Long wave instability on the parallel shear flows in the presence of insoluble surfactant

2020 ◽  
Vol 33 (02) ◽  
Author(s):  
Muhammad Sani ◽  
Keyword(s):  
Shear Flows ◽  
Wave Instability ◽  
Long Wave ◽  
Insoluble Surfactant ◽  
Parallel Shear Flows

scholarly journals The role of surfactants on the mechanism of the long-wave instability in liquid film flows

2014 ◽  
Vol 741 ◽  
pp. 139-155 ◽  
Author(s):  
George Karapetsas ◽  
Vasilis Bontozoglou
Keyword(s):  
Liquid Film ◽  
Concentration Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Wave Instability ◽  
Navier Stokes Equations ◽  
Flow Perturbation ◽  
Long Wave ◽  
Insoluble Surfactant ◽  
Interfacial Concentration

AbstractThe analysis for the physical mechanism of the long-wave instability in liquid film flow is extended to take into account the presence of a surfactant of arbitrary solubility. The Navier–Stokes equations are supplemented by mass balances for the concentrations at the interface and in the bulk, by a Langmuir model for adsorption kinetics at the interface, and are expanded in the limit of long-wave disturbances. The longitudinal flow perturbation, known to result from the perturbation shear stress which develops along the deformed interface, is shown to contribute a convective flux that triggers an interfacial concentration gradient. This gradient is, at leading order, in phase with the interfacial deformation, and as a result produces Marangoni stresses that stabilize the flow. The strength of the interfacial concentration gradient is shown to be maximum for an insoluble surfactant and to decrease with increasing surfactant solubility. The decrease is explained in terms of the spatial phase of mass transfer between interface and bulk, which mitigates the interfacial flux by the flow perturbation and leads to the attenuation of Marangoni stresses. Higher-order terms are derived, which provide corrections for disturbances of finite wavelength.

Long-Wave Instability in Marginally Stable Shear Flows

1997 ◽  
Vol 79 (21) ◽  
pp. 4155-4158
Author(s):  
N. J. Balmforth ◽  
W. R. Young
Keyword(s):  
Shear Flows ◽  
Wave Instability ◽  
Long Wave

Side-Wall Effect on the Long-Wave Instability in Kolmogorov Flow

1998 ◽  
Vol 67 (5) ◽  
pp. 1597-1602 ◽  
Author(s):  
Hiroaki Fukuta ◽  
Youichi Murakami
Keyword(s):  
Side Wall ◽  
Wall Effect ◽  
Wave Instability ◽  
Kolmogorov Flow ◽  
Long Wave

scholarly journals Exact coherent structures in an asymptotically reduced description of parallel shear flows

2014 ◽  
Vol 47 (1) ◽  
pp. 015504 ◽  
Author(s):  
Cédric Beaume ◽  
Edgar Knobloch ◽  
Gregory P Chini ◽  
Keith Julien
Keyword(s):  
Coherent Structures ◽  
Shear Flows ◽  
Parallel Shear Flows

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.

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