Journal ArticleDOI
The mechanism of long-wave instability in a shear-thinning film flow on a porous substrate
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In this article, a linear stability analysis of a thin shear-thinning film with a deformable top surface flowing down an inclined porous substrate modelled as a smooth substrate with velocity slip at the wall is examined, and the physical mechanism for the long-wave instability is analyzed.Abstract:
A linear stability analysis of a thin shear-thinning film with a deformable top surface flowing down an inclined porous substrate modelled as a smooth substrate with velocity slip at the wall is examined, and the physical mechanism for the long-wave instability is analysed. Through a phenomenological model, the influence of slip velocity and the shear-thinning rheology on the wave speed of long surface waves on a non-Newtonian shear-thinning film down a substrate with velocity slip is predicted. The viscosity disturbance plays a significant role in the destabilization of the flow system. Indeed, slip at the bottom that accounts for the characteristics of the porous/rough substrate does not affect the physical mechanism of the instability. However, it is shown that slip at the bottom enhances the inertia effects which in turn destabilizes the flow system at smaller Reynolds numbers.read more
Citations
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Journal ArticleDOI
Stability of viscosity stratified flows down an incline: Role of miscibility and wall slip
Sukhendu Ghosh,R. Usha +1 more
TL;DR: In this article, the effects of wall velocity slip on the linear stability of a gravity-driven two-fluid flow down an incline are examined, and the results show that the presence of slip exhibits a promise for stabilizing the miscible flow system by raising the critical Reynolds number at the onset and decreasing the bandwidth of unstable wave numbers beyond the threshold of the dominant instability.
Journal ArticleDOI
Stability of a non-Newtonian falling film due to three-dimensional disturbances
TL;DR: In this paper, the authors apply the normal modes method to study the linear stability of a liquid film flowing down an inclined plane, taking into account the complex rheology of the media.
Journal ArticleDOI
Long-Wave Instability of a Regularized Bingham Flow Down an Incline
TL;DR: In this paper , the linear stability of a flow down an incline when the fluid is modelled as a "mollified" Bingham material was investigated by using the long-wave approximation method.
Journal ArticleDOI
Effect of anisotropy and inhomogeneity on the stability of liquid film flowing down a porous inclined plane
TL;DR: In this article , the authors examined the linear stability of a Newtonian liquid film flow past a porous inclined plane and examined the effect of the anisotropic and inhomogeneous variations in the permeability of the porous medium on all three instability modes: surface, shear and porous mode.
References
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Book
Convection in Porous Media
Donald A. Nield,Adrian Bejan +1 more
TL;DR: In this paper, an introduction to convection in porous media assumes the reader is familiar with basic fluid mechanics and heat transfer, going on to cover insulation of buildings, energy storage and recovery, geothermal reservoirs, nuclear waste disposal, chemical reactor engineering and the storage of heat-generating materials like grain and coal.
Journal ArticleDOI
Boundary conditions at a naturally permeable wall
TL;DR: In this article, a simple theory based on replacing the effect of the boundary layer with a slip velocity proportional to the exterior velocity gradient is proposed and shown to be in reasonable agreement with experimental results.
Journal ArticleDOI
Long-scale evolution of thin liquid films
TL;DR: In this article, a unified mathematical theory is presented that takes advantage of the disparity of the length scales and is based on the asymptotic procedure of reduction of the full set of governing equations and boundary conditions to a simplified, highly nonlinear, evolution equation or to a set of equations.
Book
Stability and Transition in Shear Flows
TL;DR: In this article, the authors present an approach to the Viscous Initial Value Problem with the objective of finding the optimal growth rate and the optimal response to the initial value problem.
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