Faraday instability with a polymer solution

We present an experimental study of the Faraday instability in which we compare the behavior of a Newtonian fluid (water-glycerine mixture) with that of a semi-dilute non-Newtonian solution of high molecular weight polymer. We show that although the dispersion relation of surface waves, derived for a layer of inviscid fluid, remains valid in that particular non-Newtonian case, the behavior of the instability threshold with frequency strongly differs from the Newtonian case. We explain this effect as a result of a frequency-dependent viscosity. The linear stability analysis of the non-Newtonian case shows a perfect agreement with the experimental results both for the dispersion relation and for the reduction of the instability threshold. We discuss the use of the characteristics of the Faraday experiment as a measurement tool to determine frequency dependent properties of non-Newtonian fluids. Received 5 January 1999     

一类非牛顿系统弱解的长时间性态

本文讨论一类非牛顿系统弱解的长时间性态,证明解在L2 范数下的衰减速率为(1 t)-n/4 达到和线性热方程一致.     

Solutions to the Equation of Non－Newtonian Polytropic Filtration Under Optimal Condition On Initial Values

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Hall effect on unsteady MHD Couette flow and heat transfer of a Bingham fluid with suction and injection

The unsteady magnetohydrodynamic flow of an electrically conducting viscous incompressible non-Newtonian Bingham fluid bounded by two parallel non-conducting porous plates is studied with heat transfer considering the Hall effect. An external uniform magnetic field is applied perpendicular to the plates and the fluid motion is subjected to a uniform suction and injection. The lower plate is stationary and the upper plate moves with a constant velocity and the two plates are kept at different but constant temperatures. Numerical solutions are obtained for the governing momentum and energy equations taking the Joule and viscous dissipations into consideration. The effect of the Hall term, the parameter describing the non-Newtonian behavior, and the velocity of suction and injection on both the velocity and temperature distributions are studied.     

A parametric study of droplet deformation through a microfluidic contraction: Shear thinning liquids

Numerical simulations of a droplet passing through an axisymmetric microfluidic contraction are presented, focusing on systems where one of the two liquids present is shear thinning. The simulations are performed using a transient Volume of Fluid (VOF) algorithm. When the droplet is shear thinning and the surrounding phase Newtonian, droplets deform in a similar way to Newtonian droplets that have a viscosity equal to the average viscosity of the shear thinning fluid while it is within the contraction. When the surrounding phase is shear thinning and the droplet Newtonian, droplets deform in a similar way to droplets contained within a Newtonian liquid that has a viscosity that is lower than that of the droplet. In both cases the behaviour of the shear thinning fluid can be broadly described in terms of a ‘characteristic’ Newtonian viscosity: However, determining the exact value of this viscosity without performing a full shear thinning simulation is not possible.     

Application de l'approximation polytropique à la turbulence statistique en moyenne de FavreApplication of the polytropic approximation to turbulence statistics using Favre averaging

The application of the polytropic approximation connecting the quantities of corresponding state, to experimental analysis, is clarified. A method of polytropic determination of the exponent χ (variable but non-fluctuating) in each point of the flow is given. This approximation makes it possible the generation of representative signals of fluctuating quantities, like pressure or density. For heated gases, the problem of measurement of the equations terms written with Favre averaging is thus almost solved. Then, measurement of χ allows the determination by the experiment of crucial terms like turbulent fluxes of mass and momentum, and presso correlation. To cite this article: C. Rey, S. Benjeddou, C. R. Mecanique 332 (2004).     

Mixed convection boundary layer flow of non-Newtonian fluids along vertical wavy plates

Mixed convection boundary layer flows of non-Newtonian fluids over the wavy surfaces are studied by the coordinate transformation and the cubic spline collocation numerical method. The effects of the wavy geometry, the buoyancy parameter and the generalized Prandtl number for pseudoplastic fluids, Newtonian fluids and dilatant fluids on the skin-friction coefficient, local and mean Nusselt numbers have been graphically studied. Results show that both higher generalized Prandtl numbers and buoyancy parameters are seen to enhance the influence of wavy surfaces on the local Nusselt number, irrespective of whether the fluids are Newtonian fluids or non-Newtonian fluids. Moreover, the irregular surfaces have higher total heat flux than that of corresponding flats plate for any fluid.     

Permanent Waves in Slow Free-Surface Flow of a Herschel–Bulkley fluid

Unsteady flow of a viscoplastic fluid on an inclined plane is examined. The fluid is described by the three-parameter Herschel–Bulkley constitutive equation. The set of equations governing the flow is presented, recovering earlier results for a Bingham fluid and steady uniform motion. A permanent wave solution is then derived, and the relation between wave speed and flow depth is discussed. It is shown that more types of gravity currents are possible than in a Newtonian fluid; these include some cases of flows propagating up a slope. The speed of permanent waves is derived and the possible surface profiles are illustrated as functions of the flow behavior index.