Experimental studies of interfacial instabilities in multilayer pressure-driven flow of polymeric melts

The interfacial deformation and stability of two-(A-B) as well as three-layer symmetric (A-B-A) and asymmetric (A-B-C) pressure-driven flow of viscoelastic fluids has been investigated. Flow visualization in conjunction with digital image processing has been used to observe and measure the rate of encapsulation and interfacial stability/instability of the flow. Specifically, the encapsulation behavior as well as stability/instability of the interface and the corresponding growth or decay rate of disturbances as a function of various important parameters, namely, number of layers and their arrangement, layer depth ratio, viscosity and elasticity ratio as well as disturbance frequency, have been investigated. Based on these experiments, we have shown that the encapsulation phenomena occurs irrespective of the stability/instability of the interface and in cases when both encapsulation and instability occur simultaneously their coupling leads to highly complex and three-dimensional interfacial wave patterns. Moreover, it has been shown that the simple notion that less viscous fluids encapsulate more viscous fluids is incorrect and depending on the wetting properties of the fluid as well as their first and second normal stresses the reverse could occur. Additionally, in two- and three-layer flows it has been shown that by placing a thin, less viscous layer adjacent to the wall longwave disturbances can be stabilized while short and intermediate wavelength disturbances are stabilized when the more elastic fluid is the majority component. Furthermore, in three-layer flows it has been demonstrated that in the linear instability regime no dynamic interaction between the two interfaces is possible for short and intermediate wavenumber disturbances. However, in the nonlinear stability regime dynamic interactions between interfaces have been observed in this range of disturbance wavenumbers leading to highly chaotic flows. Finally, in the parameter space of this study no subcritical bifurcations were observed while supercritical bifurcations resulting in waves with a pointed front and a gradual tail were observed.     

Interpretation of fringes in stress-holo-interferometry

Previous studies had concluded that stressholo-interferometry patterns consist of the independent superposition of the isopachic family (with half-order fringe shifts) and the isochromatic family. It is shown here that this interpretation is not always valid and can result in serious errors in some cases. In particular, it is demonstrated that the position, and even the existence of the fringes, are affected by the interaction of the isopachics and isochromatics. This effect is most pronounced when the two families of fringes are nearly parallel and of approximately the same spatial frequency. The independent superposition interpretation is most accurate when the two families of fringes are orthogonal, whatever the ratio of spatial frequencies might be. These properties are illustrated using computer-generated holographic interference patterns.     

Effect of variable slip boundary conditions on flows of pressure driven non-Newtonian fluids

In microfluidic devices it has been suggested a scheme for enhancing the mixing of two fluids is to use patterned, slip boundary conditions. This has been shown to induce significant transverse flow for Newtonian fluids [S.C. Hendy, M. Jasperse, J. Burnell, Effect of patterned slip on micro- and nanofluidic flows, Phys. Rev. E 72 (2005) 016303]. Here we study the effect of patterned slip on non-Newtonian fluids. Using a power-law model it is shown for shear-thickening fluids patterned slip can induce significant transverse flows comparable in size to those produced for Newtonian fluids. However, for shear-thinning fluids this transverse flow is suppressed. We predict a convenient way to increase the transverse flow for shear-thinning fluids is to use a patterned slip boundary condition coupled to a sinusoidally time-varying pressure gradient. This system is studied using a simple linearized White–Metzner model which has a power-law viscosity function [R.B. Bird, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Liquids, Volume 1: Fluid Mechanics, John Wiley & Sons, New York, 1987]. In this case it is shown the two variations combine to produce transverse flow, which can be increased by increasing the frequency of the sinusoidal time-dependent fluctuation.     

Propagation of long waves of finite amplitude at the interface of two viscous fluids

The propagation of long waves of finite amplitude at the interface of two viscous fluids has been studied theoretically. For plane Couette-Poiseuille flow of two superposed layers of fluids of different viscosity, an equation is derived to determine the development in time of the shape of these finite amplitude waves. The influence of the viscosity ratio, the density difference of the fluids and an imposed pressure gradient have been investigated.     

