Actuated cilia regulate deposition of microscopic solid particles Rajat Ghosh and Alexander Alexeev George W. Woodruff School of Mechanical Engineering Georgia Institute of Technology, Atlanta, Georgia Gavin A. Buxton Department of Science Robert Morris University, Pittsburgh, Pennsylvania O. Berk Usta and Anna C. Balazs Chemical Engineering Department University of Pittsburgh, Pittsburgh, Pennsylvania November 22, 2009

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 Lung Cilia (NewScientist, April 2007) Synthetic Cilia (NewScientist, April 2007)

Computational Setup z x 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 z x L R B b h w F y X z L=4R B=3R b=0.4R h=10R W=6R

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 ζ Drag Coefficient EI Flexure Modulus R Particle Radius

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

Lattice Spring Model Poisson ratio = 1/4 Dx k M 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 Poisson ratio = 1/4 M Dx k

Particle Motion in a Period y x z Actuated cilia induce periodic particle oscillations Particle entrained via fluid viscosity No inertia effects at low Re

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 y x Sp=3 Sp=5

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 y Upward Drift Sp=5 Sp=4 Sp=3 Downward Drift

Effect of Particle Initial Position Shifting particle at different off-centric locations δ = 0, δ = 0.25c and δ = 0.5c c is inter-cilial distance z x Sp=3 Sp=5 Particle transport direction remains unchanged (most of the cases)

Mechanism for Particle Drift 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 z x : Forward :Backward y X y Sp=5 x z

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 substrates Ghosh, Buxton, Usta, Balazs, Alexeev, “Designing Oscillating Cilia That Capture or Release Microscopic Particles” Langmuir, ASAP 2009