Showing papers in "Journal of Non-newtonian Fluid Mechanics in 1988"
TL;DR: In this article, a dilute polymer solution is modelled as a suspension of dumbbells with finite extensibility, and time-dependent numerical calculations are performed of flow part cylindrical and spherical surfaces at low Reynolds number.
Abstract: A dilute polymer solution is modelled as a suspension of dumbbells with finite extensibility. Time-dependent numerical calculations are performed of flow part cylindrical and spherical surfaces at low Reynolds number. A finite-difference scheme is employed in which the evolution in time of the dumbbells is followed from an initially unstretched equilibrium. Results are calculated with (i) a no-slip, and (ii) a zero-tangential-stress boundary condition at the body surface. At large Deborah number, D , the polymer is most highly stretched in thin regions of fluid close to and downstream of stagnation points of the flow. The most important region dynamically is found to be at the rear of the obstacle. Numerical refinements in space and time are included in order properly to resolve this fine-scale structure. Numerically stable results are obtained for values of D up to 16, and show that the flow field and drag force on the obstacle tend toward finite values at large D . Experimental measurements of the drag on a falling rigid sphere, and the velocity distribution around it, are compared with the numerical results for the no-slip boundary. Observations of bubble behaviour are discussed in the light of the results for the slip boundary.
452 citations
TL;DR: In this paper, a continuum theory for dilute suspensions of large-aspect-ratio particles is applied to the flow of fiber suspensions through contractions, which incorporates the statistical orientation distribution function into the stress equation.
Abstract: A continuum theory for dilute suspensions of large-aspect-ratio particles is applied to the flow of fiber suspensions through contractions. The theory, which incorporates the statistical orientation distribution function into the stress equation, predicts that the flow of dilute suspensions will differ qualitatively from the flow of the suspending fluid. The theory is in excellent agreement with experiments on the flow of suspensions of chopped-glass fibers through axisymmetric contractions, where substantial enlargement of the recirculating corner vortex is observed at volume fractions of 0.1% and less.
335 citations
TL;DR: In this article, an approximate analysis for the flow of fluids through planar and axisymmetric contractions is presented, where independent power-law models are used to represent the shear and extensional viscosity functions.
Abstract: An approximate analysis is presented for the flow of fluids through planar and axisymmetric contractions. Energy principles are employed to relate the entry pressure drop to flow rate and fundamental rheometric properties. One of the aims of the analysis is to investigate the influence of extensional viscosity on such flows, particularly with regard to the occurrence and enhancement of vortex motion in the entry corners. For the sake of mathematical simplicity, independent power-law models are used to represent the shear and extensional viscosity functions. The analysis indicates that, once significant vortex motion is present, enhancement occurs whenever the Trouton ratio is an increasing function of shearrate (or stretch-rate). It is readily seen how the occurrence of vortices serves as a stress relief mechanism. Indeed, for highly stretch-thickening materials, the entry pressure drop is seen to be dominated by shear properties. The power-law parameters of the extensional viscosity function may be obtained in a straight-forward way from entry pressure drop versus flow rate data. Finally, the extension and application of the analysis to other similar flows, such as through converging nozzles, is briefly discussed.
298 citations
TL;DR: In this article, a new technique is presented to measure the frequency dependent complex modulus simultaneously at several frequencies instead of consecutively as in a frequency sweep, where the strain in a dynamical mechanical experiment is prescribed as a superposition of several different modes (three in our case).
Abstract: A new technique is presented to measure the frequency dependent complex modulus simultaneously at several frequencies instead of consecutively as in a frequency sweep. For this purpose, the strain in a dynamical mechanical experiment is prescribed as a superposition of several different modes (three in our case). The resulting stress is decomposed into sinusoidal components, each of them characterized by their frequency, amplitude, and phase shift with respect to the corresponding strain component. Phase shift and amplitude are expressible in a frequency dependent complex modulus. A single experiment gives, therefore, values for the complex modulus at a set of prescribed frequencies. The method was demonstrated on three stable viscoelastic fluids and was applied to determine the instant of sol-gel transition (gel point) of a crosslinking polymer.
177 citations
TL;DR: In this article, a restructured version of the constitutive equation of motion, called the Explicity Elliptic Momentum Equation (EEME), is used for viscoelastic flow analysis.
