Constant-viscosity Elastic Liquids Research Articles

Steady streaming flows in viscoelastic liquids

We discuss experimental investigations on steady streaming flows of dilute and semi-dilute polymer solutions in microfluidic devices. The effect of non-Newtonian behavior on steady streaming for different model fluids is determined by characterizing the evolution of the inner streaming layer as a function of oscillation frequency using particle tracking velocimetry. We find that steady streaming velocity profiles in constant-viscosity elastic liquids are qualitatively similar to those in Newtonian liquids. Steady streaming velocity profiles in elastic liquids with strong shear thinning, however, display two unique features: (i) a non-monotonic evolution of the inner streaming layer with increasing frequency, first growing then decreasing in width, and (ii) a clear asymmetry in the flow profile at high frequencies.

Viscoelastic drops moving on hydrophilic and superhydrophobic surfaces

So-called “superhydrophobic” surfaces are strongly non-wetting such that fluid droplets very easily roll off when the surface is tilted. Our interest here is in understanding if this is also true, all else held equal, for viscoelastic fluid drops. We study the movement of Newtonian and well-characterised constant-viscosity elastic liquids when various surfaces, including hydrophilic (smooth glass), weakly hydrophobic (embossed polycarbonate) and superhydrophobic surfaces (embossed PTFE), are impulsively tilted. Digital imaging is used to record the motion and extract drop velocity. Optical and SEM imaging is used to probe the surfaces. In comparison with “equivalent” Newtonian fluids (same viscosity, density surface tension and contact angles), profound differences for the elastic fluids are only observed on the superhydrophobic surfaces: the elastic drops slide at a significantly reduced rate and complex branch-like patterns are left on the surface by the drop's wake including, on various scales, beads-on-a-string-like phenomena. The strong viscoelastic effect is caused by stretching filaments of fluid from isolated islands, residing at pinning sites on the surface pillars, of order ∼30 µm in size. On this scale, the local strain rates are sufficient to extend the polymer chains, locally increasing the extensional viscosity of the solution, retarding the drop.

THE MEASUREMENT OF THE FLOW AROUND A SPHERE SETTLING IN A RECTANGULAR BOX USING 3-DIMENSIONAL PARTICLE IMAGE VELOCIMETRY

A novel three-dimensional particle image velocimetry technique is used to measure the planar three-dimensional flow field about the centreline of a sphere sedimenting in a rectangular shaped box. Measurements are made in the center of the container and also one diameter from a plane wall. Results are presented for a sphere falling in both a constant viscosity elastic (Boger) fluid and a shear-thinning elastic liquid. In the center of the box, the flow field is essentially two-dimensional as expected. Near the wall, there is substantial out-of-plane motion in the shear-thinning solution due to the presence of the wall. Surprisingly, there is little out-of-plane motion for a sphere sedimenting near the wall in the Boger fluid. There are significant qualitative differences in the flow field for the sphere sedimenting in the shear-thinning and constant viscosity elastic liquids. The results are compared with previously published work for a sphere settling in a non-Newtonian fluid and also with results obtained in an identical geometry for a Newtonian fluid. Reasons for the differences in the velocity maps are discussed. The drag coefficient for each geometry and fluid is calculated.

The role of dynamic surface tension and elasticity on the dynamics of drop impact

The drop dynamics of Newtonian and non-Newtonian fluids on smooth surfaces is studied experimentally using a high-speed drum camera to make observations at 1000 frames s −1 . The spreading and recoil of the drops is studied predominantly on Parafilm M surfaces to determine the factors that suppress rebound on hydrophobic surfaces. Newtonian test fluids of varying shear viscosity and equilibrium surface tension were constructed to confirm the observations of drop dynamics by previous authors. Test fluids were also constructed with a similar shear viscosity and varying concentrations of surfactants to understand the contributing roles played by hydrodynamics and dynamic surface tension in surfactant solutions. The critical micelle concentration is found to be significant in determining whether the drop dynamics correlate with the dynamic surface tension data from the maximum bubble pressure apparatus. The influence of elasticity on drop recoil is also investigated using a carefully constructed group of elastic fluids of constant and equal shear viscosity. These constant viscosity elastic liquids were constructed by varying both the molecular weight and concentration of polymer, and the concentration of a Newtonian solvent to maintain a similar and constant shear viscosity. Both the increased molecular weight and concentration of polymer were found to be responsible for increased suppression of rebound on hydrophobic surfaces.

