Suppression of purely elastic instabilities in the torsional flow of viscoelastic fluid past a soft solid (original) (raw)
Related papers
2001
Previous experimental measurements and linear stability analyses of curvilinear shearing flows of viscoelastic fluids have shown that the combination of streamwise curvature and elastic normal stresses can lead to flow destabilization. Torsional shear flows of highly elastic fluids with closed streamlines can also accumulate heat from viscous dissipation resulting in nonuniformity in the temperature profile within the flow and nonlinearity in the viscometric properties of the fluid. Recently, it has been shown by Al-Mubaiyedh et al. ͓Phys. Fluids 11, 3217 ͑1999͔͒ that the inclusion of energetics in the linear stability analysis of viscoelastic Taylor-Couette flow can change the dominant mode of the purely elastic instability from a nonaxisymmetric and time-dependent secondary flow to an axisymmetric stationary Taylor-type toroidal vortex that more closely agrees with the stability characteristics observed experimentally. In this work, we present a detailed experimental study of the effect of viscous heating on the torsional steady shearing of elastic fluids between a rotating cone and plate and between two rotating coaxial parallel plates. Elastic effects in the flow are characterized by the Deborah number, De, while the magnitude of the viscous heating is characterized by the Nahme-Griffith number, Na. We show that the relative importance of these two competing effects can be quantified by a new dimensionless thermoelastic parameter, ⌰ϭNa 1/2 /De, which is a material property of a given viscoelastic fluid independent of the rate of deformation. By utilizing this thermoelastic number, experimental observations of viscoelastic flow stability in three different fluids and two different geometries over a range of temperatures can be rationalized and the critical conditions unified into a single flow stability diagram. The thermoelastic number is a function of the molecular weight of the polymer, the flow geometry, and the temperature of the test fluid. The experiments presented here were performed using test fluids consisting of three different high molecular weight monodisperse polystyrene solutions in various flow geometries and over a large range of temperatures. By systematically varying the temperature of the test fluid or the configuration of the test geometry, the thermoelastic number can be adjusted appreciably. When the characteristic time scale for viscous heating is much longer than the relaxation time of the test fluid ͑⌰Ӷ1͒ the critical conditions for the onset of the elastic instability are in good agreement with the predictions of isothermal linear stability analyses. As the thermoelastic number approaches a critical value, the strong temperature gradients induced by viscous heating reduce the elasticity of the test fluid and delay the onset of the instability. At even larger values of the thermoelastic parameter, viscous heating stabilizes the flow completely.
AIP Advances, 2012
Viscoelastically induced flow instabilities, via a simple planar microchannel, were previously used to produce rapid mixing of two dissimilar polymeric liquids (i.e. at least a hundredfold different in shear viscosity) even at a small Reynolds number. The unique advantage of this mixing technology is that viscoelastic liquids are readily found in chemical and biological samples like organic and polymeric liquids, blood and crowded proteins samples; their viscoelastic properties could be exploited. As such, an understanding of the underlying interactions will be important especially in rapid microfluidic mixing involving multiple-stream flow of complex (viscoelastic) fluids in biological assays. Here, we use the same planar device to experimentally show that the elasticity ratio (i.e. the ratio of stored elastic energy to be relaxed) between two liquids indeed plays a crucial role in the entire flow kinematics and the enhanced mixing. We demonstrate here that the polymer stretching dynamics generated in the upstream converging flow and the polymer relaxation events occurring in the downstream channel are not exclusively responsible for the transverse flow mixing, but the elasticity ratio is also equally important. The role of elasticity ratio for transverse flow instability and the associated enhanced mixing were illustrated based on experimental observations. A new parameter De ratio = De side / De main (i.e. the ratio of the Deborah number (De) of the sidestream to the mainstream liquids) is introduced to correlate the magnitude of energy discontinuity between the two liquids. A new De ratio-De main operating space diagram was constructed to present the observation of the effects of both elasticity and energy discontinuity in a compact manner, and for a general classification of the states of flow development.