Abstract: Finite element calculations for viscoelastic flows are reported that use a restructured form of the equation of motion that makes explicit the elliptic character of this equation. We call this restructured equation the Explicity Elliptic Momentum Equation, and its use is illustrated for flow of an upper convected Maxwell (UCM) model between eccentric and concentric rotating cylinders and also for a modified upper convected Maxwell (MUCM) model in the stick-slip problem. Sets of mixed-order approximations for velocity, stress, and a modified pressure are used to test the algorithm in both problems. Both sets of calculations are shown to converge with mesh refinement and are limited at high values of Deborah number by the formation of elastic boundary layers that are identified in the momentum equation by the growth of low-order derivative terms that involve the local velocity gradient and divergence of stress. Similar convergence properties are observed for bilinear and biquadratic Lagrangian approximations to the stress components. However, calculations with the more accurate basis for stress converge to higher values of De and are sensitive to the weighted residual method used for the constitutive equation, particularly for the eccentric cylinder problem. Streamline-upwind Petroy-Galerkin (SUPG) and artificial diffusivity (AD) formulations of the constitutive equation are tested for solution of both problems by calculations of the stress fields with fixed kinematics and by solution of the coupled problem. The SUPG method improves the performance of the calculations with the biquadratic basis set for the eccentric cylinder problem. For the UCM model, adding artificial diffusion to the constitutive equation in the stick-slip problem changes the dominant balance for the stress field near the singularity, making it appear as an integrable stress approximation for fixed mesh. For the MUCM model the Newtonian-like behavior of the stress near this point is unaffected by the AD method and calculations converge to moderate De .
167 citations
TL;DR: In this paper, a modification of the bead-and-spring dumbbell model for non-Newtonian flow has been proposed, which allows the numerical solution of (some) flow problems to proceed to large Deborah numbers.
Abstract: The failure of some careful attemps to provide numerical solutions of the equations for non-Newtonian flow suggests to us some inadequacies of the constitutive equations. (After all no one would doubt the validity of the conservation of mass and momentum.) To understand the physics in the constitutive equation, and thence to correct its undesirable features, it is helpful to look at a micro-structural model which leads to the constitutive equation. The bead-and-spring dumbbell model for a dilute polymer solution leads to an Oldroyd-like equation. The simplest version of the bead-and-spring model has a linear spring and a constant friction coefficient for the beads. While this model is simple and usefully combines viscous and elastic behaviour, it has the very unphysical feature of blowing up in strong straining flows (i.e. at a Deborah number in excess of unity), with the spring lengthening indefinitely in time and the steady extensional viscosity becoming unbounded at a critical flow strength. The hope that the corresponding large stresses would not occur in a flow calculation seems to have been misguided: some simple examples show that the large stresses may not act through the momentum equation to inhibit the flow. To cure this unphysical behaviour one clearly needs to use a non-linear spring force which gives a finite limit to the extension. Incorporating this modification into the constitutive equation enables the numerical solution of (some) flow problems to proceed to large Deborah numbers. Care is of course still needed in the numerical calculations, for example in resolving thin layers of high stress. (A boundary layer theory needs to be developed for the nonlinearity introduced by the non-Newtonianness.) A further modification of the bead-and-spring model may be necessary if argument is sought between numerical calculations and experiments. Many flows of interest subject the fluid to a sudden strong strain. In such circumstances the polymer chains will not be in thermodynamic equilibrium and so will not give the standard entropic spring. It may be possible to model this behaviour by a large temporary internal viscosity.
159 citations
TL;DR: In this paper, the authors used pressure measurements in contraction flows in determination of the extensional viscosity behavior of polymer solutions, and concluded that contraction flows provide a convenient means of determining the extension viscosities of shear-thinning polymer solutions.
Abstract: We consider the use of pressure measurements in contraction flows in the determination of the extensional viscosity behaviour of polymer solutions. The experimental data are interpreted on the basis of the recent theory of Binding. The resulting extensional viscosities are compared with those obtained from a commercial Spin Line Rheometer. We conclude that contraction flows provide a convenient means of determining the extensional viscosity of shear-thinning polymer solutions. The case is not so clear for constant viscosity Boger fluids. In the course of the experiments, it is shown that excess pressure losses in the contractions can be brought about by two distinct flow mechanisms in the case of Boger fluids. In the axisymmetric case, both vortex enhancement and excess pressure loss are observed, although there is not a strict one-to-one correlation between these phenomena. In the planar case, vortex enhancement is not conspicuously present, although there is still a substantial excess pressure loss at high flow rates. This excess must be associated with the ‘bulb’ flow field which essentially replaces the vortex-enhancement regime of the axisymmetric case.
