Microscopic theory of the liquid-wall boundary conditions; Thermophoresis

1983 ◽  
Vol 33 (2) ◽  
pp. 287-306 ◽  
Author(s):  
T. Keyes
Keyword(s):  
Boundary Conditions ◽  
Microscopic Theory ◽  
Wall Boundary ◽  
Wall Boundary Conditions ◽  
Liquid Wall

Extension of classical stability theory to viscous planar wall-bounded shear flows

2019 ◽  
Vol 877 ◽  
pp. 1134-1162 ◽  
Author(s):  
Harry Lee ◽  
Shixiao Wang
Keyword(s):  
Boundary Conditions ◽  
Shear Flows ◽  
Early Stage ◽  
Linear Instability ◽  
Slip Condition ◽  
Translation Invariant ◽  
Alternative Derivation ◽  
Wall Boundary ◽  
Wall Boundary Conditions ◽  
Parallel Shear Flows

A viscous extension of Arnold’s inviscid theory for planar parallel non-inflectional shear flows is developed and a viscous Arnold’s identity is obtained. Special forms of the viscous Arnold’s identity have been revealed that are closely related to the perturbation’s enstrophy identity derived by Synge (Proceedings of the Fifth International Congress for Applied Mechanics, 1938, pp. 326–332, John Wiley) (see also Fraternale et al., Phys. Rev. E, vol. 97, 2018, 063102). Firstly, an alternative derivation of the perturbation’s enstrophy identity for strictly parallel shear flows is acquired based on the viscous Arnold’s identity. The alternative derivation induces a weight function. Thereby, a novel weighted perturbation’s enstrophy identity is established, which extends the previously known enstrophy identity to include general streamwise translation-invariant shear flows. Finally, the validity of the enstrophy identity for parallel shear flows is rigorously examined and established under global nonlinear dynamics imposed with two classes of wall boundary conditions. As an application of the enstrophy identity, we quantitatively investigate the mechanism of linear instability/stability within the normal modal framework. The investigation reveals a subtle interaction between a critical layer and its adjacent boundary layer, which determines the stability nature of the disturbance. As an implementation of the relaxed wall boundary conditions imposed for the enstrophy identity, a control scheme is proposed that transitions the wall settings from the no-slip condition to the free-slip condition, through which a flow is stabilized quickly in an early stage of the transition.

Stability of disruption precursors in a tokamak following controlled change of wall boundary conditions

1991 ◽  
Vol 66 (22) ◽  
pp. 2875-2878 ◽  
Author(s):  
D. E. Roberts ◽  
J. D. Fletcher ◽  
G. Nothnagel ◽  
D. Sherwell ◽  
J. A. M. de Villiers ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Wall Boundary ◽  
Wall Boundary Conditions
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