Effects of curvilinear anisotropy on radially symmetric stresses in anisotropic linearly elastic solids

It has been known for some time that certain radial anisotropies in some linear elasticity problems can give rise to stress singularities which are absent in the corresponding isotropic problems. Recently related issues were examined by other authors in the context of plane strain axisymmetric deformations of a hollow circular cylindrically anisotropic linearly elastic cylinder under uniform external pressure, an anisotropic analog of the classic isotropic Lamé problem. In the isotropic case, as the external radius increases, the stresses rapidly approach those for a traction-free cavity in an infinite medium under remotely applied uniform compression. However, it has been shown that this does not occur when the cylinder is even slightly anisotropic. In this paper, we provide further elaboration on these issues. For the externally pressurized hollow cylinder (or disk), it is shown that for radially orthotropic materials, the maximum hoop stress occurs always on the inner boundary (as in the isotropic case) but that the stress concentration factor is infinite. For circumferentially orthotropic materials, if the tube is sufficiently thin, the maximum hoop stress always occurs on the inner boundary whereas for sufficiently thick tubes, the maximum hoop stress occurs at the outer boundary. For the case of an internally pressurized tube, the anisotropic problem does not give rise to such radical differences in stress behavior from the isotropic problem. Such differences do, however, arise in the problem of an anisotropic disk, in plane stress, rotating at a constant angular velocity about its center, as well as in the three-dimensional problem governing radially symmetric deformations of anisotropic externally pressurized hollow spheres. The anisotropies of concern here do arise in technological applications such as the processing of fiber composites as well as the casting of metals.     

The electrohydrodynamics of superimposed fluids subjected to a nonuniform transverse electric field

This study aims to investigate electrohydrodynamics of two superimposed fluids that are confined between a pair of two-dimensional flat plates and are exposed to a sinusoidal electric field in zero gravity. The goal is to identify the parameters that affect the flow structure and interface deformation using a simple closed form solution. The governing electrohydrodynamic equations are solved analytically for Newtonian and immiscible fluids in the framework of leaky-dielectric theory and in the limit of small electric field and fluid inertia. A detailed analysis of the electric and flow fields is presented and it is shown that the electric field induces sinusoidal electrical stresses at the interface, which lead to periodic convection cells. The parameters affecting the sense of flow circulation and strength are investigated and it is shown that the former depends on the relative magnitude of the electric permittivity and conductivity ratios while the latter is controlled by the relative thicknesses of the fluid layers and the ratio of the electric conductivities and viscosities of the fluids. The maximum flow strength is achieved at a relative thickness that is set by the competition between the electric and hydrodynamic effects. For small deformation, the distortion of the interface is examined using a normal stress balance at the interface, and it is shown that the degree of interface deformation scales with the square of the amplitude of the electric potential nonuniformity, while its wavenumber is twice that of the imposed potential nonuniformity. Furthermore, a zero-deformation curve is found, which delineates the region in the permittivity-conductivity space according to the sense of interface deformation. The results show that for certain ranges of fluid layer thicknesses and permittivity ratios, the interface will remain flat, despite the action of the nonuiform field.     

Superposability in magnetohydrodynamics

Summary In the present paper, to study the non-linear terms in hydromagnetics, the concept of superposability or additivity of two hydromagnetic flows has been defined, and it has been shown that force-free fields (Chandrasekhar) and self-superposable fluid flows (Strang) are particular cases of this concept. Chandrasekhar's equations for axially symmetric hydromagnetic flows have been extended to viscous fluids, and it has been shown that some important results for non-viscous flows need not hold for viscous fluids.     

Three-dimensional solution for a hybrid cylindrical shell under axisymmetric thermoelectric load

Summary An exact axisymmetric piezothermoelastic solution is presented for a simply-supported hybrid cylindrical shell made of cross-ply composite laminate and piezoelectric layers. Numerical results for hybrid shells are presented for sinusoidal and central band thermal and electrical loads. The effect of the loading, the radius-to-thickness ratio, the span-to-radius ratio and the number of layers of the substrate on the response is investigated. The interface between the substrate and the actuated piezoelectric layer has been found to be subjected to high shear stress. It has been shown that the maximum values of the deflection and the stresses, due to thermal load, can be appreciably reduced by appropriate application of actuation potential. Accepted for publication 13 October 1996     

Conjugate natural convection heat transfer between two fluids separated by a horizontal wall: steady-state analysis

The conjugate heat transfer across a thin horizontal wall separating two fluids at different temperatures is investigated both numerically and asymptotically. The solution for large Rayleigh numbers is shown to depend on two nondimensional parameters;α/ε ², withα being the ratio of the thermal resistance of the boundary layer in the hot medium to the thermal resistance of the wall andε the aspect ratio of the plate, andβ, the ratio of the thermal resistances of the boundary layers in the two media. The overall Nusselt number is an increasing function ofα/ε ² taking a finite maximum value forα/ε ² → ∞ and tending to zero forα/ε ² → 0.     

