simulation of microorganism motion in fluid based on granular model

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]



Outline

• Introduction• Model• Results• Summary



Introduction



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).



An active fluid

• Turbulence flow can occur in high viscous fluid or in low Reynolds number (Aranson, 2013)

I. Aranson, Physics 6, 61 (2013).



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).



Shrink and swallow model

• Pressure difference can induce motion (Viridi and Nuraini, 2014)

S. Viridi, N. Nuraini, AIP Conference Proceedings 1587, 123-126 (2014).



Model



Two grain model

• Two spherical particles as cells, which are connected by a spring

mi

mj

kij



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



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



Change of spring normal length

• Spring normal length varies with time

Tbridge is oscillation period of bridge between cells

LT

tLlij

12sin

bridge

Change of drag coefficient

• Both cell can have same or different Cd

i = 1, 2 for each particle



min,max,drag

min,max, 212cos

21, ddddid CC

TtCCC



Molecular dynamics method

• Newton second law of motion

• Euler method

jijii SD

ma

1

tatvttv iii

ttvtrttr ii



Results



Displacement

Same drag constant

• Cd = 0.1, Cd = 0.1



Same drag constant (cont.)

• Cd = 0.1, Cd = 0.4




• Cd = 0.4, Cd = 0.1




• Cd = 0.4, Cd = 0.4



Influence of frequency

• Tbridge = 2



Influence of frequency

• Tbridge = 2.5



Oscillating drag constant

• Tbridge = 1, Tdrag = 0.5



Oscillating drag constant (cont.)

• Tbridge = 1, Tdrag = 1



Oscillating drag constant (cont.)

• Tbridge = 1, Tdrag = 1.5





Summary



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



Acknowledgement

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





Thank you

simulation of microorganism motion in fluid based on granular model

Science