131 citations
TL;DR: In this paper, it was shown that the dependence of this transition on the Weissenberg number and the gap width or cone angle is consistent with a viscoelastic instability predicted by Phan-Thien for Boger fluids.
Abstract: Dilute solutions of high molecular weight polyisobutylene dissolved in kerosene and low molecular weight polybutene have previously been reported to behave as ideal elastic liquids (“Boger fluids”). We report here rheological properties for similar solutions, having, however, higher molecular weights for the polyisobutylene. At low shear rates, these solutions exhibit the expected Boger-type rheological behavior, and approximately obey the Oldroyd-B constitutive equation. However, above a critical shear rate that depends upon molecular weight, prolonged shearing in a cone-and-plate or parallel-plate rheometer induces a time-dependent increase in the solution viscosity and elasticity. We find that the dependence of this transition on the Weissenberg number and the gap width or cone angle is consistent with a viscoelastic instability predicted by Phan-Thien for Oldroyd-B fluids. This instability appears to be of some generality for Boger fluids, since we have also observed it in a new monodisperse Boger fluid (polystyrene in low molecular weight polystyrene and dioctyl phthalate). Furthermore, this transition may have previously been observed (though not identified) by Jackson et al., using the Boger fluid polyacrylamide in maltose.
124 citations
TL;DR: In this article, the authors examined the behavior of viscoelastic fluid models which exhibit local extrema of the steady shear stress and constructed a variety of steady singular solutions with jumps in shear rate and their stability to one dimensional disturbances analyzed.
Abstract: We examine the behavior of viscoelastic fluid models which exhibit local extrema of the steady shear stress. For the Johnson-Segalman and Giesekus models, a variety of steady singular solutions with jumps in shear rate are constructed and their stability to one dimensional disturbances analyzed. It is found that flow-rate versus imposed stress curves in slit-die flow fit experimental observation of the “spurt” phenomenon with some precision. The flow curves involve linearly stable singular solutions, but some assumptions on the dynamics of the spurt process are required. These assumptions are tested by a semi-implicit finite element solution technique which allows solutions to be efficiently integrated over the very long time-scale involved. The Johnson-Segalman model with added Newtonian viscosity is used in the calculations. It is found that the assumptions required to model spurf are satisfied by the dynamic model. The dynamic model also displays a characteristic “latency time” before the spurt ensues and a characteristic “shape memory” hysteresis in load/unload cycles. These as well as other features of the computed solutions should be observable experimentally. We conclude that constitutive equations with shear stress extrema are not necessarily flawed, that their predicted behavior may appear to be arrested “wall slip”, and that such behavior may actually have been observed already.
120 citations
TL;DR: In this paper, a model bearing is described which is 20.0 mm in diameter and 2.5 mm in length; a short bearing of diameter to length ratio 8.5 is used, and the rotor may be run true or eccentric on its own shaft; in each case the mean load and frictional (tangential) force is measured as the centreline eccentricity is varied.
Abstract: A model bearing is described which is 20.0 mm in diameter and 2.5 mm in length; a short bearing of diameter to length ratio eight. The clearance is large (500 μm) and the rotor may be run true or eccentric on its own shaft; in each case the mean load and frictional (tangential) force is measured as the centreline eccentricity is varied. Comparison is made between the lubricating performance of Newtonian and highly elastic liquids; the latter give load enhancement ratios of up to 300 and reductions in coefficient of friction by factors of the order 30. These effects are greatly in excess of those obtained when dealing with bearing of diameter to length ratio close to unity; possible reasons for this are discussed. A Newtonian oil and a polymer-thickened oil are tested in the same way, the latter oil is found to give load enhancement ratios of 1.4 (true rotor) and 3.5 (eccentric rotor) with corresponding reductions of coefficients of friction by factors of 1.5 (true rotor) and 3.0 (eccentric rotor). Such effects had not previously been observed when using oils in the internal cylinder geometry (journal bearing type) although somewhat similar effects have been found in the external cylinder and squeeze film geometries. The rheological properties of the polymer-thickened solutions are measured and the relevance of the results to friction and load bearing discussed.
111 citations
TL;DR: In this article, the linear stability of a two-layer Couette flow of upper convected Maxwell liquids is considered and a linearly stable arrangement can be achieved by placing the less viscous fluid in a thin layer to stabilize longwaves and using elasticities to stabilize shortwaves.
