2. - CytoFluidix

Transcription

2. - CytoFluidix

Inertial Microfluidics Workshop
Manipulating Fluids and Particles
Dino Di Carlo, Ph.D.
Department of Bioengineering
University of California, Los Angeles
MicroTAS 2014, San Antonio TX USA
www.biomicrofluidics.com
Microfluidic Biotechnology
Acknowledgements
• Jerry Wu (Inertial microfluidic demo)
uFlow and flow programming
• Keegan Owsley
• Baskar Ganapathysubramanian (Iowa State)
• Dan Stoecklein (Iowa State)
Inertial microfluidic physics review (Lab on a Chip)
• Hamed Amini (Illumina)
• Wonhee Lee (KAIST)
Outline
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Why study inertial microfluidics?
Inertia in microscale flows (Reynolds Number)
Inertial focusing of particles
Inertial ordering of particles
Particle-induced flows
Channel geometry-induced flows
Inertial separation demonstration
uFlow demonstration
Why Study Inertial Microfluidics?
Focusing of cells and particles
• Flow cytometry
– No sheath fluid
– High rates of operation
• Concentrating cell
and particle solutions
– Continuous
– Size-based effects
Focusing of cells and particles
• Solution exchange
– Automated sample
preparation operations
• Uniform response to
stimuli
– Magnetic deflection
– Deformability
cytometry
Ordering of cells and particles
• Cytometry
– Non-overlapping cell
signals
– Operation at higher
rates
• Uniformizing
concentration
– Dispensing of cells
– Cell printing
• Mixing of flows
– Improve transport and
reaction in fluid
– Increase transport to
particle surface and
surface reactions
Channel geometry-induced flows
• Fabricating materials
– Complex fiber shapes
– Complex particle
shapes
• Routing reactions
Inertia in microscale flows??
typical dimensions:
w = h = 50 m
typical particle/obstacle
size and velocity:
a = ~10 m
Um = 0.1-1 m/s
typical pressure drops:
10-100 PSI
(70-700 kPa)
Channel
Reynolds Number
Rc 
U mh

= ~ 5 - 50
Particle
Reynolds Number
U ma2
Rp 
h
= ~ 0.2 - 2
No lateral migration of spherical
particles in Stokes flow
0
Navier-Stokes Equations:
 u

 u  u   p   2 u

 t

Stokes flow – linear differential equation 0  p   2 u
If for u positive, Fz is positive, linearity gives for –u, -Fz
Symmetry indicates Fz = 0
Mirror-symmetry time reversal theorem, Bretherton, JFM 1965
Two important effects
1. Confinement – Particle or obstacle dimensions
are of similar order as the channel dimensions
→ interactions with walls
2. High Shear Rates – Allow for significant
velocity differences over small length scales
and therefore inertial asymmetries
→ i.e. leads to Dean flow, obstacle-induced
secondary flows
Small channels achieve high shear
rates while avoiding turbulence
Rc
Rp

