Showing papers in "Journal of Non-newtonian Fluid Mechanics in 1983"
TL;DR: In this paper, an experimental investigation is presented in which the velocity fields around sheres and bubbles moving in a cylinder have been measured by laser-Doppler anemometry (LDA), and it is shown that the wall correction factor K is a rapidly decreasing function of the Deborah number.
Abstract: An experimental investigation is presented in which the velocity fields around sheres and bubbles moving in a cylinder have been measured by laser-Doppler anemometry (LDA). Instabilities in the flow field at rather low Deborah numbers have been discovered and these instabilities are damped by inertia forces. It is shown that the wall correction factor K is a rapidly decreasing function of the Deborah number. The experimental measurements have been compared with numerical simulations, and on the basis of this comparison it has been possible to identify a time constant and a zero-shear-rate viscosity for the test liquid.
120 citations
98 citations
TL;DR: In this paper, an exact solution for the coaxial disk flow of an Oldroyd-B fluid is reported, which is approximately generated by the parallel-plate viscometer.
Abstract: This paper reports an exact solution for the coaxial disk flow of an Oldroyd-B fluid. The flow is approximately generated by the parallel-plate viscometer. Asymptotic and numerical solutions are reported showing that there is a critical Weissenberg number based on the angular velocity and the Maxwellian relaxation time, above which the flow is unstable. A linearized stability analysis for the basic inertialess flow confirms this numerical instability and yields the critical Weissenberg number.
96 citations
TL;DR: In this article, the design and operation of a new elongational rheometer for low elastic polymer solutions is described, which is easy to operate and for suitable operating conditions a transient elongational flow with an approximately constant rate of strain can be realized.
Abstract: Design and operation of a new elongational rheometer for low elastic polymer solutions are described. The free jet elongational rheometer is easy to operate and for suitable operating conditions a transient elongational flow with an approximately constant rate of strain can be realized. In any case, convenient comparative parameters can be obtained. The method of rheological curve fitting leads to a deformation dependent ralaxation time parameter of a modified upper convected Jeffreys-law.
87 citations
TL;DR: In this paper, the roles of luid inertia and shear-rate dependent viscosity in determining the velocity field in an axisymmetric sudden contraction are assessed by finite-element analysis for a generalized Newtonian fluid with visco-ity function given by a Carreau equation.
Abstract: The roles of luid inertia and shear-rate dependent viscosity in determining the velocity field in an axisymmetric sudden contraction are assessed by finite-element analysis for a generalized Newtonian fluid with viscosity function given by a Carreau equation. Acting alone, either increasing shear-thinning of the viscosity or increasing fluid inertia suppresses the upstream vortex that surrounds the opening to the small tube. For creeping flows, shear thinning does not produce concavities and off-centered maxima in the axial velocity profile just inside the small tube, even at high Carreau numbers where the velocity field approaches the limiting form for a power-law fluid. Peaks in the axial velocity away from the center of the tube were found only for moderate and high Reynolds numbers and were enhanced by shear thinning, which decreased the viscosity and consequently increased the “local” Reynolds number near the wall of the small tube. The effect of steep velocity gradients near this surface on the accuracy of the finite-element approximations is discussed.
86 citations
TL;DR: In this paper, the authors used the finite extensible nonlinear elastic (FENE) dumbbell model for dilute polymer solutions and melts if the Brownian motion and hydrodynamic forces acting on the beads are made nonisotropic.
Abstract: The finitely extensible nonlinear elastic (FENE) dumbbell model used earlier for dilute polymer solutions may also be used for concentrated solutions and melts if the Brownian motion and hydrodynamic forces acting on the beads are made nonisotropic. This corresponds roughly to imagining that a dumbbell is constrained to move within a capsule-shaped region embedded in the surrounding fluid. The constitutive equation obtained (a modified convected Maxwell model) contains four parameters: σ and β specify the extent of anisotropy in Stokes' law and in the Brownian motion forces respectively; λ is a time constant; and b describes the finite extensibility of the dumbbell. When σ and β are set equal to unity, the dilute-solution constitutive equation is recovered. In this sense the molecular theory given here permits a description of polymeric liquids over the entire concentration range.
