Flow visualization of the elastic Taylor-Couette instability in Boger fluids

Flow visualization is performed on an elastically-dominated instability in several similar Boger fluids in Taylor-Couette flow. The onset and evolution of secondary flow are observed over a range of shear rates using reflective mica platelet seeding. Sequences of ambiently and sheet-illuminated images were digitally processed. Rotation of the inner cylinder was ramped from rest to its final value over a time on the order of a polymer relaxation time. Dilute solutions of high molecular weight polyisobutylene in oligomeric polybutene manifest a flow transition at a Deborah number, De _s = _s 1.5 with a Taylor number of 0.00022 in a cell with dimensionless gap ratio = 0.0963. At this transition, simple azimuthal shearing is replaced by steady, roughly square, axisymmetric counter-rotating vortices grossly similar to the well-known Taylor vortex flow that is observed at De _s = 0, Ta = 3612. At De _s = 3.75, Ta = 0.0014, an axisymmetric oscillatory secondary flow develops initially but is replaced by the steady vortices. At De _s = 7.5, Ta = 0.0054, the oscillatory and vortex flow coexist and possess an irregular cellular cross-section. A wide span of growth rates is observed: the ratio of onset to polymer relaxation time ranges from 170000 at De _s = 1.5 to O(10) at De _s > 5. The role of inertia was explored through changing the solvent viscosity. A transition similar to the one that occurs at De _s = 3.75, Ta = 0.0014, from the base azimuthal shearing flow to axisymmetric vortices, was also observed with a much lower viscosity fluid at De _s = 3.3, Ta = 74.     

Bifurcation phenomena in viscoelastic flows through a symmetric 1:4 expansion

In this work we present an investigation of viscoelastic flow in a planar sudden expansion with expansion ratio D/d = 4. We apply the modified FENE–CR constitutive model based on the non-linear finite extensibility dumbbells (FENE) model. The governing equations were solved using a finite volume method with the high-resolution CUBISTA scheme utilised for the discretisation of the convective terms in the stress and momentum equations. Our interest here is to investigate two-dimensional steady-state solutions where, above a critical Reynolds number, stable asymmetric flow states are known to occur. We report a systematic parametric investigation, clarifying the roles of Reynolds number (0.01 < Re < 100), Weissenberg number (0 < We < 100) and the solvent viscosity ratio (0.3 < β < 1). For most simulations the extensibility parameter of the FENE model was kept constant, at a value L² = 100, but some exploration of its effect in the range 100–500 shows a rather minor influence. The results given comprise flow patterns, streamlines and vortex sizes and intensities, and pressure and velocity distributions along the centreline (i.e. y = 0). For the Newtonian case, in agreement with previous studies, a bifurcation to asymmetric flow was observed for Reynolds numbers greater than about 36. In contrast viscoelasticity was found to stabilise the flow; setting β = 0.5 and We = 2 as typical values, resulted in symmetric flow up to a Reynolds number of about 46. We analyse these two cases in particular detail.     

Effect of purely elastic flow instability on molecular conformation and drag

Linear stability analysis has shown that viscoelastic creeping flow of an Oldroyd-B liquid through a sinusoidal channel is unstable to stationary, wall-localized and short wavelength perturbations [B. Sadanandan, R. Sureshkumar, Global linear stability analysis of non-separated viscoelastic flow through a periodically constricted channel, J. Non-Newtonian Fluid Mech. 122 (2004) 55]. In this work, time-dependent simulations are performed to determine the nonlinear evolution of finite amplitude disturbances in the post-critical flow regime. It is shown that a nonlinear transition, which is facilitated by a supercritical pitchfork bifurcation, establishes a finite amplitude state (FAS) in which the average polymer stretch is highly modulated. The maximum normal stress, observed at the channel nip, can increase by up to approximately 100% when the Weissenberg number, defined as the ratio of the fluid relaxation time to an inverse characteristic shear rate, is increased by only 10% beyond its critical value. This is attributed to the amplification of configurational perturbations by the base flow shear rate, which attains its maximum at the channel nip. The effect of finite chain extensibility on the critical condition and nonlinear instability is investigated using the FENE-CR model. The stabilizing effect of finite extensibility can be expressed through a renormalization of the Weissenberg number by accounting for the screening effect of the nonlinear force law on the transmission of configurational perturbations to polymeric stress. The principal features of the FAS are qualitatively model-independent. The FAS exhibits a small, but numerically perceptible increase in the friction factor as compared to the base flow. The implication of the findings on the experimentally observed flow resistance enhancement phenomenon in viscoelastic creeping flows through converging/diverging geometries is discussed.     

