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SIMULATION OF PLANAR WAVE FLAGELLAR
PROPULSION OF NANOROBOTS USING COMSOL
Nikhil Londhe1, R. Majumdar1, J.S. Rathore1, N.N. Sharma1 1.Department of Mechanical Engineering
Birla Institute of Technology and Science, Pilani 333031, India
Presented by Rwitajit Majumdar at the 2011 COMSOL Conference
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Typical µorganism
Cell body Flagella
Fig1: Schematics of a micro organism
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Spectrum of flagellated motion
Review by Eric Lauga and Thomas R. Powers The hydrodynamics of swimming microorganisms - 2008
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Background
• Sir James Gray – Resistive Force theory
• 1955
• Dr. K. E. Machin – Elasto-hydrodynamics
• 1958
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Elemental Modeling
Fig 3: FBD of the tail element
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Governing Equation
Euler-Bernoulli beam equation Drag coefficient
Transverse velocity
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Algorithm to solution Governing fourth order equation
2 second order PDE
4 Boundary conditions
2 Dirichlet condition
2 Flux / Source terms
y=f(x,t)
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Remapping Governing Equation
Damping Coefficient (da)
Mass Coefficient(ea)
Conservative Flux (Γ)
Source Term (f)
0[ ] ¶2u
¶t2+ -C 0
0 0
é
ëê
ù
ûú¶u
¶t+Ñ.
A¶p
¶x
¶y
¶x
é
ë
êêêê
ù
û
úúúú
=0
p
é
ëêê
ù
ûúú
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Dirichlet condition
• The head and tail is connected and is fixed
• Bending moment vanishes at the distal end ! 2y
! x2= 0
y = 0
x=0 x=L
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Natural Boundary Condition
• Slope at the proximal end
• Shear stress vanishes at the distal end
! y! x
=Gsin! t
! 3y
! x3= 0
x=0 x=L
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Parameters Parameters Expression/Value Description
Re 0.0001 Reynolds’s Number
µ 0.001 Ns/m2 Viscosity
C Drag Coefficient
ω 100 rad/s Forcing frequency
G 4E-9 Slope amplitude
A 1E-22 Nm2 E*I
l0 Characteristic length
L 10*l0 Total length
-A
Cw
æ
èç
ö
ø÷
0.25
-4pm
2 - log(Re)
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General Settings
Geometry
Dimension: 1D Scale: nanometers
Total Length: 54650 nm
Meshing
Discretized in 100 elements.
Solver settings Time dependent solver
(0s : 0.007854s : 0.06283s)
Meshing was done such that discreet time and space slicing was possible
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Wave pattern
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Parametric variation of length
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Last time impression for Parametric variation
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Waveform at a time instance
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Wave motion
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Application
drug delivery
environment monitoring
medical technology
http://nanotechweb.org/cws/article/lab/32077
http://xlink.rsc.org/?DOI=b704002d
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Future Scope - study
• Calculation of derived values – Velocity – Efficiency – Thrust force
• Parametric variation for optimization • Study of tapered diameter flagella
peritrichous
lophotrichous
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Input from day 1 of conference
• Using Matlab livelink for various parametric studies.
– But for regular ones Comsol is simpler
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Future Scope – application of COMSOL
• Redefining the problem as a fluid-structure interaction problem – Study the wave patterns that the fluid would
generate around the flexible filament. • Particle tracing for swarm
– Brownian motion study
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THANK YOU
This work is carried on at NPMASS National MEMS Design Center (NNMDC), BITS Pilani, funded by ADA under the aegis of NPMASS