simulation of microorganism motion in fluid based on granular model
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The International Symposium on BioMathematics (Symomath) 2015
4-6 November 2015, Bandung, Indonesia 1
Simulation of Microorganism Motion in Fluid Based on Granular ModelSparisoma Viridi1 and Nuning Nuraini2
1Physics Department, Institut Teknologi Bandung2Mathematics Department, Institut Teknologi Bandung Jalan Ganesha 10, Bandung 40132, [email protected], [email protected]
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The International Symposium on BioMathematics (Symomath) 2015
4-6 November 2015, Bandung, Indonesia 2
Outline
• Introduction• Model• Results• Summary
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The International Symposium on BioMathematics (Symomath) 2015
4-6 November 2015, Bandung, Indonesia 3
Introduction
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The International Symposium on BioMathematics (Symomath) 2015
4-6 November 2015, Bandung, Indonesia 4
Motion patterns of microorganism
• The patterns are unique: (1) orientation, (2) wobbling, (3) gyration, and (4) intensive surface probing (Leal-Taixé et al., 2010)
L. Leal-Taixé, M. Heydt, S. Weiße, A. Rosenhahn, B. Rosenhahn, Pattern Recognition 6376, 283-292 (2010).
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The International Symposium on BioMathematics (Symomath) 2015
4-6 November 2015, Bandung, Indonesia 5
An active fluid
• Turbulence flow can occur in high viscous fluid or in low Reynolds number (Aranson, 2013)
I. Aranson, Physics 6, 61 (2013).
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The International Symposium on BioMathematics (Symomath) 2015
4-6 November 2015, Bandung, Indonesia 6
Flagella as thruster
• Flagella introduces force and torque to the fluid (Yang et al., 2012)
C. Yang, C. Chen, Q. Ma, L. Wu, T. Song, Journal of Bionic Engineering 9, 200-210 (2012).
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The International Symposium on BioMathematics (Symomath) 2015
4-6 November 2015, Bandung, Indonesia 7
Shrink and swallow model
• Pressure difference can induce motion (Viridi and Nuraini, 2014)
S. Viridi, N. Nuraini, AIP Conference Proceedings 1587, 123-126 (2014).
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The International Symposium on BioMathematics (Symomath) 2015
4-6 November 2015, Bandung, Indonesia 8
Model
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The International Symposium on BioMathematics (Symomath) 2015
4-6 November 2015, Bandung, Indonesia 9
Two grain model
• Two spherical particles as cells, which are connected by a spring
mi
mj
kij
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The International Symposium on BioMathematics (Symomath) 2015
4-6 November 2015, Bandung, Indonesia 10
Push and pull spring force
• Spring force
lij is normal length of the spring
kij is spring constant
rij is distance between mass mi and mj
ijijijijij rlrkS ˆ
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The International Symposium on BioMathematics (Symomath) 2015
4-6 November 2015, Bandung, Indonesia 11
Fluid drag force
• Drag force
Cd is drag constant
A is cross sectional areaρf is fluid density
vf is fluid velocity
fi
fidfi vv
vvCAD
3
21
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4-6 November 2015, Bandung, Indonesia 12
Change of spring normal length
• Spring normal length varies with time
Tbridge is oscillation period of bridge between cells
LT
tLlij
12sin
bridge
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Change of drag coefficient
• Both cell can have same or different Cd
i = 1, 2 for each particle
The International Symposium on BioMathematics (Symomath) 2015
4-6 November 2015, Bandung, Indonesia 13
min,max,drag
min,max, 212cos
21, ddddid CC
TtCCC
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The International Symposium on BioMathematics (Symomath) 2015
4-6 November 2015, Bandung, Indonesia 14
Molecular dynamics method
• Newton second law of motion
• Euler method
jijii SD
ma
1
tatvttv iii
ttvtrttr ii
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4-6 November 2015, Bandung, Indonesia 15
Results
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Displacement
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Same drag constant
• Cd = 0.1, Cd = 0.1
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4-6 November 2015, Bandung, Indonesia 17
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Same drag constant (cont.)
• Cd = 0.1, Cd = 0.4
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4-6 November 2015, Bandung, Indonesia 18
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Same drag constant (cont.)
• Cd = 0.4, Cd = 0.1
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4-6 November 2015, Bandung, Indonesia 19
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Same drag constant (cont.)
• Cd = 0.4, Cd = 0.4
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4-6 November 2015, Bandung, Indonesia 20
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Influence of frequency
• Tbridge = 2
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4-6 November 2015, Bandung, Indonesia 21
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Influence of frequency
• Tbridge = 2.5
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4-6 November 2015, Bandung, Indonesia 22
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Oscillating drag constant
• Tbridge = 1, Tdrag = 0.5
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4-6 November 2015, Bandung, Indonesia 23
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Oscillating drag constant (cont.)
• Tbridge = 1, Tdrag = 1
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4-6 November 2015, Bandung, Indonesia 24
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Oscillating drag constant (cont.)
• Tbridge = 1, Tdrag = 1.5
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4-6 November 2015, Bandung, Indonesia 25
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Summary
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Summary
• Microorganism motion can be modeled by oscillating spring normal length and drag constant
• Noticeable displacement is observed ifTspring ~ Tdrag
• Other than that condition gives zero displace-ment in average for long observation time
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4-6 November 2015, Bandung, Indonesia 28
Acknowledgement
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Acknowledgement
• This work is supported by Institut Teknologi Bandung, and Ministry of Higher Education and Research, Indonesia, through the scheme Penelitian Unggulan Perguruan Tinggi – Riset Desentralisasi Dikti with contract number 310i/I1.C01/PL/2015
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4-6 November 2015, Bandung, Indonesia 29
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Thank you