Abstract: The linear stability of a two-layer Couette flow of upper convected Maxwell liquids is considered. The fluids have different densities, viscosities, and elasticities, with surface tension at the interface. At low speeds, the interfacial mode may become unstable, while other modes stay stable. The shortwave asymptotics of the interfacial mode is analyzed. It is found that an elasticity difference can stabilize or destabilize the flow even in the absence of a viscosity difference. As the viscosity difference increases, the range of elasticities for which there is shortwave stability widens. A linearly stable arrangement can be achieved by placing the less viscous fluid in a thin layer to stabilize longwaves and using elasticities to stabilize shortwaves. Such an arrangement can be stable even when the density stratification is adverse.
TL;DR: In this paper, the theoretical and experimental consequences of slip phenomena are reviewed, and it is maintained that future progress will depend heavily on productive interplay between fluid mechanics and materials science.
Abstract: Non-Newtonian fluid mechanics is often distinguished from its Newtonian counterpart by the additional requirement that a constitutive equation be specified as part of the problem statement. For some modeling problems important to polymer processing, a wall boundary condition in which provision is made for slip is also a necessary ingredient. This requires that attention be directed to microscopic processes influencing flow behavior on a macroscopic scale. In this paper theoretical and experimental consequences of slip phenomena are reviewed. It is maintained that future progress will depend heavily on productive interplay between fluid mechanics and materials science.
TL;DR: In this paper, a new mixed algorithm for calculating viscoelastic flow is proposed, where the coupling between velocity and stress components is solved by means of multiple bilinear stress sub-elements embedded in the Lagrangian element for the velocity field while streamline upwinding is used for solving the advection dominated constitutive equations.
Abstract: In a recent paper, Marchal and Crochet have proposed a new mixed algorithm for calculating viscoelastic flow. The coupling between velocity and stress components is solved by means of multiple bilinear stress sub-elements embedded in the Lagrangian element for the velocity field while streamline upwinding is used for solving the advection dominated constitutive equations. The paper reviews the motivation and the contents of the new method and explores in detail the flow of Oldroyd-B, Phan Thien-Tanner and Giesekus-Leonov fluids through a circular abrupt contraction. No limitation based on the value of the Weissenberg number has been found for the calculation of such flows. The sensitivity of the macroscopic flow features upon a variation of the material parameters is also investigated.
TL;DR: In this paper, the effects of extensional viscosity and first normal stress difference in axisymmetric flows were studied and it was shown that a high Trouton's ratio leads to vortex enhancement in an abrupt 4:1 circular contraction and to drag increase for the flow round a sphere moving along the axis of a circular tube.
Abstract: By including the dependence of the viscosity function upon the third as well as the second invariant in the flow equation governing generalized Newtonian and viscoelastic fluids, it is possible to isolate the effects of extensional viscosity and first normal stress difference in axisymmetric flows. It is shown that a high Trouton's ratio leads to vortex enhancement in an abrupt 4:1 circular contraction and to drag increase for the flow round a sphere moving along the axis of a circular tube. For low values of elasticity, it is shown that the first normal stress difference has the opposite effect.
TL;DR: In this article, the nonlinear viscoelastic behavior of aqueous solutions consisting of a cationic detergent, cetyltrimethylammonium bromide, and sodium salicylate as an added salt was examined with varying salt concentration.
Abstract: Nonlinear viscoelastic behavior of aqueous solutions consisting of a cationic detergent, cetyltrimethylammonium bromide, and sodium salicylate as an added salt was examined with varying salt concentration. The nonlinear properties varied markedly with varying C*S, the concentration of free salicylate ion not caught in the detergent-salt complex. The systems with low C*S exhibited a kind of strain-hardening: the shear relaxation modulus, G(t, γ), increased with increasing magnitude of strain, γ; the shear stress, σI(t, γ . ) increased enormously and exhibited a marked overshoot at the start of shear flow of high rate of shear, γ . . The nonlinear behavior of systems with high C*S is somewhat similar to those of polymeric liquids: G(t, γ) decreased with increasing γ; the ratio σI(t, γ . / γ . was always a decreasing function of γ . . On the other hand, σI(t, γ . ) at high γ . exhibited a damped oscillatory behavior, which has not been reported for most of the polymeric systems. Evidently the viscoelastic properties cannot be described by the integrated constitutive equation with strain-dependent memory function which are suitable for polymeric liquids.