Swirling flow of viscoelastic fluids. Part 2. Elastic effects

A torsionally driven cavity has been used to examine the influence of elasticity on the swirling flow of constant-viscosity elastic liquids (Boger fluids). A wealth of phenomena is observed as the degree of inertia, elasticity and viscous forces are varied by using a range of low- to high-viscosity flexible polyacrylamide Boger fluids and a semi-rigid xanthan gum Boger fluid. As the inertia is decreased and elasticity increased by using polyacrylamide Boger fluids, the circulation rates for a ‘Newtonian-like’ secondary flow decreases until flow reversal occurs owing to the increasing magnitude of the primary normal stress difference. For each polyacrylamide fluid, the flow becomes highly unstable at a critical combination of Reynolds number and Weissenberg number resulting in a new time-dependent elastic instability. Each fluid is characterized by a dimensionless elasticity number and a correlation with Reynolds number is found for the occurrence of the instability. In the elasticity dominated flow of the polyacrylamide Boger fluids, the instability disrupts the flow dramatically and causes an increase in the peak axial velocity along the central axis by as much as 400%. In this case, the core vortex spirals with the primary motion of fluid and is observed in some cases at Reynolds numbers much less than unity. Elastic ‘reverse’ flow is observed for the xanthan gum Boger fluid at high Weissenberg number. As the Weissenberg number decreases, and Reynolds number increases, counter-rotating vortices flowing in the inertial direction form on the rotating lid. The peak axial velocity decreases for the xanthan gum Boger fluid with decreasing Weissenberg number. In addition, several constitutive models are used to describe accurately the rheological properties of the fluids used in this work in shear and extensional flow. This experimental investigation of a complex three-dimensional flow using well-characterized fluids provides the information necessary for the validation of non-Newtonian constitutive models through numerical analysis of the torsionally driven cavity flow.

Well-Characterized Low Viscosity Elastic Liquids

Abstract A series of low and constant viscosity elastic liquids are constructed and are studied rheologically. Steady shear viscosity and normal stresses, dynamic properties, and an apparent extensional viscosity are measured using well-established techniques. The rheological characteristics of the solution are used to help explain the physical basis for non-Newtonian phenomena in short time scale processes such as jet breakup, splash, spray atom-isation and swirling flow. It is demonstrated that even when the shear viscosity is maintained at a constant value, significant differences occur in processes due to the differences in the elasticity of the fluids. Some implications for these observations are discussed. The paper is an overview on our work on elastic effects in the flow of low viscosity fluids. It reflects the verbal presentation made at the Professor John D. Ferry Symposium at the 71st Annual Meeting of the Society of Rheology.

Influence of fluid elasticity on drops impacting on dry surfaces

The impact of Newtonian and non-Newtonian fluids on surfaces of varying and known roughness is studied experimentally using a high-speed drum camera to make observations at 1000 frames/s. A new technique was devised to establish when splash occurs on a hydrophilic surface. Experimental results for the onset of splash for Newtonian fluids agree with those of previous authors. The influence of elasticity on the onset of splash was examined using a carefully constructed group of elastic fluids of constant and equal viscosity. These constant viscosity elastic liquids were constructed by varying the polymer concentrations and Newtonian solvent concentrations to maintain a nearly constant shear viscosity and equilibrium surface tension. The apparent extensional viscosities for these materials increased dramatically with molecular weight. Great care was taken to eliminate the influence of dynamic surface tension. Photographs of the elastic fluid drops impinging on metal surfaces showed that the dilute polymer solutions exhibited splash and that the splash threshold increased with increasing Rouse relaxation time. All data obtained for the onset of splash can be collapsed onto a single functional relationship between the threshold for splashing and a dimensionless roughness parameter.

Viscoelastic fluid mechanics: Interaction between prediction and experiment

The extent to which elastic effects in the flow of viscoelastic fluids can be predicted is reviewed. For this purpose, constant-viscosity elastic liquids (Boger fluids) are used for observation where shear-rate-dependent viscosity effects and inertial effects can be eliminated. By comparing observations with predictions in squeeze film flows, jet flows, isothermal spinning, and for instabilities observed in various torsion flows, it is tempting to conclude that elastic effects in complex flows of viscoelastic fluids can be predicted with a relatively simple constitutive equation like the Oldroyd B model. However, this conclusion is not valid for flows for which the elongational rates are high or for regions of high stress concentration like tubular entry flows and creeping flow around a sphere. The importance of the elongational viscosity and its variation with strain rate in such, strong flows is clearly illustrated. Elongational viscosity is often a foreign concept in classical fluid mechanics, and hence its importance in viscoelastic fluid mechanics is stressed.

The effect of oscillation on the drainage of an elastico-viscous liquid

The oscillatory drainage of liquids simulated by the Oldroyd four-constant model is investigated using a numerical time-marching technique. The drainage of constant-viscosity elastic liquids is not significantly affected by the oscillatory motion whether applied parallel or orthogonal to the direction of the main flow. During the oscillatory drainage of shear-dependent elastic liquids, there is evidence of drainage enhancement and elastic recoil on applying the vibration parallel to the direction of the main flow. The recoil has the effect of thickening parts of the liquid film. On applying the vibration orthogonal to the direction of the main flow, for such liquids, enhancement is obtained for all film thicknesses.

