Stability Analysis of a Plane Poiseuille Flow of Multilayered Viscoelastic Fluids: An Energetic Approach

Author(s):  
Franc¸ois Rousset ◽  
Patrick Bourgin ◽  
Liviu-Iulian Palade

Coextrusion flows of compatible polymers are known to be generally more stable than the same flows of incompatible systems. It is shown in this paper that the weak response to disturbance of such flows can be predicted by formulating an energetic approach of the problem. The energy dissipated by the interdiffusion process is evaluated which allows stability maps to be obtained for Newtonian and Oldroyd-B fluids. These maps show the increase of the stable domain in the case of compatible polymeric systems for both Newtonian and viscoelastic fluids.

2004 ◽  
Author(s):  
Franc¸ois Rousset ◽  
Patrick Bourgin ◽  
Liviu-Iulian Palade

This paper deals with coextrusion flows of two compatible polymers which are known to be generally more stable than the same flows of incompatible systems. We show that the weak response to disturbance of such flows can be predicted by considering an interphase of non-zero thickness (corresponding to an interdiffusion zone) instead of a purely geometrical interface between the two layers. As a first step we try to explain the weak sensibility to disturbance of compatible systems by the sole presence of this intermediate layer. For that purpose we study the linear stability response to very long waves of a three-layer plane Poiseuille flow with an inner thin layer which represents the interphase. This first approach (corresponding to a reduction in the effective viscosity ratio) is shown to explain the diminished growth rates but not the reduction in the size of the unstable region. As a second step, we formulate an energetic approach of the problem. We evaluate the energy dissipated during the interdiffusion process and the variation of kinetic energy of the global system. A modified growth rate is then determined by taking into account the energy dissipated by the interdiffusion process. This lower growth rate enables us to explain the increase of the stable domain in the case of compatible polymeric systems.


2005 ◽  
Vol 128 (1) ◽  
pp. 27-33 ◽  
Author(s):  
François Rousset ◽  
Patrick Bourgin ◽  
Liviu-Iulian Palade

This paper deals with coextrusion flows of two compatible polymers which are known to be generally more stable than the same flows of incompatible systems. We show that the weak response to disturbance of such flows can be predicted by considering an interphase of nonzero thickness (corresponding to an interdiffusion zone) instead of a purely geometrical interface between the two layers. As a first step we try to explain the weak sensibility to disturbance of compatible systems by the sole presence of this intermediate layer. For that purpose we study the linear stability response to very long waves of a three-layer phase Poiseuille flow with an inner thin layer which represents the interphase. Although this fact is an approximation, it nevertheless takes into account the diffusion phenomena which are generated in the interphase. This first approach (corresponding to a reduction in the effective viscosity ratio) is shown to explain the diminished growth rates but not the reduction in the size of the unstable region. As a second step, we formulate an energetic approach of the problem. We evaluate the energy dissipated during the interdiffusion process and the variation of kinetic energy of the global system. A modified growth rate is then determined by taking into account the energy dissipated by the interdiffusion process. This lower growth rate enables us to explain the increase of the stable domain in the case of compatible polymeric systems.


1995 ◽  
Vol 299 ◽  
pp. 241-265 ◽  
Author(s):  
Sang W. Joo

An evolution equation is derived that describes the nonlinear development of the interface between two viscoelastic fluids flowing, under the action of imposed pressure gradient and gravity, in a vertical channel. The channel walls are kept at different temperatures, resulting in heat transfer across the layers. The equation, based on the lubrication approximation, models the effects of stratifications in density, viscosity, elasticity, shear thinning, and thermal conductivity. It also describes the capillary and thermocapillary effects, as well as the sensitivity of viscosities to temperature. Linear-stability analysis is performed based on the evolution equation to understand the competing effects of viscous, elastic, and Marangoni instabilities. Particular attention is paid to the active control of the interfacial instabilities through the thermocapillarity.


Author(s):  
Masahiro Watanabe ◽  
Eiji Tachibana ◽  
Nobuyuki Kobayashi

This paper deals with the theoretical stability analysis of in-plane parametric vibrations of a curved bellows subjected to periodic internal fluid pressure excitation. The curved bellows studied in this paper are fixed at both ends rigidly, and are excited by the periodic internal fluid pressure. In the theoretical stability analysis, the governing equation of the curved bellows subjected to periodic internal fluid pressure excitation is derived as a Mathieu’s equation by using finite element method (FEM). Natural frequencies of the curved bellows are examined and stability maps are presented for in-plane parametric instability. It is found that the natural frequencies of the curved bellows decrease with increasing the static internal fluid pressure and buckling occurs due to high internal fluid pressure. It is also found that two types of parametric vibrations, longitudinal and transverse vibrations, occur to the curved bellows in-plane direction due to the periodic internal fluid pressure excitation. Moreover, effects of axis curvature on the parametric instability regions are examined theoretically.


2005 ◽  
Vol 293-294 ◽  
pp. 409-416 ◽  
Author(s):  
N. Lesaffre ◽  
Jean Jacques Sinou ◽  
F. Thouverez

In any high-performance turbo-machinery, instability and damage are commonly occurring problems. The aim of this paper is to present a stability analysis of a fully-bladed flexible rotor. The flexural vibrations of the blades as well as those of the shaft are considered; the energetic approach used includes the effect of the rotational inertia. A stability detection method, bringing loci separation phenomena and coalescence, in case of an asymmetric rotor, to the fore, is made in order to determine a parametric domain where turbomachinery cannot encounter damage. Moreover, extensive parametric studies including for instance the length and the stagger angle of the blades are presented in order to obtain robust criteria for stable and unstable areas prediction. Finally, rotor/stator contact is introduced and the effect of the radial load acting on the blades when rubbing against a casing is considered.


2017 ◽  
Vol 26 (01) ◽  
pp. 1750001 ◽  
Author(s):  
Xin Li ◽  
Rangang Yu ◽  
Neng Zhang

We report on the formation and stability of induced surface solitons in parity–time ([Formula: see text]) symmetric periodic systems with spatially modulated nonlinearity. We discover that the spatially modulation of the nonlinearity can affect the existence and stability of surface solitons. These surface solitons can be formed in the semi-infinite and first bandgap. Stability analysis shows that odd surface solitons belonging to semi-infinite bandgap are linearly stably in low power domain, and the stable domain becomes narrow with increasing the strength of spatially modulated nonlinearity, both even surface solitons in semi-infinite bandgap and surface solitons in first bandgap are unstable in their existence domain.


1976 ◽  
Vol 24 (1-2) ◽  
pp. 1-12
Author(s):  
M. J. Crochet ◽  
G. Tackels

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