THE FORMATION OF SHEAR LAYERS IN A FLUID WITH TEMPERATURE-DEPENDENT VISCOSITY (original) (raw)

Analysis of Shear Layers in a Fluid with Temperature-Dependent Viscosity

Journal of Computational Physics, 2001

The presence of viscosity normally has a stabilizing effect on the flow of a fluid. However, experiments show that the flow of a fluid in which viscosity decreases as temperature increases tends to form shear layers, narrow regions in which the velocity of the fluid changes sharply. In general, adiabatic shear layers are observed not only in fluids but also in thermo-plastic materials subject to shear at a high-strain rate and in combustion and there is widespread interest in modeling their formation. In this paper, we investigate a well-known model representing a basic system of conservation laws for a one-dimensional flow with temperature-dependent viscosity using a combination of analytical and numerical tools. We present results to substantiate the claim that the formation of shear layers can only occur in solutions of the model when the viscosity decreases sufficiently quickly as temperature increases and we further analyze the structure and stability properties of the layers.

The role of second viscosity in the velocity shear-induced heating mechanism

Physica Scripta, 2018

In the present paper we study the influence of second viscosity on non-modally induced heating mechanism. For this purpose we study the set of equations governing the hydrodynamic system. In particular, we consider the Navier Stokes equation, the continuity equation and the equation of state, linearise them and analyse in the context of non-modal instabilities. Unlike previous studies in the Navier Stokes equation we include the contribution of compressibility, thus the second viscosity. By analysing several typical cases we show that under certain conditions the second viscosity might significantly change efficiency of the mechanism of heating.

On the role of viscosity in shear instabilities

Physics of Fluids, 1998

This paper aims at investigating the viscous corrections to mode selection and associated growth rate in the inflectional instability of shear layers. While, in the inviscid limit, the most unstable mode and its growth rate are fully determined by the initial thickness of the layer 2L and the velocity jump 2u it experiences, we show here that these quantities are modified by a factor $11@(a/0.2)/Re# 2 % 21/2 in the small Reynolds number Re5uL/n limit, with a a constant depending on the detailed shape of the initial velocity profile. This result agrees well with early numerical computations of Betchov and Szewczyk @Phys. Fluids 6, 1391~1963!# and its interest is discussed in several different contexts.

Instability of a free-shear layer in the vicinity of a viscosity-stratified layer

Journal of Fluid Mechanics, 2014

The stability of a mixing layer made up of two miscible fluids, with a viscosity-stratified layer between them, is studied. The two fluids are of the same density. It is shown that unlike other viscosity-stratified shear flows, where species diffusivity is a dominant factor determining stability, species diffusivity variations over orders of magnitude do not change the answer to any noticeable degree in this case. Viscosity stratification, however, does matter, and can stabilize or destabilize the flow, depending on whether the layer of varying velocity is located within the less or more viscous fluid. By making an inviscid model flow with a slope change across the ‘viscosity’ interface, we show that viscous and inviscid results are in qualitative agreement. The absolute instability of the flow can also be significantly altered by viscosity stratification.

On the stability of the simple shear flow of a Johnson–Segalman fluid

Journal of Non-Newtonian Fluid Mechanics, 1998

We solve the time-dependent simple shear flow of a Johnson-Segalman fluid with added Newtonian viscosity. We focus on the case where the steady-state shear stress/shear rate curve is not monotonic. We show that, in addition to the standard smooth linear solution for the velocity, there exists, in a certain range of the velocity of the moving plate, an uncountable infinity of steady-state solutions in which the velocity is piecewise linear, the shear stress is constant and the other stress components are characterized by jump discontinuities. The stability of the steady-state solutions is investigated numerically. In agreement with linear stability analysis, it is shown that steady-state solutions are unstable only if the slope of a linear velocity segment is in the negative-slope regime of the shear stress/shear rate curve. The time-dependent solutions are always bounded and converge to a stable steady state. The number of the discontinuity points and the final value of the shear stress depend on the initial perturbation. No regimes of self-sustained oscillations have been found.

Stability of stratified two-phase channel flows of Newtonian/non-Newtonian shear-thinning fluids

International Journal of Multiphase Flow, 2018

Linear stability of horizontal and inclined stratified channel flows of Newtonian/non-Newtonian shearthinning fluids is investigated with respect to all wavelength perturbations. The Carreau model has been chosen for the modeling of the rheology of a shear-thinning fluid, owing to its capability to describe properly the constant viscosity limits (Newtonian behavior) at low and high shear rates. The results are presented in the form of stability boundaries on flow pattern maps (with the phases' superficial velocities as coordinates) for several practically important gas-liquid and liquid-liquid systems. The stability maps are accompanied by spatial profiles of the critical perturbations, along with the distributions of the effective and tangent viscosities in the non-Newtonian layer, to show the influence of the complex rheological behavior of shear-thinning liquids on the mechanisms responsible for triggering instability. Due to the complexity of the considered problem, a working methodology is proposed to alleviate the search for the stability boundary. Implementation of the proposed methodology helps to reveal that in many cases the investigation of the simpler Newtonian problem is sufficient for the prediction of the exact (non-Newtonian) stability boundary of smooth stratified flow (i.e., in case of horizontal gas-liquid flow). Therefore, the knowledge gained from the stability analysis of Newtonian fluids is applicable to those (usually highly viscous) non-Newtonian systems. Since the stability of stratified flow involving highly viscous Newtonian liquids has not been researched in the literature, interesting findings on the viscosity effects are also obtained. The results highlight the limitations of applying the simpler and widely used power-law model for characterizing the shear-thinning behavior of the liquid. That model would predict a rigid layer (infinite viscosity) at the interface, where the shear rates in the viscous liquid are low, and thereby unphysical representation of the interaction between the phases.

Unsteady shear flow of fluids with pressure-dependent viscosity

International Journal of Engineering Science, 2006

We study the unsteady shear flow of fluids with pressure-dependent viscosity, situated between two parallel horizontal plates with the upper plate moving while the flow is subjected to an oscillating pressure gradient. The dimensionless form of the momentum equation is solved numerically using a central difference approximation for the spatial derivative terms and a forward difference approximation for the time derivative term. In addition to providing the velocity profiles at the midsection between the two plates, the values of shear stress at the lower (stationary) plate for various values of the dimensionless numbers are also plotted.

Shear-driven flows of locally heated liquid films

International Journal of Heat and Mass Transfer, 2008

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The flow of a variable viscosity fluid between parallel plates with shear heating

Applied Mathematical Modelling, 2006

A model for the flow of a fluid through a channel with parallel plates is investigated. The channel is narrow, so that the lubrication approximation may be applied. The channel walls are maintained at a constant temperature. Shear heating effects are included and the fluid viscosity decreases exponentially with temperature. When the flow is driven solely by shear stress or imposed velocity at the top, analytical progress is possible. When pressure gradient also drives the flow the problem is solved numerically.