GAČR Grant no. 102/08/H081 “Nonstandard application of physical fields” Arindam SARKAR Jiří...
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Transcript of GAČR Grant no. 102/08/H081 “Nonstandard application of physical fields” Arindam SARKAR Jiří...
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