Stability of two-layer poiseuille flow of Carreau-Yasuda and Bingham-like fluids

In this paper we present the linear stability analysis of the interface between two non-Newtonian inelastic fluids in a straight channel driven by a pressure gradient. Two rheological models of non-Newtonian behavior are studied: (a) Bingham-like fluids and (b) Carreau-Yasuda fluids. For each rheolo...

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Vydáno v:Journal of non-Newtonian fluid mechanics Ročník 57; číslo 2; s. 227 - 241
Hlavní autoři: Pinarbasi, A, Liakopoulos, A
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 1995
Elsevier
Témata:
Bingham-like fluids
Carreau-Yasuda fluids
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Hydrodynamic stability
Inelastic fluids
Interfacial instability
Non-newtonian fluid flows
Physics
Poiseuille flow
Bingham-like fluids
Carreau-Yasuda fluids
Poiseuille flow
Inelastic fluids
Constitutive equation
Interfaces
Bingham plastic
Numerical simulation
Linear stability
Two layer medium
Viscoplastic fluid
ISSN:0377-0257, 1873-2631
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Popis
Shrnutí:In this paper we present the linear stability analysis of the interface between two non-Newtonian inelastic fluids in a straight channel driven by a pressure gradient. Two rheological models of non-Newtonian behavior are studied: (a) Bingham-like fluids and (b) Carreau-Yasuda fluids. For each rheological model, the linearized equations describing the evolution of small two-dimensional disturbances are derived and the stability problem is formulated as an eigenvalue problem for a set of ordinary differential equations of the Orr-Sommerfeld type. Discretization is performed using a pseudospectral technique based on Chebyshev polynomial expansions. The resulting generalized matrix eigenvalue problem is solved using the QZ algorithm. The results on the onset of instability are presented in the form of stability maps for a range of zero-shear-rate viscosity ratios, thickness ratios, power-law constants, material time constants, Yasuda constants, apparent yield stresses and stress growth exponents. Increasing the stress growth exponents or apparent yield stresses of the viscoplastic fluids has a stabilizing effect on the interface. For shear thinning fluids, increasing the zero-shear-rate viscosity ratio or shear thinning of the fluids destabilizes the interface. The effect of other parameters can be stabilizing or destabilizing depending on the flow configuration and wavelength.
ISSN:0377-0257
1873-2631
DOI:10.1016/0377-0257(94)01330-K