Effect Of Fluid Elasticity Research Articles

Flow of non-Newtonian fluids through tubes with abrupt expansions and contractions (square wave tubes)

The steady and dynamic shear properties of three different non-Newtonian fluids (an Acrysol TT615 solution, a 50% creosote-in-water emulsion and a Separan AP-30 solution) are determined. Their flow behaviour through tubes with abrupt expansions and contractions (`square wave tubes') is investigated. The steady shear viscosity of these fluids can be described with a modified Quemada model. The geometric parameter method proposed previously by Kozicki et al. for duct of arbitrary cross section can be extended to the present systems with the use of a volume-average diameter. Flow in square wave tubes can be readily obtained from the straight capillary data by means of a shift factor ( a+ b). The shift factor is related to a pressure-average diameter. Conversely, using the pressure-average diameter eliminates the necessity of the shift factor. Corrections of inertial and entrance effects from Newtonian results can be approximately applied to non-Newtonian results. These corrections are relatively insignificant as compared with the effects of fluid elasticity and elongational-viscosity for viscoelastic fluids.

The penetration of a long bubble through a viscoelastic fluid in a tube

The penetration of a long gas bubble through a tube filled with a viscoelastic fluid is studied. This problem has practical applications in gas-assisted injection molding, enhanced oil recovery, production of hollow fiber membranes, and coating of ceramic monoliths for the manufacture of catalytic converters. A hydrodynamic coating is formed on a capillary tube wall by injecting a single long gas bubble through the fluid. This problem has been studied extensively for Newtonian fluids, but little work has been done to understand how non-Newtonian fluids behave in this flow. The work presented in this paper is directed at identifying the effects of fluid elasticity on the hydrodynamic fractional coverage created by a long penetrating bubble. Experiments were performed with four test fluids including two Newtonian fluids and two highly elastic, constant shear viscosity fluids. Hydrodynamic fractional coverage, m was characterized in terms of the capillary number, Ca and Deborah number, De. For small Deborah number, De<1, both viscoelastic fluids exhibit a fractional coverage identical to that of a Newtonian fluid at an equivalent capillary number. The fractional coverage for both viscoelastic fluids begins to increase relative to the Newtonian result at De≈1. Fractional coverage continues to increase with Deborah number for all De≥1. At De≈5 fractional coverage is 30% greater than the Newtonian fluid result. A plot of fractional coverage versus capillary number is found to be independent of tube diameter for a Newtonian fluid. However, for a viscoelastic fluid, fractional coverage is found to be a strong function of tube diameter. The Deborah number is found to collapse fractional coverage data for experiments conducted with different tube diameters.

Stability of viscoelastic flow around periodic arrays of cylinders

Low Reynolds number flow of Newtonian and viscoelastic Boger fluids past periodic square arrays of cylinders with a porosity of 0.45 and 0.86 has been studied. Pressure drop measurements along the flow direction as a function of flow rate as well as flow visualization has been performed to investigate the effect of fluid elasticity on stability of this class of flows. It has been shown that below a critical Weissenberg number (Wec), the flow in both porosity cells is a two-dimensional steady flow, however, pressure fluctuations appear above Wec which is 2.95±0.25 for the 0.45 porosity cell and 0.95±0.08 for the higher porosity cell. Specifically, in the low porosity cell as the Weissenberg number is increased above Wec a transition between a steady two-dimensional to a transient three-dimensional flow occurs. However, in the high porosity cell a transition between a steady two-dimensional to a steady three-dimensional flow consisting of periodic cellular structures along the length of the cylinder in the space between the first and the second cylinder occurs while past the second cylinder another transition to a transient three-dimensional flow occurs giving rise to time- dependent cellular structures of various wavelengths along the length of the cylinder. Overall, the experiments indicate that viscoelastic flow past periodic arrays of cylinders of various porosities is susceptible to purely elastic instabilities. Moreover, the instability observed in lower porosity cells where a vortex is present between the cylinders in the base flow is amplifieds spatially, that is energy from the mean flow is continuously transferred to the disturbance flow along the flow direction. This instability gives rise to a rapid increase in flow resistance. In higher porosity cells where a vortex between the cylinders is not present in the base flow, the energy associated with the disturbance flow is not greatly changed along the flow direction past the second cylinder. In addition, it has been shown that in both flow cells the instability is a sensitive function of the relaxation time of the fluid. Hence, the instability in this class of flows is a strong function of the base flow kinematics (i.e., curvature of streamlines near solid surfaces), We and the relaxation time of the fluid.

Effects of fluid elasticity on the static and dynamic settling of a spherical particle

The results of an experimental investigation of the settling velocity of spherical particles in viscoelastic fluids are presented. As well as being fundamentally interesting, this problem is also of relevance to the under- standing of particle transport by well-technology fluids used in the oil industry. It is shown that the settling velocity is reduced by elastic effects in the fluid (e.g., presence of normal stress differences and high elongational viscosity), and that this effect becomes significantly higher with increasing shear rates experienced by the falling sphere, i.e. the ratio of settling velocity to sphere diameter. Imposing an orthogonal shear-flow field on the settling particle causes a further dramatic reduction of the settling velocity in viscoelastic fluids.

