Actuated cilia regulate deposition of microscopic solid particles
Rajat Ghosh and Alexander AlexeevGeorge W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology, Atlanta, Georgia
Gavin A. BuxtonDepartment of Science
Robert Morris University, Pittsburgh, Pennsylvania
O. Berk Usta and Anna C. BalazsChemical Engineering Department
University of Pittsburgh, Pittsburgh, Pennsylvania
November 22, 2009
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Motivation
Controlling motion of microscopic particle in fluid-filled micro-channel Use bio-inspired oscillating cilia
Finding new routes to regulate micro-particle deposition in
micro-fluidic devices
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Lung Cilia(NewScientist, April 2007)
Synthetic Cilia(NewScientist, April 2007)
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Computational Setup
L=4RB=3Rb=0.4Rh=10RW=6R
Fluid-filled microchannel Elastic ciliated layer tethered to wall
Arranged in square pattern
Neutrally buoyant particle of radius R Small enough to move freely Not affected by Brownian fluctuations
Simulation Box Four oscillating cilia Suspended particle Viscous fluid
Actuation External period force
Methodology Hybrid LBM/LSM
zx
LR
B b
h
w
w
F
X
y
z
Parameters
Cilia dynamics characterized by Sp Sperm Number, Vary by modulating actuation frequency Range: 3-5
Cilia actuated by external periodic force Applied at free end Oscillating in x-direction (x-y plane) Amplitude a and angular frequency ω Amplitude characterized by, A=(1/3)aL2 /(EI)
Study effect of oscillating cilia on motion Use hybrid LBM/LSM
LBM for hydrodynamics of viscous incompressible fluid LSM for micromechanics of elastic cilia Coupled by boundary conditions
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ζ Drag Coefficient
EI Flexure Modulus
R Particle Radius
25.0EILSp
5
Lattice Boltzmann Model
Dynamic behavior governed by Navier-Stokes equation
Particles move along lattice while undergoing collisions
Collisions allow particles to reach local equilibrium
Simple two step algorithm Collision and propagation steps
Local in space and time Needs only local boundary conditions (bounce back rule)
Collisions Propagation
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Dynamic behavior governed by continuum elasticity theory
Network of harmonic springs connecting mass points
3D: 18 springs connecting regular square lattice
Integrate Newton’s equation of motion
Verlet algorithm
Lattice Spring Model
ss
Ec
5
6
Poisson ratio = 1/4
x
kE
2
5 3x
Ms
M
xk
Particle Motion in a Period
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x
Actuated cilia induce periodic particle oscillations Particle entrained via fluid viscosity
No inertia effects at low Re
y
z
Trajectory Path
Direction of particle drift motion changes with Sp Sp=3: particle moves towards wall Sp=5: particle moves away from wall
Sp controls particle drift across cilial layer Change Sp to regulate drift direction
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Sp=3 Sp=5
y
x
Drift Characterization
Unidirectional motion normal to channel wall
Cilia transport particles through entire layer Can deliver particle from free flow to wall surface and vice versa
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-0.1
-0.05
0
0.05
0.1
0.2 0.6 1 1.4Particle position, y/L
Vel
ocity
, URv-
1 Sp
4
Sp=5
Sp=3
Sp=4
Downward Drift
Upward Drift
y
Effect of Particle Initial Position
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Shifting particle at different off-centric locations δ = 0, δ = 0.25c and δ = 0.5c c is inter-cilial distance
Sp=3 Sp=5
Particle transport direction remains unchanged (most of the cases)
x
z
Mechanism for Particle Drift
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Mode of cilia oscillation changes with Sp Different secondary flow patterns Secondary flow changes direction with Sp
Sp=3 Sp=5 Sp=3 Secondary flows transport particle across cilial layer
xz
Sp=5
:Backward
: Forward
X
y
zx
y
Summary
Use actuated cilia to control of particle deposition Regulate drift direction by changing frequency
– Low frequency: particle moves down
– High frequency: particle moves up
Applications Regulate particle deposition in microchannel Lab-on-a-chip systems Self-cleaning substratesGhosh, Buxton, Usta, Balazs, Alexeev, “Designing Oscillating Cilia That Capture or Release
Microscopic Particles” Langmuir, ASAP 2009
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