Numerical simulations of negatively buoyant jets in an immiscible fluid using the Particle Finite Element Method

Negatively buoyant jets consist in a dense fluid injected vertically upward into a lighter ambient fluid. The numerical simulation of this kind of buoyancy‐driven flows is challenging as it involves multiple fluids with different physical properties. In the case of immiscible fluids, it requires, in addition, to track the motion of the interface between fluids and accurately represent the discontinuities of the flow variables. In this paper, we investigate numerically the injection of a negatively buoyant jet into a homogenous immiscible ambient fluid using the Particle Finite Element Method and compare the two‐dimensional numerical results with experiments on the injection of a jet of dyed water through a nozzle in the base of a cylindrical tank containing rapeseed oil. In both simulations and experiments, the fountain inlet flow velocity and nozzle diameter have been varied to cover a wide range of Froude Fr and Reynolds Re numbers ( 0.1 < Fr < 30, 8 < Re < 1350), reproducing both weak and strong laminar fountains. The flow behaviors observed for the different numerical simulations fit in the regime map based on the Re and Fr values of the experiments, and the maximum fountain height is in good agreement with the experimental observations, suggesting that particle finite element method is a useful tool for the study of immiscible two‐fluid systems. Copyright © 2011 John Wiley & Sons, Ltd.     

Flooded countercurrent two-phase flow in horizontal tubes and channels

A criterion for flooding in the countercurrent flow of two fluids in horizontal tubes and channels is developed. It exhibits a dependence upon the density ratio of the fluids beyond that present in the criterion of Wallis (1969). Experiments were carried out with air and water in a horizontal tube at atmospheric pressure and these, together with others reported in the literature, are shown to be in fair agreement with the prediction of the criterion, though it is emphasised that more experimental work is desirable.Work reported in the literature with miscible fluids with a density ratio close to unity confirms the extra dependence upon the density ratio.     

Thermal performance of an open loop closed end pulsating heat pipe

This paper presents an experimental study of an open loop pulsating heat pipe (OLPHP) of 0.9 mm inner diameter. The performance characterization has been done using four working fluids at vertical and horizontal orientations. Water, Methanol, 2-Propanol and Acetone has been employed as the working fluid with 50% fill ratio. The experimental results indicate a strong influence of gravity and thermo physical properties of the working fluids on the performance of OLPHP. Considering all the working fluids used, Water has shown better thermal performance in vertical orientation while Methanol has shown better performance in horizontal orientation. All the working fluids perform better at horizontal orientation.     

Convective magnetohydrodynamic two fluid flow and heat transfer in an inclined channel

 The problem of fully developed free convection two fluid magnetohydrodynamic flow in an inclined channel is investigated. The governing momentum and energy equations are coupled and highly nonlinear due to dissipation terms, solutions are found employing perturbation technique for small values of Pr · Ec (=ɛ) the product of Prandtl number and Eckert number. Effects of Grashof number, Hartmann number, inclination angle, the ratios of electrical conductivities, viscosities and heights of two fluids on the flow are explored. It is observed that the flow can be controlled effectively by suitable adjustment of the values for the ratios of heights, electrical conductivities and viscosities of the two fluids. Received on 10 December 1999     

Drag of a sphere in dilute polymer solutions in high Reynolds number range

We have measured by means of four ultrasonic transducers the fall velocity of a sphere at high Reynolds number range in dilute polyacrylamide solutions which have viscoelastic effects. The polymer solutions were 5, 20 and 50ppm in the concentration. Basset-Bousinessq-Oseen equation for the falling sphere was analyzed numerically on Newtonian fluids in order to compare with the fall velocity of a sphere in the polymer solutions, and the experimental data of the fall velocity in tap water is in agreement with the range of no effect of the test tank wall. In polymer solutions, it was shown that the fall velocity is larger than that in Newtonian fluids within the critical Reynolds number range such that the drag reduction occurs and is smaller than that of Newtonian fluids over the range. The experimental data for the drag reduction ratio of polymer solutions is arranged by Weissenberg number calculating the experimental data of the first normal stress differences. It was shown that the maximum drag reduction ratio in the polymer solutions lies in the range of We=3∼10. Received: 15 October 1997 Accepted: 12 May 1998     

Convective instability in a two-layer system of reacting fluids with concentration-dependent diffusion