2
h
a2

2
h
a2

Rc  2000
R p  0.1
Constraints: Avoid turbulence
while achieving significant
shear-rate induced inertial
effects
For 10 m particles implies:
h < ~1.4 mm
Inertial focusing
Segre and Silberberg. Nature. 1962
Particle Focusing and Ordering in Microchannels
Flow velocity:
~ 0.1-1 m/s
Channel size:
~ 50 m wide
Particle size:
~ 10 m wide
Polystyrene
Flow
Hur et al. Lab Chip
2010
Origins of inertial migration
An interlude of mathematics… Close your eyes 
Cox and Brenner. Chem. Eng. Sci. 1968, Ho and Leal. J. Fluid Mech. 1974, Schonberg and Hinch. J. Fluid
Mech. 1989, Asmolov. J. Fluid Mech. 1999, Matas et al. J. Fluid Mech. 2004
Di Carlo Lab Chip 2009
Implications of the dependence
on curvature in velocity
Amini et al. Lab Chip
2014
Effect of channel shape on
equilibrium position
Finite size effects on inertial lift
Di Carlo PRL 2009
Particle size and viscosity
affects focusing position
Hur et al. Lab Chip
2011
Deformability-induced lift
• Generally towards regions of lowest shear
rate (i.e. channel centerline)
Chan and Leal. J. Fluid Mech. 1979
Tam and Hyman. J. Fluid Mech. 1973
Doddi and Bagchi. Int. J. Multi. Flow. 2008
Pozrikidis. Ann. Biomed. Eng. 2005
26
Particle equilibrium position
depends on rotational diameter
Hur et al. Appl. Phys. Lett. 2011
Separating particles by shape
Masaeli et al. Phys
Microfluidic Rev X. 2012
Biotechnology
Inertial ordering
Mechanism of dynamic self-assembly?
Channel
cross
section
Equilibrium
positions
What repulsive and attractive interactions are there?
Lee, Amini,
Stone, Microfluidic
Di Carlo. Biotechnology
PNAS 2010
Stokes flow with confinement
Shear flow
Unconfined
Confined
Wall reflection of the stresslet
Flow field due to scattering of external flow (perturbation velocity field)
Viscous reversing streamlines
Stokes Flow, Re = 0
Reversing stream lines
Experimental observation of
reversing streamlines
Lee, Amini,
Stone, Microfluidic
PNAS 2010
Confinement and inertia = ordering
Lee, Amini,
Stone, Microfluidic
PNAS 2010
Channel Wall
1.
2.
3.
4.
5.
Viscous disturbance from neighboring particle (repulsive)
Flow profile amplifies interparticle distance (repulsive)
Inertial lift leads to return to focusing position or
Overshooting leads to reduction in distance again (transient attractive)
Settling towards the inertial focusing equilibrium
Key Point: No attractive interaction once focused!
Lee, Amini,
Stone, Microfluidic
PNAS 2010
Implications of this mechanism:
Controlling Particle Spacing
1. Expansion reinitiates repulsive interaction
2. Distances stretched by contraction
3. No attractive interaction to pull particles back to pre-expansion distances
Lee, Amini,
Stone, Microfluidic
PNAS 2010
Net disturbance around a particle
net recirculation
Amini et al.
PNAS 2012
Particle position in the channel
affects disturbance flow
Amini et al.
PNAS 2012
Particle rotation increases trasnsport
and translation decreases transport
Amini et al.
PNAS 2012
Implications of this Mechanism:
Channel
geometry-induced
flows
Controlling Particle Spacing
1. Expansion reinitiates repulsive
interaction
2. Distances stretched by contraction
3. No attractive interaction to pull
particles back to pre-expansion
distances
Amini
et al.Microfluidic
Nature Comm
2013
Biotechnology
Dean flow
Secondary rotational flows – two counter-rotating vortices for
most conditions
Superposition of inertial lift and dean flow
r
1
2
Dean number
H
De  Re 
 2r 
Dean flow velocity
U D ~ De 2 / H
Dean drag force if particle is held
stationary in an inertial lift equilibrium position
FD ~ U m2 aH 2 r 1
Balance of forces in curved channels
Inertial lift
FL  U m2 a 2

a
H
Dean drag

f c1  xc , Rc   ( Ha )4 f c 2  xc , Rc 
Compare to weaker
portion of lift
2
FL
r a
   f Rc 
Rf ~
FD H  H 
FD ~ U m2 aH 2 r 1
1. Differential focusing of
different sized particles
2. Variation of focusing
with flow rate
If Rf < 1 over entire domain then solution will be mixed
Improved focusing in curved channels
Mixing action of Dean flow is important
Gossett
and Di Microfluidic
Carlo. Anal.
Chem. 2009
Biotechnology
Focusing phase diagram in
curving channels
Gossett
and Di Microfluidic
Carlo. Anal.
Chem. 2009
Biotechnology
Inertial flow
deformation
around a
pillar
Operating range for pillars with relatively
uniform transport
normalized transport

V  
y mean
z 0
Vx avg
λ
Reynolds number
Pillar diameter can tune the strength of
the secondary flow

V  
y mean
z 0
Vx avg
   D w
2.2
normalized
transport
λ
normalized pillar diameter
channel aspect ratio
Mode of operation is governed
by flow parameters
normalized pillar diameter
Position-dependent
fluid manipulation
Net secondary flows can be sequentially
superimposed, enabling fluid shape engineering
OPERATOR LIBRARY
s
operations on cross section of flow
f1
x
f1 ( x )
f2
x
f2
f2 ( s )
f2 ( x )
f1 ( f 2 ( s ))
f3
x
f3 ( x )
f 3 ( f1 ( f 2 ( s )))
f 2 ( f 3 ( f1 ( f 2 ( s ))))
f1
f3
s undergoes a sequence of local transformations:
f2, f1, f3, f2
associated with a sequence of specific channel structures to achieve a complex final shape F(s)
f2
F( s )
Sculpting flow with sequences of pillars
Discretization, similar to musical notes:
Designing a CAD program to
control flow shape
Hierarchical assembly of complex
operations on the flow
Steps to a higher level function
Creation of add vertex function via recursion
(i), mirroring (ii), and shaping (iii).
Demonstrations
• Inertial focusing / separation
• uFlow – flow programming.
End
Thank you !

2. - CytoFluidix

Transcription

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