79 citations
TL;DR: In this paper, the circumferential and radial profiles of velocity, pressure and stress are derived for the flow of model viscoelastic liquids between two slightly eccentric cylinders with the inner one rotating.
Abstract: The circumferential and radial profiles of velocity, pressure and stress are derived for the flow of model viscoelastic liquids between two slightly eccentric cylinders with the inner one rotating. Singular perturbation methods are used to derive expansions valid for small gaps between the cylinders, but for all Deborah numbers. Results for Newtonian, second-order, Criminale-Ericksen-Filbey, upper-convected Maxwell, and White-Metzner constitutive equation separate the effects of elasticity, memory, and shear thinning on the development of the large stress gradients that hinder numerical solutions with these models in more complicated geometries. The effect of the constitutive equation on the critical Deborah number for flow separation is presented.
67 citations
66 citations
TL;DR: In this paper, a Lagrangian method for the simulation of flow of non-Newtonian liquids is implemented, where fluid mechanical equations are formulated in the form of a variational principle, and a discretization is performed by finite elements.
Abstract: A Lagrangian method for the simulation of flow of non-Newtonian liquids is implemented. The fluid mechanical equations are formulated in the form of a variational principle, and a discretization is performed by finite elements. The method is applied to the slow of a contravariant convected Maxwell liquid around a sphere moving axially in a cylinder. The simulations show that the friction factor for a sphere in a narrow cylinder is a rapidly decreasing function of the Deborah number, while the friction factor for a sphere in a very wide cylinder is not significantly affected by fluid elasticity. It is demostrated that the simulated wall effect on the motion of the sphere may be utilized in an experimental identification of a time constant for a given liquid.
62 citations
TL;DR: In this paper, the finite element formulation was extended to handle problems involving free surfaces, and an algorithm was proposed to track particles on the free surface and a new free surface updating scheme was proposed.
Abstract: The finite element formulation recently developed [1] for viscoelastic fluids of singly memory type has been extended to handle problems involving free surfaces. Previously [1], flows without free surfaces were demonstrated by solving the die entry and reverse entry flows. The single integral Maxwell fluid is retained here as the constitutive model for this further test of the technique. New work in this paper includes an algorithm to track particles on the free surface and a new free surface updating scheme. For the present die swell problem, the method successfully converged up to Deborah number of about 1. As in the previous problems, convergence appears to be limited by numerically induced incompatibility of large strains. The resulting errors in the computed stress field have a more pronounced impact on free surface flows.
61 citations
TL;DR: In this article, a consitutive theory for polymetric liquids based on the transient network concept is developed, following Wiegel and Jongschaap, and the Phan-Thien-Tanner equation is shown to follow from the general theory with two critical assumption, one of these is quasi-equilibrium of the internal structure, which preludes consistency of application in fast flows.
Abstract: A consitutive theory for polymetric liquids based on the transient network concept is developed, following Wiegel and Jongschaap. The Phan-Thien-Tanner equation is shown to follow from the general theory with two critical assumption, one of these is quasi-equilibrium of the internal structure, which preludes consistency of application in ”fast flows“. The Marrucci model can be made consistent with the general format with a small change in the kinetic equation that can be deduced from asymptotic behaviour and leaves the steady viscometric behavior unchanged. The simplest genaral formulation requires the linear viscoelastic spectrum and two parameters; the latter cannot be determined uniquely from steady viscometric flow data.
TL;DR: A review of several important constitutive equations with an eye towards determining those most suitable for use in modelling polymer melt processing is conducted in this paper, where general principles are invoked for a priori screening of the equations without needing detailed comparison of the model predictions with experimental data.
