Thin film flow down a porous substrate in the presence of an insoluble surfactant: Stability analysis
TLDR
In this paper, the stability of a gravity-driven film flow on a porous inclined substrate is considered, when the film is contaminated by an insoluble surfactant, in the frame work of Orr-Sommerfeld analysis.Abstract:
The stability of a gravity-driven film flow on a porous inclined substrate is considered, when the film is contaminated by an insoluble surfactant, in the frame work of Orr-Sommerfeld analysis. The classical long-wave asymptotic expansion for small wave numbers reveals the occurrence of two modes, the Yih mode and the Marangoni mode for a clean/a contaminated film over a porous substrate and this is confirmed by the numerical solution of the Orr-Sommerfeld system using the spectral-Tau collocation method. The results show that the Marangoni mode is always stable and dominates the Yih mode for small Reynolds numbers; as the Reynolds number increases, the growth rate of the Yih mode increases, until, an exchange of stability occurs, and after that the Yih mode dominates. The role of the surfactant is to increase the critical Reynolds number, indicating its stabilizing effect. The growth rate increases with an increase in permeability, in the region where the Yih mode dominates the Marangoni mode. Also, the growth rate is more for a film (both clean and contaminated) over a thicker porous layer than over a thinner one. From the neutral stability maps, it is observed that the critical Reynolds number decreases with an increase in permeability in the case of a thicker porous layer, both for a clean and a contaminated film over it. Further, the range of unstable wave number increases with an increase in the thickness of the porous layer. The film flow system is more unstable for a film over a thicker porous layer than over a thinner one. However, for small wave numbers, it is possible to find the range of values of the parameters characterizing the porous medium for which the film flow can be stabilized for both a clean film/a contaminated film as compared to such a film over an impermeable substrate; further, it is possible to enhance the instability of such a film flow system outside of this stability window, for appropriate choices of the porous substrate characteristics.read more
Citations
More filters
Journal ArticleDOI
Role of slip on the linear stability of a liquid flow through a porous channel
TL;DR: In this article, the linear stability of a liquid flow bounded by slippery and porous walls is studied for infinitesimal disturbances of arbitrary wavenumbers, and the Orr-Sommerfeld type eigenvalue problem is formulated by using the normal mode decomposition and resolved based on the Chebyshev spectral collocation method along with the QZ algorithm.
Journal ArticleDOI
Linear stability analysis of a surfactant-laden shear-imposed falling film
Farooq Ahmad Bhat,Arghya Samanta +1 more
TL;DR: Wei et al. as discussed by the authors studied the long-wave instability of a shear-imposed liquid flow down an inclined plane, where the free surface of the fluid is covered by an insoluble surfactant.
Journal ArticleDOI
Linear stability of a contaminated fluid flow down a slippery inclined plane
Farooq Ahmad Bhat,Arghya Samanta +1 more
TL;DR: In this paper, the linear stability analysis of a fluid flow down a slippery inclined plane is carried out when the free surface of the fluid is contaminated by a monolayer of insoluble surfactant.
Journal ArticleDOI
Instabilities in viscosity-stratified two-fluid channel flow over an anisotropic-inhomogeneous porous bottom
TL;DR: In this paper, a linear stability analysis of a pressure driven, incompressible, fully developed laminar Poiseuille flow of immiscible two-fluids of stratified viscosity and density in a horizontal channel bounded by a porous bottom supported by a rigid wall, with anisotropic and inhomogeneous permeability, and a rigid top is examined.
Journal ArticleDOI
Instabilities of a confined two-layer flow on a porous medium: An Orr–Sommerfeld analysis
TL;DR: In this paper, an analysis of a pressure driven two-layer Poiseuille flow confined between a rigid wall and a Darcy-Brinkman porous layer is explored, and a linear stability analysis of the conservation laws leads to an Orr-Sommerfeld system to identify the time and length scales of the instabilities.
References
More filters
Journal ArticleDOI
A falling film down a slippery inclined plane
TL;DR: In this paper, a gravity-driven film flow on a slippery inclined plane is considered within the framework of long wave and boundary layer approximations, and two coupled depth-averaged equations are derived in terms of the local flow rate and the film thickness H (x,t).
Journal ArticleDOI
Jump momentum boundary condition at a fluid-porous dividing surface: Derivation of the closure problem
TL;DR: In this article, a volume averaging method is used to derive a stress jump boundary condition that takes the form of a mixed stress tensor, which combines the global and Brinkman stresses at the dividing surface.
Journal ArticleDOI
Stability analysis of thin film flow along a heated porous wall
TL;DR: In this article, the authors investigated the time evolution of a thin liquid film flowing down a heated solid porous substrate using the Navier-Stokes and Darcy-Brinkman equations in the film and the porous layer.
Journal ArticleDOI
Instability of power-law fluid flow down a porous incline
TL;DR: In this paper, the authors investigated the generation and structure of roll waves developing on the surface of a power-law fluid layer flowing down a porous incline, where the unsteady equations of motion were integrated according to the von Karman momentum integral method accounting for the variation of the velocity distribution with depth.
Journal ArticleDOI
Effect of surfactants on the stability of two-layer channel flow
Mark Blyth,C. Pozrikidis +1 more
TL;DR: In this article, the effect of insoluble surfactant on the stability of two-layer viscous flow in an inclined channel confined by two parallel walls is considered, and a lubrication-flow model applicable to long waves and low Reynolds-number flow is developed, and pertinent nonlinear evolution equations for the interface position and surface concentration are derived.
Related Papers (5)
Thin Newtonian film flow down a porous inclined plane: Stability analysis
I. Mohammed Rizwan Sadiq,R. Usha +1 more
Effect of surfactant on the stability of film flow down an inclined plane
Mark Blyth,C. Pozrikidis +1 more