Model Pergerakan Dua-Dimensi Mikroorganisme dalam Fluida berbasiskan Butiran

SKF 2015 16 - 17 Desember 2015, Bandung, lndonesia 1

Model Pergerakan Dua-Dimensi Mikroorganisme dalam Fluida

berbasiskan Butiran

Sparisoma Viridi1* dan Nuning Nuraini2

1Physics Department, Institut Teknologi BandungJalan Ganesha 10, Bandung 40132, Indonesia2Mathematics Department, Institut Teknologi Bandung Jalan Ganesha 10, Bandung 40132, Indonesia*[email protected]


Outline

• Introduction• Model 1, Results 1, Summary 1• Model 2, Results 2, Summary 2• Model 3, Results 3, Summary 3• Acknowledgements


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).


Motion observations

• Sperm of sea urchin(Psammechinusmiliaris)

• Planar sinusoidalmotion (Keller &Rubinow, 1976)

J. B. Keller, S. I. Rubinow, Biophysical Jounal 16, 151-170 (1976).


Motion observations (cont.)

• Same motion modewith multipleexposure

J. B. Keller, S. I. Rubinow, Biophysical Jounal 16, 151-170 (1976).


Prokaryote propulsion data

C. Brennen, H. Winet, Annual Review of Fluid Mechanics 9, 339-398 (1977).


Prokaryote propulsion data (cont.)



Eukaryote propulsion data



Eukaryote propulsion data (cont.)



Brennen, ibid.


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).


Self-electrophoretic through membran

• Flow of ions thrusts the microorganism

P. Mitchell, FEBS Letters 28, 1-4 (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 1

S. Viridi, N. Nuraini, The International Symposium on BioMathematics (Symomath) 2015, 4-6 November 2015, Bandung, Indonesia


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


Comprehensive view of the model


Results 1


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 1


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


Model 2S. Viridi, F. Haryanto, N. Nuraini, S. N. Khotimah, SEACOMP 2015, 2015, 10-12 December 2015, Yogyakarta, Indonesia


More complex cell

• A cell could havemore than onelocomotive organ,e.g. eight organs


More complex cell (cont.)

• Or just four organs


Synchronization

• Each locomotive organ should have certain initial phase in order the organism to have directional motion

• Supposed there is M locomotive organs• Assumed that each is positioned at

2Mj

j


Synchronization (cont.)

• And have initial phase φj

• But with same period T

• Resultant motion is simple sum of each locomotive organ


Results 2


No motion

• 8-dot0.eps 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

• 8-dot1.eps 0.000 0.5000.000 0.500 0.000 0.5000.000 0.500

• 4-dot0.eps 0.000 0.0000.000 0.000

• 4-dot1.eps 0.000 0.0001.000 0.000


Linear oscillating motion

• 4-lin0.eps 0.0000.000 0.250 0.250

• 4-lin1.eps 0.0000.250 0.250 0.000

• 4-lin2.eps 0.2500.250 0.000 0.000

• 4-lin3.eps 0.2500.000 0.000 0.250

01

23


Circular motion φj = 2π/M

1 2 3 4

5 6 7 8


M = 4, φj / T = 0.3, 0.4, 0.5, 0.6

0.3 0.4

0.5 0.6

4-cur0.eps 0.000 0.000 0.250 0.500


Summary 2


Summary

• Synchronization of locomotive organs can produce interesting motion

• Circular-like motion must obey that

φj = 2π/M and

• No motion can produced if all organs have the same initial phase

2Mj

j


Model 3


Gerak Organ Lokomotif

• Periode sampling berbeda (T): 1, 2, 3, 4


Gerak Organ Lokomotif (cont.)


Pengaruh frekuensi sampling

• 1 dan 4 ( fassa ) 2Mj

j


Frekuensi satu organ saja

• 1, 2, 3, 4 (fasa seperti sebelum

-nya)


Summary 3


Summary

• Frekuensi sampling yang sama pada setiap organ lokomotif untuk sebuah gerak hampir melingkar tidak memberikan pengaruh pada mode gerak


Summary (cont.)

• Gerak hampir melingkar yang memenuhi

φj = 2π/M and

dapat menjadi gerak berarah bila salah satu organ lokomotif memiliki frekuensi sampling berbeda (2, 3, 4, ..)

2Mj

j


Summary (cont.)

• Sinkronisasi antara panjang pegas dan koefi-sien gesek dalam suatu organ lokomotif i,

berbeda dengan sinkronisasi antar organ loko-motif i dan j agar organisme dapat mengha-silkan gerak berarah

MiTT iidragispring ,,,

kspringjspring TT ,,


Acknowledgement


Acknowledgement

• Riset ini didukung oleh Institut Teknologi Bandung, Penelitian Unggulan Perguruan Tinggi – Riset Desentralisasi Dikti bernomor 310i/I1.C01/PL/2015

• Presentasi ini didukung oleh FMIPA dan Panitia SKF 2015


Thank you

Model Pergerakan Dua-Dimensi Mikroorganisme dalam Fluida berbasiskan Butiran

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Transcript of Model Pergerakan Dua-Dimensi Mikroorganisme dalam Fluida berbasiskan Butiran