Gas displacement of polymer melts in a cylinder: Experiments and viscoelastic simulations

Series of isothermal gas-displacement of a polystyrene melt in a circular cylinder were performed. The experiments show an increase in the steady fractional coverage above a Newtonian level (m = 0.6) at very low Deborah numbers, where the melt behaves like a diluted un-entangled system. At higher Deborah numbers, where the melt behaves as an entangled melt system, the steady fractional coverage decreases.     

Analytical elasto-creep model of interfacial thermal stresses and strains in trilayer assemblies

A two-dimensional model has been developed for thermal stresses, elastic strains, creep strains, and creep energy density at the interfaces of short and long trilayer assemblies under both plane stress and plane strain conditions. Both linear (viscous) and non-linear creep constitutive behavior under static and cyclic thermal loading can be modeled for all layers. Interfacial stresses and strains are approximated using a combination of exact elasticity solutions and elementary strength of materials theories. Partial differential equations are linearized through a simple finite difference discretization procedure. The approach is mathematically straightforward and can be extended to include plastic behavior and problems involving external loads and a variety of geometries. The model can provide input data for thermal fatigue life prediction in solder or adhesive joints. For a typical solder joint, it is demonstrated that the predicted cyclic stress–strain hysteresis shows shakedown and a rapid stabilization of the creep energy dissipation per cycle in agreement with the predictions of finite element analysis.     

Solving viscoelastic problems with cyclic symmetry via a precise algorithm and EFGM

The paper combines a self-adaptive precise algorithm in the time domain with Meshless Element Free Galerkin Method (EFGM) for solving viscoelastic problems with rotationally periodic symmetry. By expanding variables at a discretized time interval, the variations of variables can be described more precisely, and iteration is not required for non-linear cases. A space-time domain coupled problem with initial and boundary values can be converted into a series of linear recursive boundary value problems, which are solved by a group theory based on EFGM. It has been proved that the coefficient matrix of the global EFG equation for a rotationally periodic system is block-circulant so long as a kind of symmetry-adapted reference coordinate system is adopted, and then a partitioning algorithm for facilitating parallel processing was proposed via a completely orthogonal group transformation. Therefore instead of solving the original system, only a series of independent small sub-problems need to be solved, leading to computational convenience and a higher computing efficiency. Numerical examples are given to illustrate the full advantages of the proposed algorithm. The project supported by the National Natural Science Foundation of China ((10421002, 10472019 and 10172024); NKBRSF (2005CB321704) and the Fund of Disciplines Leaders of Young and Middle Age Faculty in Colleges of Liaoning Province. The English text was polished by Yunming Chen.     

A viscoelastic fluid model for describing the mechanics of a coarse ligated plasma clot

Thrombi are formed at the end of a series of complex biochemical processes. There are various types of thrombi, and their rheological properties change depending on the conditions during clot formation. In this paper, a model for a particular type of clot, formed from human plasma, is proposed within a thermodynamic framework that recognizes that viscoelastic fluids possess multiple natural configurations.     

Slow visco-elastic flow past a cylinder in a rectangular channel

This paper is concerned with the flow of a visco-elastic liquid through a rectangular channel containing a cylindrical obstruction placed either in a symmetric or asymmetric position with respect to the centre of the channel. Numerical predictions of the flow are obtained using a well established finite element Galerkin mixed formulation. The influence of elasticity on the streamline pattern is found to be negligible, and one only observes changes due to different geometries, i.e. relative positions of cylinder and channel. However, both elasticity and a variable viscosity are found to have significant effects on the forces exerted on the cylinder.     

An analytical solution for a linear viscoelastic layer loaded with a cylindrical punch: Evaluation of the rebound indentation test with application for assessing viability of articular cartilage

A general closed-form solution for the so-called rebound indentation test’ is obtained for a cylindrical flat-ended punch indenting a linear viscoelastic layer lying on a rigid substrate. Under the assumption of time-independent Poisson's ratio, we derive closed-form analytical expressions for the contact force (in a displacement controlled regime) and for the indentation displacement (in a load-controlled regime) and we consider in detail the case of standard viscoelastic solid. Our results indicate that the rebound displacement (in other words the indentation displacement in the load-controlled stage) is independent of the relaxed elastic modulus and Poisson's ratio, and also of the layer's thickness. Our analytical solution can be used for layered samples of arbitrary materials exhibiting viscoelastic properties; however, since the rebound indentation test has been recently suggested for assessing the viability of biomedical materials, we have applied our theoretical framework to the identification of materials parameters from experiments on articular cartilage. In this context, we have found a pretty good agreement for the rebound deformation, even until the strain becomes relatively large.