scholarly journals Lattice-Boltzmann method applied to the pattern formation on periodic surface structures generated by multiline nanosecond laser

DYNA ◽  
2014 ◽  
Vol 81 (187) ◽  
pp. 108-114
Author(s):  
Frank Rodolfo Fonseca-Fonseca ◽  
José Edgar Alfonso-Orjuela ◽  
Darío Fernando Andrade
Keyword(s):  
Pattern Formation ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Surface Structures ◽  
Nanosecond Laser ◽  
Periodic Surface ◽  
Boltzmann Method

Enslaved Phase-Separation Fronts and Liesegang Pattern Formation

2011 ◽  
Vol 9 (5) ◽  
pp. 1081-1093 ◽  
Author(s):  
E. M. Foard ◽  
A. J. Wagner
Keyword(s):  
Phase Separation ◽  
Pattern Formation ◽  
Numerical Simulations ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Critical Value ◽  
Exact Form ◽  
Analytical Derivation ◽  
Boltzmann Method

AbstractWe show that an enslaved phase-separation front moving with diffusive speeds can leave alternating domains of increasing size in their wake. We find the size and spacing of these domains is identical to Liesegang patterns. For equal composition of the components we are able to predict the exact form of the pattern analytically. To our knowledge this is the first fully analytical derivation of the Liesegang laws. We also show that there is a critical value for C below which only two domains are formed. Our analytical predictions are verified by numerical simulations using a lattice Boltzmann method.

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