Onset of transition in the flow of polymer solutions through deformable tubes
Physics of Fluids
Experiments are performed to investigate laminar-turbulent transition in the flow of Newtonian and viscoelastic fluids in soft-walled microtubes of diameter ∼400 μm by using the micro-particle image velocimetry technique. The Newtonian fluids used are water and water-glycerine mixtures, while the polymer solutions used are prepared by dissolving polyacrylamide in water. Using different tube diameters, elastic moduli of the tube wall, and polymer concentrations, we probe a wide range of dimensionless wall elasticity parameter Σ and dimensionless fluid elasticity number E. Here, Σ = (ρGR 2)/η 2 , where ρ is the fluid density, G is the shear modulus of the soft wall, R is the radius of the tube, and η is the solution viscosity. The elasticity of the polymer solution is characterized by E = (λη 0)/R 2 ρ, where λ is the zero-shear relaxation time, η 0 is the zero-shear viscosity, ρ is the solution density, and R is the tube radius. The onset of transition is detected by a shift in the ratio of centerline peak to average velocity. A jump in the normalized centerline velocity fluctuations and the flattening of the velocity profile are also used to corroborate the onset of instability. Transition for the flow of Newtonian fluid through deformable tubes (of shear modulus ∼50 kPa) is observed at a transition Reynolds number of Ret ∼ 700, which is much lower than Ret ∼ 2000 for a rigid tube. For tubes of lowest shear modulus ∼30 kPa, Ret for Newtonian fluid is as low as 250. For the flow of polymer solutions in a deformable tube (of shear modulus ∼50 kPa), Ret ∼ 100, which is much lower than that for Newtonian flow in a deformable tube with the same shear modulus, indicating a destabilizing effect of polymer elasticity on the transition already present for Newtonian fluids. Conversely, we also find instances where flow of a polymer solution in a rigid tube is stable, but wall elasticity destabilizes the flow in a deformable tube. The jump in normalized velocity fluctuations for the flow of both Newtonian and polymer solutions in soft-walled tubes is much gentler compared to that for Newtonian transition in rigid tubes. Hence, the mechanism underlying the soft-wall transition for the flow of both Newtonian fluids and polymer solutions could be very different as compared to the transition of Newtonian flows in rigid pipes. When Ret is plotted with the wall elasticity parameter Σ for different moduli of the tube wall, by taking Newtonian fluids of different viscosities and polymer solutions of different concentrations, we observed a data collapse, with Ret following a scaling relation of Ret ∼ Σ 0.7. Thus, both fluid elasticity and wall elasticity combine to trigger a transition at Re as low as 100 in the flow of polymer solutions through deformable tubes.
Physical Review E, 2007
The linear stability of viscoelastic ͑Oldroyd-B͒ film flow down an inclined plane lined with a deformable ͑neo-Hookean͒ solid layer is analyzed using low-wave-number asymptotic analysis and the Chebyshev-Tau spectral numerical method. The free surface of film flows of viscoelastic liquids, unlike that of their Newtonian counterparts, becomes unstable in flow down a rigid inclined surface even in the absence of fluid inertia, due to the elastic nature of the liquids. For film flow past a deformable solid, our low-wave-number asymptotic analysis reveals that the solid deformability has a stabilizing effect on the free-surface instability, and, remarkably, this prediction is insensitive to rheology of the liquid film, be it viscoelastic or Newtonian. Using the spectral numerical method, we demonstrate that the free-surface instability can be completely suppressed at all wave numbers when the solid becomes sufficiently deformable. For the case of pure polymeric liquids without any solvent, when the solid layer is made further deformable, both the free surface and the liquid-solid interface are destabilized at finite wave numbers. We also demonstrate a type of mode exchange phenomenon between the modes corresponding to the two interfaces. Importantly, our numerical results show that there is a sufficient range of shear modulus of the solid where both the modes are stable at all wave numbers. For polymer solutions described by the Oldroyd-B model, while the free-surface instability is suppressed by the deformable solid, a host of new unstable modes appear at finite Reynolds number and wave number because of the coupling between liquid flow and free shear waves in the solid. Our study thus demonstrates that the elastohydrodynamic coupling between liquid flow and solid deformation can be exploited either to suppress the free-surface instability ͑present otherwise in rigid inclines͒ in viscoelastic film flows, or to induce new instabilities that are absent in flow adjacent to rigid surfaces.
Transitional pathway to elastic turbulence in torsional, parallel-plate flow of a polymer solution
Journal of Fluid Mechanics, 2006
Multiple scenarios have been discovered by which laminar flow undergoes a transition to turbulence in Newtonian fluids. Here we show in non-Newtonian fluids a transition sequence to 'elastic turbulence' due to elasticity from polymers, with negligible inertia. Multiple dynamic states are found linking the base flow to 'elastic turbulence' in the flow between a rotating and stationary disk, including circular and spiral rolls. Also, a surprising progression from apparently 'chaotic' flow to periodic flow and then to 'elastic turbulence' is found. These transitions are found in experiments where either shear stress or shear rate is incrementally increased and then held at fixed values; the modes found following stable base flow are 'stationary ring', 'competing spirals', 'multi-spiral chaotic' and 'spiral bursting' modes, followed then by 'elastic turbulence'. Each mode has a distinct rheological signature, and accompanying imaging of the secondary-flow field (simultaneous with rheological measurement) reveals kinematic structures including stationary and time-dependent rolls. The time-dependent changes in the secondary-flow structure can be related to the time-dependent viscosity in the case of several of the modes. Finally, the effect of polymer concentration on the transitional pathway modes is studied systematically.