Abstract: A review of several important constitutive equations is herein conducted with an eye towards determining those most suitable for use in modelling polymer melt processing. General principles are invoked for a priori screening of the equations without needing detailed comparison of the model predictions with experimental data. These principles, which are derived from continuum mechanics, thermodynamics and molecular kinetic theory, and dela with convection and diffusion of entangled polymer strands during flow, are: (1) During sudden deformations, the stress is a unique function of the total strain. (2) The second law of thermodynamics holds for all deformations. (3) The constitutive equation can be derived from a plausible molecular model which describes the convection and diffusion. (4) The model parameters can be determined by a reasonable number of rheometric experiments. Based on these principles, it is concluded that separable free energy models are the most promising. These are either BKZ integral models with a kernel factorable into a time-dependent and a strain-dependent part. or sets of Maxwell-type differential equations that employ a generalized convected derivative, and that are linear in stress in the absence of flow.
TL;DR: In this paper, the motion of a Newtonian fluid containing solid particles in the case of high concentration (the partial volume of solid is comparable to that of fluid) by using a homogeniztion technique associated with the small parameter ϵ (the ratio of the particle length to the characteristic macroscopical length) was considered.
Abstract: We consider the motion of a Newtonian fluid containing solid particles in the case of high concentration (the partial volume of solid is comparable to that of fluid) by using a homogeniztion technique associated with the small parameter ϵ (the ratio of the particle length to the characteristic macroscopical length). The limit behaviour as ϵ → 0 is that of fluid with anisotropy properties associated with a microstructure. The evolution equations for the limit flow and for the microstructure are given.
TL;DR: In this article, the stability of the flow of two "power-law" liquids between two infinite parallel planes when one of the planes moves with constant velocity in its own plane was investigated.
Abstract: Consideration is given to the stability of the flow of two ”power-law“ liquids between two infinite parallel planes when one of the planes moves with constant velocity in its own plane. It is found that the ratios of the power-law parameters for each layer have a dramatic effect and can be chosen to destabilize the flow.
TL;DR: In this paper, the effects of soap-naphthol ratio, soap molecular weight and solution temperature upon drag reduction and swirl decay time are reported. And the critical wall shear stresses above which the drag-reducing properties cease correlate well with swirl decay.
Abstract: The pipe flow drag-reducing properties of mixtures of alkyltrimethylammonium halides with 1-naphthol in aqueous solution have been investigated. The effects of solution concentration, soap-naphthol ratio, soap molecular weight and solution temperature upon drag reduction and swirl decay time are reported. The critical wall shear stresses above which the drag-reducing properties cease correlate well with swirl decay time. At low soap concentrations greater than equimolar proportions of 1-naphthol with the soap are required for maximum drag reduction. The drag-reducing properties of these solutions are greatest at and around the Krafft point of the pure soap. A phenomenon similar to onset for polymer solution drag reduction is reported for these soap solutions.
TL;DR: In this paper, a procedure for determining the four independent model parameters (λ H, b, σ, β) from experimental data was suggested for determining steady-state and time-dependent material functions.
Abstract: The consitutive equation derived in Part I [1] is used to compute steady-state and time-dependent material functions. A procedure is suggested for determining the four independent model parameters (λ H , b , σ, β) from experimental data. Material functions have been calculated using parameters determined by experimental data for concentrated solutions of nearly monodisperse linear polymers. The theoretical curves for steady shear properties (η and Ψ 1 ) are in quantitative agreement with the data well into the range of nonlinear behavior. The calculated time-dependent properties (η*, η + , Ψ + , η − ) are in qualitative agreement with observed behavior. Theoretical curves for elongational viscosity are reasonable, but suitable experimental data are not available for comparison.
TL;DR: In this paper, the development of plane Couette flow for viscoelastic fluids is analyzed using a constitutive equation that can be obtained from molecular theory, in which the molecules are regarded as finitely extensible dumbbells.
