GAČR Grant no. 102/08/H081 “Nonstandard application of

physical fields”

Arindam SARKARJiří Chvojka

ADavid LUKÁŠ

Journal of Statistical Physics

Auto-model based computer simulation of Rayleigh Instability

(A.S.) has been supported by GACR Grant no. 102/08/H081 “Nonstandard application of physical fields”.

Dispersion relation

20

20

00

013

0

2 1)(

)(rkrk

krI

krI

r

Dispersion law for the Rayleigh instability plots dimensionless angular frequency against the dimensionless wave-number.

Auto-model

(a) The original longitudinal and cross sectional configurations of the liquid coated fibre. (b) Detailed cross-sectional shape of the original liquid layer on a fibre and the liquid nodes distribution along the fibre axis after the detachment into individual unduloids at the time of MCSPS=20,000.

Dynamics of Rayleigh instability

The time versus the droplet numbers for (a) the liquid coating the fibre; (b) the pure liquid jet. Unduloids on the fibre merge and those, which

disappeared, are marked in grey.

Time versus the droplet numbers

The time versus the droplet numbers for the system of liquid coating fibre with the original cross-section sketched. (a) the droplet numbers n ~ MCSPS; (b) ln(n) versus MCSPS with a regression result.

Outputs

The Rayleigh wavelength l versus the original radius ro as predicted by the

analytical theory (solid line) and by the computer simulations (points). (a) is for pure liquid jet and (b) for liquid coating a fibre.

Hammersley and Clifford theorem

Markov random field

Clans and clan functions g

...,,,1

,,1

,1

nkji

kjikjinji

jijini

ii xxxgxxgxgxP

nn xxxxxxxpxP ,...,,,...,, 32321

Bayes’ rule

Clan functions and marginal pobabilitioes

iii xxg

ji

jijiji xx

xxxxg

,

,,

kjkiji

jiikjikjikji xxxxxx

xxxxxxxxxg

,,,

,,,,,,

jiikjilkjlkjljikji

lkljkjlikijilkjilkjilkji xxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxg

,,,,,,,,,,

,,,,,,,,,,,,,,,

Energy function, Hamiltonian and exchange energies

nji

jijini

ii xxqxqxQ1

,1

,

n

njiji

n

njijiji xxExxqxQ

11, ,

1,

Interaction energiesE(xi,xj) in [e.u.]

Gas xi = 0 Liquid xi = 1 Fiber xi = 2

Gas xj = 0 -40 -10 20

Liquid xj = 1 -10 -26 -10

Fiber xj = 2 20 -10 0

xPxQ

ln

ELECTROHYDRODYNAMICS OF FREE LIQUID SURFACE IN A CIRCULAR CLEFT;

AN APPLICATION TO ELECTROSPRAYING AND

ELECTROSPINNING

Journal: Acta Materialia

A. Sarkar, Jiří Chvojka a D.Lukáš

Journal: Textile ProgressArindam+Jiří+David