HEAT TRANSFER TO SPHERES FROM A POLYMER MELT

A Galerkin mixed finite-element method was used to predict the effect of fluid elasticity, temperature-dependent fluid properties, shear-dependent fluid properties, and viscous dissipation on the overall rate of heat transfer between a polymer melt and a sphere. A correlation is developed for the Nusselt number that accounts for changes in Peclet number, viscous dissipation, and a temperature-dependent viscosity function

The effect of fluid elasticity on power consumption and mixing times in stirred tanks

Results are presented to show the effects of fluid elasticity on the power required for mixing and the time necessary to obtain a certain degree of homogenization (i.e. mixing time) in the viscous regime. To separate the effects of elasticity from those of shear thinning viscosity, elastic fluids with constant viscosities are used. Experiments in baffled tanks with Rushton turbine impellers show that elastic fluids require more power than inelastic fluids having equal viscosities. A correlation for the increased torque required to agitate an elastic fluid is presented that has a form suggested by the analytical solution for the effect of elasticity on the torque required to spin a sphere in a second-order elastic fluid. Elasticity also increases mixing time. Mixing time measurements are made using three probes at different locations in the vessel. The probes, based on fiber-optic sensors, detect a fluorescent dye tracer at the parts per billion concentration level.

On Newtonian and non-Newtonian flow in complex geometries

A flow visualization technique by means of an expanded laser beam and trace amounts of particulate additives is used to study the behaviour of Newtonian and non-Newtonian elastic liquids in a number of complex geometries. Particular attention is paid to the effect of fluid elasticity on the flow characteristics. Attempts are made to simulate numerically the observed flows by using finite-difference techniques. The agreement between theory and experiment is very satisfactory.

The influence of fluid elasticity on the drag coefficient for creeping flow around a sphere

Drag coefficients are measured for the creeping motion of a sphere in nonshear-thinning elastic fluids. The data obtained cover a Weissenberg number range of 1.66 × 10 −4 to 2.02. For 0 ⩽ We ⩽ 0.1 no significant deviation from the Stokes drag is observed as a result of fluid elasticity. For We > 0.1 a continuous reduction in drag below the Stokes value is observed until an asymptotic reduction of 26% is reached for We >/ 0.7. Existing theoretical analyses are inadequate for predicting the reduction in drag observed and its asymptotic value. The effect of fluid elasticity on the drag coefficient in the absence of any significant shear-thinning effects is clearly demonstrated.

A Preliminary Study of the Fluid Mechanics of Liquid Penetrant Testing.

Some aspects of the fluid mechanics of liquid penetrant testing are considered. Penetration is represented by surface tension driven flow into defects of small defect width to depth ratio. Defect width is chosen so that both gravitational and non-continuum effects may be ignored. Penetration time is found to follow a Rideal-Washburn relation, in which where t is time, l defect depth, μ the dynamic viscosity, γ the surface tension, R the defect width and θ the contact angle. The proportionality constant, however, is shown to be strongly dependent on defect geometry and penetrant application procedure. The effect of slight fluid elasticity is shown to be negligible.

Boundary layer analysis of viscoelastic flow in annuli

The behaviour of viscoelastic fluids, represented by a modified Rivlin-Ericksen constitutive equation, in the inlet region of an annulus has been studied using a boundary layer analysis. It was found that viscoelasticity changes the magnitude of the entrance length depending upon the fluid parametersn, s and Ws/Re. There exist certain values ofn ands below which the entrance length for viscoelastic fluids is longer and above which is shorter than the inelastic fluids of the samen. The effect of fluid elasticity on the flow field depends strongly on the relative magnitudes of elastic and inertial forces, or the ratio of Weissenberg to Reynolds numbers. It was also found that the excess pressure drop in the entrance region is greater for viscoelastic fluids.

Viscous Dissipation in the Flow Between Eccentric Rotating Disks (Orthogonal Rheometer)

The orthogonal rheometer has become increasingly popular for determination of the viscoelastic properties of fluids. Here we present an analytical solution for the steady-state temperature distribution arising from the dissipation due to flow between infinite, isothermal eccentric rotating disks. This information is necessary to experimentalists concerned with obtaining accurate rheological characterizations for materials whose properties are temperature dependent, e.g., polymer melts. The results, temperature profiles and the maximum temperature rise, are presented using two dimensionless parameters which indicate the effects of inertia and fluid elasticity. Thus, the results can be easily used by practitioners to estimate the importance of dissipation in their experiments. For conditions of practical interest, temperature rises large enough to be of concern may be encountered.

Laminar boundary layer over a flexible surface in oscillatory flow

Oscillatory flow of an elastico-viscous fluid (Walters fluid B′) over a flexible surface is analysed. The study is limited to fluids with short memories. The effects of fluid elasticity on flow are brought out by comparing the results with those obtained in case of a Newtonian fluid.