The development of convective instability in a two-layer system of miscible fluids placed in a narrow vertical gap has been studied theoretically and experimentally. The upper and lower layers are formed with aqueous solutions of acid and base, respectively. When the layers are brought into contact, the frontal neutralization reaction begins. We have found experimentally a new type of convective instability, which is characterized by the spatial localization and the periodicity of the structure observed for the first time in the miscible systems. We have tested a number of different acid–base systems and have found a similar patterning there. In our opinion, it may indicate that the discovered effect is of a general nature and should be taken into account in reaction–diffusion–convection problems as another tool with which the reaction can govern the movement of the reacting fluids. We have shown that, at least in one case (aqueous solutions of nitric acid and sodium hydroxide), a new type of instability called as the concentration-dependent diffusion convection is responsible for the onset of the fluid flow. It arises when the diffusion coefficients of species are different and depend on their concentrations. This type of instability can be attributed to a variety of double-diffusion convection. A mathematical model of the new phenomenon has been developed using the system of reaction–diffusion–convection equations written in the Hele–Shaw approximation. It is shown that the instability can be reproduced in the numerical experiment if only one takes into account the concentration dependence of the diffusion coefficients of the reagents. The dynamics of the base state, its linear stability and nonlinear development of the instability are presented. It is also shown that by varying the concentration of acid in the upper layer one can achieve the occurrence of chemo-convective solitary cell in the bulk of an almost immobile fluid. Good agreement between the experimental data and the results of numerical simulations is observed.     

Multilayer film casting of modified Giesekus fluids Part 2. Linear stability analysis

A linear stability analysis of the multilayer film casting of polymeric fluids has been conducted. A modified Giesekus model was used to characterize the rheological behaviors of the fluids. The critical draw ratio at the onset of draw resonance was found to depend on the elongational and shear viscosities of the fluids. Extensional-thickening has a stabilizing effect, whereas shear-thinning and extensional-thinning have destabilizing effects. The critical draw ratios for bilayer films of various thickness fractions are bounded by those for single layer films of the two fluids. When the two fluids have a comparable elongational viscosity, the critical draw ratio at a given Deborah number varies linearly with thickness fraction. When one fluid has a much larger elongational viscosity, it dominates the flow and the critical draw ratios at most thickness fractions remain close to its critical draw ratio as a single layer film. When the dominating fluid exhibits extensional-thickening, a film with a certain thickness fraction has more than one critical draw ratio at a given Deborah number and may not exhibit draw resonance within some range of the Deborah number.     

Two fluid flow and heat transfer in an inclined channel containing porous and fluid layer

Convective flow and heat transfer in an inclined channel bounded by two rigid plates held at constant different temperatures with one region filled with porous matrix saturated with a viscous fluid and another region with a clear viscous fluid different from the fluid in first region is studied analytically. The coupled nonlinear governing equations are solved using regular perturbation method. It is found that the presence of porous matrix in one of the region reduces the velocity and temperature. Results have been presented for a wide range of governing parameters such as Grashof number, porous parameter, angle of inclination, ratio of heights of the two layers and also the ratio of viscosities.     

Instabilities in two-liquid layers subject to a horizontal temperature gradient

We study theoretically the stability of two superposed fluid layers heated laterally. The fluids are supposed to be immiscible, the interface undeformable and of infinite horizontal extension. Combined thermocapillary and buoyancy forces give rise to a basic flow when a temperature difference is applied. The calculations are performed for a melt of GaAs under a layer of molten B₂O₃, a configuration of considerable technological importance. Four different flow patterns and five temperature configurations are found for the basic state in this system. A linear stability analysis shows that the basic state may be destabilized by oscillatory motions leading to the so-called hydrothermal waves. Depending on the relative height of the two layers these hydrothermal waves propagate parallel or perpendicular to the temperature gradient. This analysis reveals that these perturbations can alter significantly the liquid flow in the liquid-encapsulated crystal growth techniques. PACS 47.20.Dz, 47.20.Bp, 47.54.+r, 47.27.Te, 44.25.+f, 47.20.Ma     

Heat transfer to reattached fluid flow downstream of a fence

In this paper we present heat transfer experiments performed at the reattachment of turbulent flows of fluids (Pr= 0.7 and 84) over surface-protruding fences of various heights. The location of the heat transfer maximum was found to depend onPr. The reattachment influences the thickness of the near-wall viscous layer, in which the universal velocity and temperature distribution is preserved.     

Flow seeding with an air nebulizer

 In the framework of studies on anemometric measurements or tomographic visualizations, the seeding of a reactive flow by a nebulizer has been analyzed. In order to determine the performances of this apparatus, different liquids have been tested to evaluate the influence of their physical properties on the droplets size distribution. Measurements have been made using a Phase Doppler Anemometer. It is shown that the mean D ₁₀ diameter lies between 2 and 3 μm, whatever the liquid may be, except pure water, and that, within a certain range, viscosity and surface tension have little influence on the size distribution. The ability of these liquids to seed reactive mixture is also discussed and especially their interaction in premixed flames. Received: 4 May 1998/Accepted: 15 February 1999