TL;DR: In this paper, a steady state analysis and a linear stability analysis for three-dimensional flow disturbances have been conducted using a modified convected Maxwell model, with shear-rate dependent viscosity and fluid characteristic time.
Abstract: In order to understand the role of viscoelasticity on draw resonance in the isothermal film casting process, a steady state analysis and a linear stability analysis for three-dimensional flow disturbances have been conducted. The constitutive equation used is a modified convected Maxwell model, with shear-rate dependent viscosity and fluid characteristic time. The numerical results indicate that the flow is stable below a lower critical draw ratio and above an upper critical draw ratio. Shear thinning in viscosity reduces the lower critical draw ratio and somewhat increases the upper critical draw ratio—thereby enlarging the region of instability. Slower shear reduction in fluid characteristic time dramatically decreases the upper critical draw ratio but has no significant effect on the lower critical draw ratio; therefore, fluids with higher characteristic time are more stable.
TL;DR: In this paper, a modified upper-convected Maxwell (MUCM) model is proposed which partially alleviates this difficulty and yields stress fields that reduce to the a symptotic expressions for a Newtonian fluid near singularities at non-deformable boundaries.
Abstract: Calculations of viscoelastic flows using the upper-convected Maxwell (UCM) model in geometries which include sharp corners or moving and free liquid/fluid contact lines are known to be non-convergent with mesh refinement. A modified upper-convected Maxwell (MUCM) model is proposed which partially alleviates this difficulty. The MUCM model is derivable from network theory and allows the fluid relaxation time to decrease at increasing values of the trace of the stress tensor. The MUCM model yields stress fields that reduce to the a symptotic expressions for a Newtonian fluid near singularities at non-deformable boundaries. Calculations using a Galerkin finite element method are presented for the planar stick-slip problem of the flow between two no-slip surfaces joined to two shear-free surfaces. Results for fine meshes show the correct asymptotic behavior near the singularity for the MUCM model and converge to much higher values of the Deborah number than for the UCM model. However, the results for the MUCM model are still constrained by numerical instabilities related to approximating the stress behavior near the singularity.
TL;DR: In this paper, the critical strain-rate for bond scission was found to depend on molecular weight as (M W ) −2, in agreement with the theoretical predictions of the bead-norm model.
Abstract: Recent experimental investigations have shown that large macromolecules can be fully stretched and fractured in an extensional flow. In this situation, the critical strain-rate for bond scission was found to depend on molecular weight as (M W ) −2 , in agreement with the theoretical predictions of the beadrod model. One of the conditions prerequisite to full chain extension is that the residence time at the appropriate strain-rate must be much larger than the terminal relaxation time of the macromolecule. If this requirement is not fulfilled, chain fracture could still occur at sufficiently high strain-rate, but in a partially uncoiled state. In the present studies we have measured the critical strain-rate for chain scission in transient extensional flow of extremely sharp PS fractions dissolved in dekalin at the θ-temperature. The molecular weight range investigated varied from 2.86 × 10 6 to 426,000. The critical strain-rate for chain scission was found experimentally to scale as (M W ) −0.95 instead of (M W ) −2 as predicted for stagnant extensional flow. Our results are in good accord with a recent theory for rupture of partly extended coils. Even in the partially uncoiled state, the degraded macromolecules showed a remarkable propensity for chain halving, indicating that midchain scission in flow is a general property that is not uniquely reserved to the fully extended chain.
TL;DR: In this paper, a constitutive equation of the K.K.B.Z. type is used to describe the flow behavior of LDPE melts in abrupt contractions and the numerical algorithm is the finite element method based on a fixed mesh while the strain history is calculated along streamlines.
Abstract: A constitutive equation of the K.B.K.Z. type is used to describe the flow behavior of LDPE melts in abrupt contractions. The numerical algorithm is the finite element method based on a fixed mesh while the strain history is calculated along streamlines. It is shown that the calculations based on the K.B.K.Z. model do predict the occurrence of vortices at relatively low values of the Weissenberg number, which in general is not the case with other less realistic models.
TL;DR: In this article, the authors presented flow visualization and flow birefringence results for polystyrene and low density polyethylene (LDPE) in planar entry flow for contraction ratios of 4 : 1 and 8 : 1.
