the
recommendations given to increase physicality
References
[1] Dino Di Carlo, Daniel Irimia, Ronald G. Tompkins, and Mehmet Toner,
Continuous inertial focusing, ordering, and separation of particles in micro-
channels, PNAS, 27 November 2007, Vol. 104, No. 48
[2]-Lginglinh Shi, Tsorng-Whay Pan and Roland Glo
Numerical simulation of lateral migration of red blood cells in Poiseuille flows
Int. J. Numer. Meth. Fluids (2012), Vol. 68 Pp.
[3] -Tobias Kempe, Jochen Fröhlich, An improved immersed boundary method
with direct forcing for the simulation of particle laden flows, Journal of
Computational Physics (2012) Vol. 231 Pp. 3663-3684
Master in Engineering, Final Year Project, Aero & Auto Department
Loughborough University, Loughborough, LE11 3TU, UK
Numerical Simulation of Modelled Blood
Cells in a Viscous Flow Through a Duct
Computing time provided by ZIH, TU
Dresden is greatfully acknowledged.
Fig. 1: Focusing
locations [1] Fig. 7: Cross sectional comparison
ellipsoid-RBC (left), experimental
focusing observed [1] (right)
N u m e r i c a l S im u la t i o n o f M o d e l le d B l o o d C e l ls
i n a V is c o u s S h e a r F lo w t h r o u g h a S q u a r e
D u c t P r ä s e n t a t io n s n a m e X Y Z
3 6
0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0
0 . 0
0 . 1
0 . 2
0 . 3
0 . 4
0 . 5
0 . 6
0 . 7
0 . 8
0 . 9
1 . 0
D i C a r lo M e a s u r in g P o in t : x / L y = 2 0 0
y/Ly
z / L z
• 3 6 p a r t ic le s
Fig. 5: Particle
location at X/Ly=200
X/Ly=200 X/Ly=400 X/Ly=600 X/Ly=1200
Fig. 2: Particles re-focus to 2 locations
Fig. 3: Location PDF, X/Ly=150-250
Part. conc. = 1% Part. conc. = 0.4% Part. conc. = 0.2%
y
z
z
y
Fig. 8: Instantaneous
particle location, X/Ly=200.
Particles concentrate at a
radius in the duct
Fig. 9: PDF location analysis,
X/Ly=200 to X/Ly=500
Project supervisors:
- Prof. Dr. -Ing. habil. J. Fröhlich
- Dipl. -Hydrol. Berhard Vowinckel
- Dr. Adrian Spencer
-Blurred focusing obtained:
-Flow re-circulation as a
result of particle focusing:
Fig. 4: Streamlines added
on U contour background
-Higher particle concentration =
more collisions and less focusing:
Fig. 10: Snapshot from simulation
Future Improvements:
- Simulation of deformable
particles based on the
spring model by Shi et
al.[2]
- Exact RBC shape
- Higher collision damping
- Finer grid and increased
simulation time
Focusing behaviour is
Stokes number based:
2
0.738
18( / 2)
m p
k
y f
D U
S
L
ρ
νρ
= =
Fig. 6: Snapshot of
further 2-point focusing Fig. 11: Ellipsoid rotational velocities
No rotation
Blured focusing