On the Interaction of Insoluble Spherical Particles with a Solidifying Interface in the Presence of Morphological Instabilities

1998 ◽  
Vol 529 ◽  
Author(s):  
L. Hadji ◽  
A.M.J. Davis
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Binary Alloy ◽  
Linear Stability Analysis ◽  
Control Parameter ◽  
Critical Value ◽  
Planar Interface ◽  
Unidirectional Solidification ◽  
Spherical Particles ◽  
Dilute Suspension

AbstractThe interaction of a dilute suspension of spherical particles with a moving solidifying front is investigated analytically. The front emerges during the unidirectional solidification of a dilute binary alloy. A linear stability analysis of the planar interface reveals that the presence of the particles has a destabilizing effect, i.e. the critical value of the control parameter, taken here to be the concentration faraway from the interface, for the onset of the Mullins-Sekerka instability is lowered due to the particles' presence.

scholarly journals Sediment dynamics. Part 2. Dune formation in pipe flow

2009 ◽  
Vol 636 ◽  
pp. 321-336 ◽  
Author(s):  
MALIKA OURIEMI ◽  
PASCALE AUSSILLOUS ◽  
ÉLISABETH GUAZZELLI
Keyword(s):  
Phase Diagram ◽  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Pipe Flow ◽  
Particle Flux ◽  
Sediment Dynamics ◽  
Spherical Particles ◽  
Incipient Motion

We present a phase diagram of the different dune patterns observed when a bed composed of spherical particles is subjected to a pipe flow. While the threshold for incipient motion is determined by the Shields number, that for dune formation seems to be controlled by the Reynolds number. A simple linear stability analysis based on a particle flux derived by Ouriemi, Aussillous & Guazzelli (J. Fluid Mech., 2009) accounts reasonably well for the experimental observations.

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