Abstract: Both flow visualization and flow birefringence results are presented for polystyrene and low density polyethylene (LDPE) in planar entry flow for contraction ratios of 4 : 1 and 8 : 1. It was found that vortex growth was a different function of Weissenberg number ( We ) for each polymer and hence fluid elasticity could not be solely used to account for the onset and growth of vortices. Based on extensional stress measurements along the centerline,a normalized by means of the down-stream wall shear stress, it was proposed that vortex growth and intensity are a function of the extensional viscosity and to some degree the shear viscosity. In particular, LDPE, which exhibits a strain hardening extensional viscosity and an early onset of shear-thinning, exhibits large and intense vortices while polystyrene, which does not exhibit strain hardening, exhibits only small low intensity vortices. The purpose of the study was to emphasize the importance of a fluid's extensional properties, relative to its shear properties, in determining entry flow behavior.
TL;DR: In this paper, the authors presented a truncated set of three first-order quasilinear hyperbolic equations for the time-dependent fiber-spinning problem, which admits an analytic steady-state solution which exactly reproduces the high Deborah number viscoelastic limit behaviors.
Abstract: The one-dimensional approximation to the time-dependent fiber spinning equations for an upper-convected Maxwell model is shown to consist of a set of four first-order quasilinear hyperbolic equations. The sign of the characteristics is shown to validate the customarily assigned boundary conditions for the time-dependent problem. A truncated set of three equations is presented which admits an analytic steady-state solution which exactly reproduces the Newtonian and high Deborah number viscoelastic limit behaviors. In the truncated set, the hyperbolic character of the equations is preserved and the previous results of a linear stability analysis at zero Reynolds number are well approximated. The normal forms of both the full and truncated fiber spinning equations are derived which are used to formulate stable numerical schemes in the companion paper [1].
TL;DR: The results from numerical calculations for steady shear, start-up and cessation of steady shears, and the stress relaxation after a step shear stain are discussed in detail for a bead-spring chain model with consistently averaged hydrodynamic interaction between the beads and consistently averaged finite extensible springs.
Abstract: The results from numerical calculations for steady shear, the start-up and cessation of steady shear, and the stress relaxation after a step shear stain are discussed in detail for a bead-spring chain model with consistently averaged hydrodynamic interaction between the beads and consistently averaged finite extensible springs. Calculations are made for a large range of spring stiffnesses 10 ⩽ b ⩽ ∞ and a hydrodynamic interaction strength h* = 0.15 a value which has been estimated from experimental results. This model is found to satisfy the Hassager-Bird and the Lodge-Meissner relations.
TL;DR: In this article, the authors describe the utilization of idealized stagnation point extensional flows, produced by opposed jets, for birefringence visualization of induced molecular strain and flow resistance measurements, and identify rheological changes associated with the coil-stretch transition which occurs beyond a critical strain-rate in elongational flow fields.
Abstract: We describe the utilization of idealized stagnation point extensional flows, produced by opposed jets, for birefringence visualization of induced molecular strain and flow resistance measurements. We identify rheological changes associated with the coilstretch transition which occurs beyond a critical strain-rate in elongational flow-fields. In dilute solutions of monodisperse atactic polystyrene, increases in extensional viscosity are observed as isolated molecules become stretched. The largest increases in extensional viscosity, however, are found only beyond a critical concentration and strain rate, and are associated with the stretching of transient networks of interacting molecules. These results parallel similar effects seen in porous media flow and capillary entrance experiments. We determine the molecular weight dependence of the critical concentration which scales as M−0.55 in agreement with pairwise interaction of coils, but is much lower than conventional values of the critical polymer concentration, c*. We believed that polydispersity may play an important role in the development of such transient networks, and in controlling the degradation behaviour during flow.
Journal Article•
TL;DR: In this article, the results obtained from a series of experiments dealing with the flow of four polydimethylsiloxanes (PDMS) having different molecular characteristics through an orifice die are reported.
Abstract: The results obtained from a series of experiments dealing with the flow of four polydimethylsiloxanes (PDMS) having different molecular characteristics through an orifice die are reported. A particular orifice die has been chosen for its convenience in view of numerical simulation. The use of adequate methods of visualization has permitted us to obtain the structure of both stable and unstable recirculating vortices developing upstream of the orifice, and to measure the velocity profiles on the axis by analysing the photonegatives. The whole set of experimental results, including rheometrical data and the measurement of the total pressure loss, permits the evaluation of non-dimensional parameters typical of the flow. The effect of shear-thinning, elongation, and elasticity have been quantified and discussed by using current results available in the literature. Finally, this study provides a fundamental experimental basis, which may be quite useful for the validation of numerical models using appropriate constitutive laws relative to mixed flows of viscoelastic materials with axisymetrical boundaries.
