Berthier Jean COMSOL 2008cn.comsol.com/paper/download/36402/Berthier_pres.pdf · Title: Microsoft...
Transcript of Berthier Jean COMSOL 2008cn.comsol.com/paper/download/36402/Berthier_pres.pdf · Title: Microsoft...
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Interfacing continuum and discrete methods: convective diffusion of microparticles and chemical species in microsystems
J. Berthier
2008
Presented at the COMSOL Conference 2008 Hannover
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• Diffusion of species, nanoparticles, macromolecules in microfluidics
• Model
• Applications to diffusion in cellular networks
• Convective transport
• Model: interfacing COMSOL (carrier fluid flow field) and Monte-Carlo (particles)
• Applications : • transport in a straight channel• recirculation regions for particle trapping• flow past micropillars• flow through a micro/nano aperture
• Conclusions and perspectives
Contents
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(a) (b) (c)
Modeling diffusion at the microscale: the Monte-carlo approach
Comparison between COMSOL and Monte-Carlo model
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• Starting point: Langevin’s equation (Newton’s equation + stochastic term)
• Mimic of the random walk (l << L)
• Geometry description
• Boundary conditions
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3D
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(a) (b)
(c)
54 33
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(d)
In-vivo application: modeling diffusion in extra-cellular spacesApplication to cellular uptake
Fluorescent image of a cellular network
Image of the calculated network after 10 mn Cellular uptake rate after 10 mn
Schematic of the network
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Modeling diffusion at the microscale: the Monte-carlo approach
• Carrier fluid is a continuum (Kn ~1 l ~ 10 nm for a liquid)
• Transported species may be in a discrete quantity
• Starting point: Langevin’s equation
• Geometry description + boundary conditions
J. Berthier et al., “The physics of a coflow micro-extractor: interface stability and optimal extraction length,”Sensors and Actuators A, in print.
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Absorbing walls
3D
LLE microdevice
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COMSOL Carrier fluid velocity field
Tabulation Nodes and velocities
Particle current locationtime t
Monte-carlo algorithm Particle location
time t+dt
interpolation
t+dt t
Schematic of the numerical approach
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Assessment of the method in the geometry of a straight channel
COMSOL (velocity field+ convective transport)
COMSOL velocity field+ Monte-Carlo
convective transport (200 particles)
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Convective diffusion in a straight channel - viscoelastic liquid
Ballistic random walk of particulates Concentration after 7 mm transport
Random walk near the wall(large shear rate)
Random walk in the channel middle(small shear rate)
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a b
J.P. Shelby, D. S.W. Lim, J. S. Kuo, D. T. Chiu, “High radial acceleration in microvortices,” Nature, Vol. 425, p.38, 2003
Application: Convective trapping of particles in recirculation regions
A. Manbachi et al. “Microcirculation within grooved substrates regulates cell positioning and cell docking inside microfluidics channels,” Lab chip, 8, 747–754, 2008
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(c) (d)
Small diffusion coefficientD = 10-10 m2/s
Larger diffusion coefficientD = 10-9 m2/s
Particles do not escape Particles slowly escape
Application: Convective trapping of particles in recirculation regions
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COMSOLCOMSOL / Monte-Carlo
(a) (b)
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(a)
(b)
(c)
Transport of species past a micropillar
COMSOL
COMSOL / Monte Carlo
• Carrier fluid flow: Poiseuille profile at inlet
• Bolus of concentration released at t=0 from a circular volume above the middle axis
500 particles
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(a) (b)
(c) (d)
Convective diffusion of species / nanoparticles through a micro-hole
• Two chambers separated by a 10 µm aperture• Bolus of concentration released at t=0 from a rectangular volume
200 particles
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3D approach: feasible ?
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Convective diffusion from a source point Convective diffusion in a curved micro-channel
• Limitation in the number of particles
• Algorithm not complicated
• Geometry and boundaries much more difficult to describe
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Conclusion / perspectives
• Continuum method probability of presence
• COMSOL/ Monte-Carlo interfacing
• Mimic the transport (to some extend) – visualization tool• Avoid numerical problems• Easy statistics• Necessity for nanopores, nanoporous materials, encapsulation
H.A. Makse et al., “Tracer dispersion in a percolation network with spatial correlations,” Physical Review E, Vol 61, n°1, p. 583, 2000
Le Vot et al. “Non-Newtonian fluids in Flow Focusing Devices: encapsulation with alginates,” Proceedings of the 1st European Conference on Microfluidics -Microfluidics 2008 - Bologna, December 10-12, 2008
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Thanks
2006