Experimental removal of the re‐entrant corner singularity in tubular entry flows

Understanding the behavior of viscoelastic fluids in regions of high stress is an important generic problem in viscoelastic fluid mechanics, while understanding the re‐entrant corner singularity in tubular entry flow is of significant importance in the numerical solution of this important test problem. Two constant viscosity elastic liquids (Boger fluids) are used for making streakline photographic observations in the 4 to 1 circular contraction. The first fluid is the organically based international test fluid M1, constructed by dissolving polyisobutylene in polybutene using kerosene as a third solvent. The second fluid is a 0.03% polyacrylamide (Separan MG500) dissolved in corn syrup using water as the third solvent. Both fluids exhibit significant elasticity, while at the same time a constant viscosity. Each is used for flow visualization in an abrupt and in a rounded entry with a 2 mm radius. The nature of the secondary flow vortex is examined for both fluids with and without the rounded entry. Although both fluids are constant viscosity elastic liquids with about the same zero shear relaxation time, each reacts very differently to the rounded corner. Dramatic changes are observed for the polyacrylamide based elastic fluid while less dramatic results and changes, as a result of the rounded corner, are observed for the polyisobutylene based fluid. The differences are explained in terms of the extendability of the molecules in a solution relative to their configuration at equilibrium, which is dependent upon the polymer–solvent interaction.

The impact of ideal elastic liquids in the development of non-newtonian fluid mechanics

Research in non-Newtonian fluid mechanics has been characterized by the theoretical types (the left wing) who make predictions that cannot be observed and by the experimental types (the right wing), on the other hand, who make observations that no one can predict. In this paper, the authors demonstrate how the left wing and the right wing have been forced to interact as a result of the discovery and subsequent development of constant-viscosity elastic liquids, the so-called Boger fluids. They review the use of constant-viscosity elastic liquids in experimental programs to observe elastic effects in flows in the absence of fluid inertia and a shear rate dependent viscosity and show how these observations have motivated the numerical solutions of real problems. Particular attention is directed to tubular exit (spinning) flows and the interaction that has occured between observation and prediction.

The influence of rheological properties on the slow flow past spheres

The present communication is intended as part of a systematic investigation of the influence of rheological properties of various fluids upon the translational motion of a sphere. Drag measurements are presented for spheres of various diameters moving longitudinally with constant translational velocity, along the central axis of cylindrical containers of different radii. Four different types of fluids (based upon measurements of shear viscosity and first normal stress difference) are considered, namely Newtonian, viscoelastic, inelastic and constant viscosity-elastic liquids. The influence of each rheological property of these fluids upon the drag force is evaluated and analyzed. In the case of negligible wall effects, it is concluded that small perturbation theories provide an adequate description of the flow field for the creeping flow regime. The drag departure for viscoelastic liquids from the purely viscous Newtonian value has a quadratic dependence on the We number. Elastic effects are of primary importance at extremely low shear rates. For higher shear rates, shear thinning effects become predominant and an accurate drag prediction based on simple shear dependent viscosity values is presented. For non-Newtonian fluids, wall proximity effects are considerably reduced from the purely viscous Newtonian value. Both elasticity and shear thinning properties of the fluid contribute to that reduction. Elastic effects on the drag may be accounted for using Caswell's wall correction term derived from small perturbation theories for creeping flow and its validity exceeds the limit of small We numbers; this is substantiated by numerical techniques. Fluid elasticity diminishes wall effects but is a rapidly decreasing function, valid only for small We numbers and large sphere/container ratios. Beyond this region, shear thinning effects are predominant both upon the drag force and upon the wall correction term. These inelastic effects may be evaluated quite accurately using a modified version of Caswell's correction formula, which requires only a simple knowledge of the shear thinning viscosity function.

Further observations of elastic effects in tubular entry flows

The current understanding of tubular entry flows for Newtonian fluids and the influence of elasticity on these flows in the absence of shear thinning and significant fluid inertia is reviewed. While tubular entry flow for Newtonian fluids both with and without fluid inertia is now a solved problem, no single worker has been able to predict any of the significant elastic effects observed for constant viscosity elastic liquids in such flows. New elastic flow phenomena are reported which complicate the problem even more. Two distinctly different flow patterns are observed in a four to one contraction for two constant viscosity elastic fluids with essentially the same characteristics times. Tubular entry flows of elastic liquids develop (with increasing λγ) in the same way only if the contraction ratio is high enough. At sufficiently low contraction ratio, a lip vortex (at the tube entrance) and a corner vortex (in the upstream tube corner) can both be present and interacting with the lip vortex dominating the flow when vortex enhancement and growth occurs. The entry flow problem for elastic liquids is far more complex than originally imagined and is indeed a challenge for numerical simulation and selection of constutitive equations.