TL;DR: In this paper, a theoretical analysis is presented which brings steady laminar film flow of power-law fluids within the framework of classical boundary layer theory, and an exact similarity solution for the velocity field in the film boundary layer is thus made available.
Abstract: A theoretical analysis is presented which brings steady laminar film flow of power-law fluids within the framework of classical boundary layer theory. The upper part of the film, which consists of a developing viscous boundary layer and an external inviscid freestream, is treated separately from the viscous dominated part of the flow, thereby taking advantage of the distinguishing features of each flow region. It is demonstrated that the film boundary layer developing along a vertical wall can be described by a generalized Falkner-Skan type equation originally developed for wedge flow. An exact similarity solution for the velocity field in the film boundary layer is thus made available. Downstream of the boundary layer flow regime the fluid flow is completely dominated by the action of viscous shear, and fairly accurate solutions are obtained by the Von Karman integral method approach. A new form of the velocity profile is assumed, which reduces to the exact analytic solution for the fully-developed film. By matching the downstream integral method solution to the upstream generalized Falkner-Skan similarity solution, accurate estimates for the hydrodynamic entrance length are obtained. It is also shown that the flow development in the upstream region predicted by the approximate integral method closely corresponds to the exact similarity solution for that flow regime. An analytical solution of the resulting integral equation for the Newtonian case is compared with previously published results.
TL;DR: In this paper, the authors investigated the rheology and the associated changes that arise in sheared molecular and colloidal liquids and demonstrated the importance of hydrodynamic coupling between macromolecule trajectories at high packing fractions.
Abstract: The rheology and the associated changes that arise in sheared molecular and colloidal liquids are investigated by Molecular and Brownian Dynamics Computer Simulation. Significant shear thinning and normal pressure effects occur in all liquids when the shear rate approximately equals an inverse characteristic relaxation time for the material. The shear and bulk moduli, and self-diffusion coefficients increase with shear rate for all liquids and stable dispersions. The importance for rheology of hydrodynamic coupling between macromolecule trajectories at high packing fractions is demonstrated. The infinite frequency moduli depend on the packing fraction to a power which is effectively the same for all materials, i.e. ca. 3.5, above a percolation transition at a packing fraction 0.25. The suspending fluid enhances the degree of shear thinning above that of the corresponding single component fluid consisting of pure macroparticles.
TL;DR: In this paper, the rheological properties of rubber carbon black compounds are studied in various shear flow histories, including stress relaxation, transient and steady state shear flows, and stress relaxation after steady flow.
Abstract: The rheological properties of rubber carbon black compounds are studied in various shear flow histories. In particular we studied (i) stress relaxation, (ii) transient and steady state shear flow, (iii) stress relaxation after steady flow, (iv) sequential shear flow history, (v) storage effects, (vi) programmed step shear histories. At low carbon black concentrations, the rheological response is similar in character to that of unfilled elastomers. For carbon black concentrations of 20 percent by volume and above, the compounds exhibit yield values which increase with carbon black concentration and decreasing particle size. The rubber carbon black compounds exhibit ‘hysteresis loops’ in programmed step shear histories and rheological property growth in storage experiments.
TL;DR: The measured viscosity of semi-dilute solutions at low strain rates agree qualitatively with a theory developed by Doi and Edwards describing the strain-thinning behavior of semi ofilute rigid rod solutions and quantitatively with Batchelor's theory.
Abstract: Effective uniaxial extensional and biaxial extensional viscosities of dilute and semi-dilute solutions of collagen, a rigid rod molecule, have been measured with an opposing jet apparatus. The concentration of collagen in the glycerin/water solvent ranged from 50 to 2300 ppm. The data agree quantitatively with a theory developed by Batchelor describing the extensional viscosity of perfectly aligned rigid rods. The viscosity measured for the dilute rigid rod solutions is independent of the rate of strain as predicted by Batchelor's theory. Data taken on the semi-dilute, strain-thinning solutions at strain rates sufficiently high to align the rods in the extension direction also agree with the predictions of Batchelor's theory. The measured viscosity of semi-dilute solutions at low strain rates agree qualitatively with a theory developed by Doi and Edwards describing the strain-thinning behavior of semi-dilute rigid rod solutions.