Abstract: Unsteady-state development of plane Couette flow for viscoelastic fluids is analyzed using a constitutive equation that can be obtained from molecular theory, in which the molecules are regarded as finitely extensible dumbbells. Typical features of the flow situation are as follows: (i) For a fluid with moderate elasticity, not only stress overshoot but also velocity overshoot are predicted. (ii) For suitable combinations of elasticity and gap width, and for some time intervals stress propagation and reflection phenomena are predicted. (iii) After a sufficient time has elapsed, the stress state behaves similarly to that corresponding to the start-up of a steady simple shear flow.
TL;DR: In this article, the relation between applied force and plate separation for squeezing flows of viscoelastic liquids between closely-spaced parallel disks is analyzed, and solutions are presented for liquids with power-law viscometric functions.
Abstract: The theoretical analysis is made of the relation between applied force and plate separation for squeezing flows of viscoelastic liquids between closely-spaced parallel disks. The lubrication approximation and the quasi-steady-state assumption are employed in the development. Elastic effects are incorporated through inclusion of normal stresses. Solutions are presented for liquids with power-law viscometric functions, and a numerical procedure is used for fluids having viscometric functions of arbitrary form. For fast and slow squeezing, calculated values of t 1 2 , the time required to squeeze out half the fluid, are found to agree with the constant force data of Leider [1,2].
TL;DR: In this article, the injection capillary flow of various unfilled and glass fibre or calcium carbonate filled polypropylene and nylon 6.6 melts is studied using either a single capillary of five capillaries in series, separated by small reservoirs.
Abstract: The injection capillary flow of various unfilled and glass fibre or calcium carbonate filled polypropylene and nylon 6.6 melts is studied using either a single capillary of five capillaries in series, separated by small reservoirs. Only unfilled nylon 6.6 yields instability during flow through a single capillary due to mechanochemical degradation in the capillary at extremely high shear rates above 5 × 105 s−1. It is found that only short glass fibre reinforced polypropylene yields high frequency oscillations in the reservoir pressure and extrudate diameter and has discontinuity in the flow curve when the apparent shear rate is above 4 × 105 s−1 and the flow is through multiple capillaries. Further increase in the shear rate restores the stable flow. The intensity of the oscillations and the range of shear rate during which unstable flow occurs are increased with increasing melt temperature. The mechanism of this unstable flow is investigated by studying fibre orientation at the capillary entrance and exit using mouldings simulating capillary entry-exit flows.
TL;DR: In this article, a modification to existing equipment is described which permits continuous squeeze-film flow to be obtained between parallel-sided strips of material rather than between disc-shaped surface.
Abstract: A modification to existing equipment is described which permits continuous squeeze-film flow to be obtained between parallel-sided strips of material rather than between disc-shaped surface. Squeeze film flow is simulated by having liquid move through one of the surfaces via an array of equispaced holes. The Squeeze-film behavior of a Newtonian base oil is first tested at temperatures of 24°C and 55°C. It is shwon that loads are in reasonable agreement with theretical predictions and that end effects (corrected by means of a guard ring) and fluid maldistribution effects are of small proporitons. At the very highest liquid flowrates, the rapid liquid flow through the holes may influence the measured load. The Polymer-thickened oils, representinhg 10 W/30 and 10 W/50 motor oils, are tested at temperatures of 24°C and 55°C. Both oils five marked load enhancement, compared with Newtonian oil under similar flow conditions, at the higher flowrates used. The 10 W/50 oil gives load enhancement of 76 per cent at 55°C, increasing rapidly with the simulated approach velocity. Fluid inertia effects in the squeeze film flow aslo increase the load significantly. The results confirm earlier data using disc-shaped surfaces; load enhancement is greater in the present work on strip squeeze films because the fluid deformation rates are greater (2000 s t-1 in planar extention and 2 x 10 5 s t-1 in shear). It is suggested that the fuel consumption of cars could be improved by the development of elastic, shear stable oils of lower viscosity than those currently in use.