Journal of Fluid Mechanics, 1993
The stability of the viscometric motion of a viscoelastic fluid held between rotating parallel disks with large radii to small-amplitude perturbations is studied for the Oldroyd-B constitutive model. The disturbances are assumed to be radially localized and are expressed in Fourier form so that a separable eigenvalue problem results; these disturbances describe either axisymmetric or spiral vortices, depending on whether the most dangerous disturbance has zero or non-zero azimuthal wavenumber, respectively. The critical value of the dimensionless radius R* for the onset of the instability is computed as a function of the Deborah number De, a dimensionless time constant of the fluid, the azimuthal and radial wavenumbers, and the ratio of the viscosities of the solvent to the polymer solution. Calculations meant to match the experiments of McKinley et al. (1991) for a Boger fluid show that the most dangerous instabilities are spiral vortices with positive and negative angle that start at the same critical radius and travel outward and inward toward the centre of the disk; the axisymmetric mode also becomes unstable at only slightly greater values of R*, or De for fixed R*. The predicted dependence of the value of De for a fixed R* on the gap between the disks agrees quantitatively with the measurements of McKinley et al., when the longest relaxation time for the fluid at the shear rate corresponding to the maximum value of R* is used to define the time constant in the Oldroyd-B model. H / R < 1, and inertial effects are small enough that secondary motions are unimportant (Griffiths, Jones & Walters 1969; Hill 1972). An additional condition is that the flow does not become unstable by mechanisms caused by the non-Newtonian nature of the fluid. It is this type of instability that is the subject of this paper. A transition to time-dependent behaviour was first seen by Jackson, Walters & Williams (1984) in experiments with a Boger fluid in a parallel-plate rheometert. They t Boger fluids are highly elastic polymer solutions composed of a high-molecular-weight polymer dissolved in an almost Newtonian solvent with high viscosity. The viscosity of the fluid remains 16 FLM 255
Stress relaxation and elastic decohesion of viscoelastic polymer solutions in extensional flow
Journal of Non-Newtonian Fluid Mechanics, 1996
The evolution of the transient extensional stresses in dilute and semi-dilute viscoelastic polymer solutions was measured with a filament stretching rheometer of a design similar to that first introduced by Sridhar et al. The solutions were polystyrene-based Boger fluids which were stretched at constant strain rates in the range 0.6 ~< ~0 ~< 4 s -~ and to Hencky strains of ¢ > 4. The test fluids all strain-hardened and Trouton ratios exceeding 1000 were obtained at high strains. In addition to measuring the transient tensile stress growth, the decay of the tensile viscoelastic stress in the fluid column following cessation of uniaxial elongation was also monitored as a function of the total imposed Hencky strain and the strain rate. The measured relaxation functions were found to be significantly different from those observed following cessation of steady shear flow. The extensional stresses initially decayed very rapidly upon cessation of uniaxial elongation followed by a slower viscoelastic relaxation. For the most elastic fluids, partial decohesion of the fluid filament from the endplates of the rheometer was observed in tests conducted at high strain rates. This elastic instability is initiated near the rigid endplate fixtures of the device and it results in the progressive breakup of the fluid column into individual threads or 'fibrils' with a regular azimuthal spacing. These fibrils elongate and bifurcate as the fluid sample is elongated further. In tests conducted at the highest Deborah numbers, complete sample decohesion from the endplates and rapid elastic recoil were sometimes observed. The critical stress and strain at the onset of the instability were determined by monitoring the tensile force exerted by the filament, the sample radius, and were used to construct an approximate stability diagram. Flow visualization experiments using a modified stretching device showed that the instability develops as a consequence of an axisymmetry-breaking meniscus instability in the non-homogeneous region of highly deformed fluid near the rigid endplate.
Perspectives on viscoelastic flow instabilities and elastic turbulence
arXiv (Cornell University), 2021
Viscoelastic fluids are a common subclass of rheologically complex materials that are encountered in diverse fields from biology to polymer processing. Often the flows of viscoelastic fluids are unstable in situations where ordinary Newtonian fluids are stable, owing to the nonlinear coupling of the elastic and viscous stresses. Perhaps more surprisingly, the instabilities produce flows with the hallmarks of turbulence-even though the effective Reynolds numbers may be O(1) or smaller. We provide perspectives on viscoelastic flow instabilities by integrating the input from speakers at a recent international workshop: historical remarks, characterization of fluids and flows, discussion of experimental and simulation tools, and modern questions and puzzles that motivate further studies of this fascinating subject. The materials here will be useful for researchers and educators alike, especially as the subject continues to evolve in both fundamental understanding and applications in engineering and the sciences. I.
A transition occurring in ideal elastic liquids during shear flow
Journal of Non-newtonian Fluid Mechanics, 1988
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 coneand-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.
Elastic vs . inertial instability in a polymer solution flow
Europhysics Letters (EPL), 1998
The interrelation between elastic and inertial effects in destabilizing the flow of a polymer solution is studied experimentally. To achieve this goal, solution elasticity is varied by three orders of magnitude and a diagram of the flow states in a Couette-Taylor system is obtained. The regions of purely elastic and purely inertial flow instabilities and a crossover region between them are characterized. The main feature of the elastic instability, constant Deborah number at the instability threshold, is verified. An analogy between inertial and elastic flow transitions and dynamics is found and the concept of viscoelastic similarity is introduced.