-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 , 00 , 0

0 , 1

0 , 2

0 , 3

0 , 4

0 , 5

0 , 6

0 , 7

0 , 8

0 , 9

1 , 0

y /

L y

z / L z

• 3 2 p a r t i c l e 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 spheresconcentrate 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 GloNumerical simulation of lateral migration of red blood cells in Poiseuille flowsInt. 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 DepartmentLoughborough 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 i m u l a t i o n o f M o d e l l e d B l o o d C e l l s i n a V i s c o u s S h e a r F l o 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 i o 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 . 00 . 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 l o M e a s u r i n g P o i n t : x / L y = 2 0 0

y /

L y

z / L z

• 3 6 p a r t i c l e 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%

yz

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

0.73818( / 2)

m pk

y f

D US

L

ρνρ

= =

Fig. 6: Snapshot of further 2-point focusing Fig. 11: Ellipsoid rotational velocities

No rotation

Blured focusing