TL;DR: In this article, a low-power laser-speckle photographic technique has been developed and used for the measurement of point velocities in slow laminar flows where the two velocity components can be easily measured.
Abstract: A low cost, low power laser-speckle photographic technique has been developed and is duscussed for the measurement of point velocities in slow laminar flows. The technique is particularly suitable for axisymmetric flows where the two velocity components can be easily measured. The accuracy of the technique is established by measurement of the velocity distribution for Poiseuille flow and from data obtained for acceleration of an inelastic Newtonian fluid through a four-to-one circular contraction. Preliminary results are also presented in the contracting flow field for a non shear-thinning highly elastic fluid. These data are particularly significant for verification of finite element numerical solutions currently being developed for viscoelastic fluids in circular entry flows.
TL;DR: For non-Newtonian fluids of the power-law type, where the viscosity is an exponential function of the temperature, increasing the exponential coefficient α (or decreasing the Peclet number Pe) causes an increase in ϵ when the power law index n and the modified Brinkman number Br are kept fixed as mentioned in this paper.
Abstract: Some finite element results of the non-isothermal extrusion process are presented. For Newtonian fluids, increasing the Nahme-Griffith number Na is found to increase the swelling ratio ϵ. The temperature distribution near the exit plane is shown to be a critical factor determining whether the extrudate would swell or contract relative to the isothermal, Newtonian case. In this waya recent theory by Tanner has been partly verified. For non-Newtonian fluids of the power-law type, where the viscosity is an exponential function of the temperature, increasing the exponential coefficient α (or decreasing the Peclet number Pe causes an increase in ϵ when the power-law index n and the (modified) Brinkman number Br are kept fixed. However, the effects are small for shear-thinning fluids (n<1), but become stronger as n increases. On the other hand, at fixed (Br) and (Pe) (thus fixing α) increasing n causes rapid increases in ϵ
TL;DR: In this article, the rheological behavior of progressively shear thickening FM-9 solutions, a time-dependent shear-thickening material with characteristics of threshold behavior, has been investigated as part of a study of the Rheological properties of antimisting jet fuel.
Abstract: The rheological behavior of progressively shear thickening FM-9 solutions, a time-dependent shear thickening material with characteristics of threshold behavior, is investigated as part of a study of the rheological properties of antimisting jet fuel. Flammability test results and test configurations from various sources are evaluated. A correlation is obtained between the rheological behavior and the flammability tests such that, for a given system, such as a fixed solvent system and the FM-9 polymer system, the flammability criterion can be applied to a wide range of concentrations and temperatures.
TL;DR: In this article, an extension of earlier work is made to determine both theoretically and experimentally the coefficient of discharge and spray cone angle of a swirl nozzle using a time-independent purely viscous power-law non-Newtonian fluid.
Abstract: An extension of earlier work is made in the present paper to determine both theoretically and experimentally the coefficient of discharge and spray cone angle of a swirl nozzle using a time-independent purely viscous power-law non-Newtonian fluid. The theoretical predictions are made through an approximate analytical solution of the hydrodynamics of flow inside the nozzle. Experiments are carried out with aqueous solutions of CMC (carboxymethyl cellulose sodium salt) powder of various concentrations as the working fluids. The rheological properties of the working fluids are established by a capillary tube viscometer. From both the theoretical and experimental analyses, the pertinent independent input parameters are recognised as the generalised Reynolds number at inlet to the nozzle ReGi, the flow behaviour index of the fluid n, length-to-diameter ratio of the swirl chamber L1/D1, spin chamber angle 2α and the orifice-to-swirl-chamber-diameter ratio D1/D1. Although the theory predicts the correct qualitative trend in all cases, it does not agree well with the experimental results. Therefore, on the basis of the theoretical results, emperical relationships between nozzle characteristics and input parameters heve been established. Finally it is recognised that, regarding the injection conditions and fluid properties, the generalised Reynolds number at nozzle inlet ReGi and the flow behaviour index n have inverse and direct effects, respectively, on the coefficient of discharge, but have a negligible influence on the spray cone angle. Amongst the nozzle geometries, an increase in the values of D2/D1 and 2α or a decrease in the value of L1/D1 decrease the coefficient of discharge and increase the spray cone angle.
TL;DR: In this article, the flow between a stationary small diameter needle and a moving drum of much larger diameter, seen as a moving plane, is compared to that of a Newtonian fluid used under the same kinematic conditions.
Abstract: This experimental study is related to the flow between a stationary small diameter needle and a moving drum of much larger diameter, seen as a moving plane. Our visualisation experimental set-up adds new results regarding the flow behaviour of a polymer solution. This flow is compared to that of a Newtonian fluid used under the same kinematic conditions. Important differences between Newtonian and polymeric flows concern mainly streamlines, stagnation point positions, and reverse flow. A second experimental set-up enabled us to obtain normal stress profiles along the needle wall and the flow rate through the gap. Reslts related to Newtonian flows are compared to the well-known analytical solutions for a bidimensional laminar flow.
TL;DR: In this article, the motion of a flexible thread-like filament suspended in an unbounded Stokes shear flow is considered, and the model is solved in closed form, for inextensible filaments and general time-dependent shear flows.
Abstract: We consider the motion of a flexible threadlike filament suspended in an unbounded Stokes shear flow. As the extension of a well-established slender-body theory, we treat the case of a highly anisotropic drag relation, as reflected by a small ratio ϵ of transverse to longitudinal filament mobility. This provides one potentially useful model of hindered filament motion in highly concetrated filamentary suspensions. In the limit ϵ → 0, which corresponds to the kinematics associated with a recent model (of Doi and Edwards) for polymer chains, the filament motion is governed by a non-linear kinematic-wave equation. We show that this equation can be solved in closed form, for inextensible filaments and general time-dependent shear flows. We investigate the permanence and stability of threads having uniform axial mobility, showing that only piecewise straight threads have permanent shape. Also, we investigate the stability of fully-extended treads by means of both finite and infinitesimal stability analyses, and we provide equations for the growth rate of arbitrary intial disturbances. These are applied to simple shear and simple-extensional flows. Finally, we discuss the failure of our model for small but non-zero ϵ, near points of extreme curvature of “entaglement”, and the possible relevance to the rheology of fibrous composites and suspensions.
TL;DR: In this paper, the intrinsic spinnability of a fluid is defined in terms of the asymptotic behavior of the velocity profile of a spin-threadline at high elongation rates under such conditions that the profile is determined solely by the material rheology.
Abstract: The intrinsic spinnability of a fluid is herein defined in terms of the asymptotic behavior of the velocity profile of a spin-threadline at high elongation rates under such conditions that the profile is determined solely by the material rheology. Spinnability can be categorized as draw-ratio-limited, threadline length-limited, residence-time-limited and unlimited; this indexing is linked to the dependence of the spinning viscosity upon strain rate, thinning materials being the less spinable. A method for deriving bounds on spinnability directly from the constitutive equation for single-relaxation-time integral models is presented, and, as an example, the lower-convected Maxwell model is shown to have length-limited spinnability.
TL;DR: In this article, a new systematic method has been developed for estimating rheological properties (such as relaxation time, viscosity, primary normal stress difference) for various polymer solutions form the zero-shear-rate specific viscoity and a dimensionless shear rate.
Abstract: A new systematic method has been developed for estimating rheological properties (such as relaxation time, viscosity, primary normal stress difference) for various polymer solutions form the zero-shear-rate specific viscosity and a dimensionless shear rate. A linear relation has been found between the relaxation time and the zero-shear-rate specific viscosity on a double-logarithmic plot, and a new master plot for the primary normal stress difference has been established. In addition the applicability of the FENE-P dumbbell model to high-polymer solutions is discussed.