Presence Of Viscoelasticity Research Articles

A new perspective on static bifurcations in the presence of viscoelasticity

This manuscript explores the effect of viscoelasticity on static bifurcations: such as pitchfork, saddle-node, and transcritical bifurcations, of a single-degree-of-freedom mechanical oscillator. The viscoelastic behavior is modeled via a differential form, where the extra degree of freedom represents the internal force provided by the viscoelastic element. The governing equations are derived from a simplified lumped parameter model consisting of a rigid rod incorporating a viscoelastic element and subjected to axial and transverse forces at the free end, in addition to an external time-varying moment applied to the rod. In order to study the effect of viscoelasticity on bifurcation diagrams, the equations of motion are non-dimensionalized. Next, a review of static bifurcations in the absence of viscoelasticity is conducted, followed by an examination of the effect of viscoelasticity on the bifurcation diagrams. Finally, this paper investigates the effects of viscoelasticity on the transient behavior of the oscillator. Results show that the Deborah number, which measures the ratio of the viscoelastic time constant to the natural periodic time of the system, controls the duration of time needed to maintain oscillations around an unstable point before jumping to a stable equilibrium point.

Dynamic Response of a Cracked Viscoelastic Anisotropic Plane Using Boundary Elements and Fractional Derivatives

Abstract The aim of this study is to develop an efficient numerical technique using the non-hypersingular, traction boundary integral equation method (BIEM) for solving wave propagation problems in an anisotropic, viscoelastic plane with cracks. The methodology can be extended from the macro-scale with certain modifications to the nano-scale. Furthermore, the proposed approach can be applied to any type of anisotropic material insofar as the BIEM formulation is based on the fundamental solution of the governing wave equation derived for the case of general anisotropy. The following examples are solved: (i) a straight crack in a viscoelastic orthotropic plane, and (ii) a blunt nano-crack inside a material of the same type. The mathematical modelling effort starts from linear fracture mechanics, and adds the fractional derivative concept for viscoelastic wave propagation, plus the surface elasticity model of M. E. Gurtin and A. I. Murdoch, which leads to nonclassical boundary conditions at the nano-scale. Conditions of plane strain are assumed to hold. Following verification of the numerical scheme through comparison studies, further numerical simulations serve to investigate the dependence of the stress intensity factor (SIF) and of the stress concentration factor (SCF) that develop in a cracked inhomogeneous plane on (i) the degree of anisotropy, (ii) the presence of viscoelasticity, (iii) the size effect with the associated surface elasticity phenomena, and (iv) finally the type of the dynamic disturbance propagating through the bulk material.

On the tails of probability density functions in Newtonian and drag-reducing viscoelastic turbulent channel flows

Direct numerical simulations (DNS) of Newtonian and drag-reducing viscoelastic turbulent channel flows generate crucial data to analyze and understand the nature of turbulence and its modification due to viscoelasticity. Such an understanding is necessary to enable better drag reduction technologies. Previously (Samanta et al., Phys. Fluids, 21, 115106, 2009) we have shown that viscoelasticity can significantly alter the non-Gaussian character of the probability density functions (PDFs) of many of the turbulent statistics in the flow. In this work, we investigate further the non-Gaussian characteristics of the PDFs generated in viscoelastic turbulence by focusing on their tail behavior. In particular, we show that many of the tails of the PDFs of the velocity and its derivatives obey a power law, as opposed to an exponential one exhibited by Gaussian PDFs, with power law indices that sometimes, for viscoelastic flows, are low enough to imply unbounded fourth- (kurtosis), or even third-(skewness) moments of the distribution, what we can call “strong fat tails” behavior. We use Hill's estimator to evaluate the power law index of the tails, as well as statistical inference methods to perform hypothesis testing for the appropriateness of the power law fit. We have found that fat tails corresponding to power law tail distribution behavior are observed in the PDFs for both Newtonian and viscoelastic cases. However, viscoelasticity leads to PDFs that exhibit consistently fatter tails than the Newtonian ones and it is only in the presence of viscoelasticity that turbulence leads to “strong fat tails” as defined above. We infer that drag-reducing viscoelastic turbulence involves more infrequent and more correlated and more extreme events which makes DNS of viscoelastic turbulent flows much more computationally demanding than Newtonian DNS, requiring finer spatial resolutions, longer integration times, and larger computational domain sizes.

Reduction of production rate in Y-shaped microreactors in the presence of viscoelasticity

The viscoelasticity effects on the reaction-diffusion rates in a Y-shaped microreactor are studied utilizing the PTT rheological model. The flow is assumed to be fully developed and considered to be created under a combined action of electroosmotic and pressure forces. In general, finite-volume-based numerical simulations are conducted to handle the problem; however, analytical solutions based on the depthwise averaging approach are also obtained for the case for which there is no reaction between the inlet components. The analytical solutions are found to predict accurate results when the width to height ratio is at least 10 and acceptable results for lower aspect ratios. An investigation of the viscoelasticity effect reveals that it is accompanied by a significant reduction of the production rate and the production efficiency, defined as the ratio of the average product concentration to the inlet concentration of the limiting reactant. In addition, this effect gives rise to a more uniform transport with more symmetric concentration distributions. The pressure effects on the reaction-diffusion rates are also pronounced in the presence of viscoelasticity. Finally, the influences of the product diffusivity are investigated for the first time revealing that the lower it is the thinner the area of significant production becomes.

Depletion of cross‐stream diffusion in the presence of viscoelasticity

An effort to analyze the viscoelasticity effects on transverse transport of neutral solutes between two miscible streams in an electrokinetic T‐sensor is presented. The analysis is based on an approximate analytical solution for the depthwise averaged concentration, assuming a channel of large width to depth ratio for which a one‐dimensional profile is sufficient for describing the velocity field. We show that the solution derived is surprisingly accurate even for very small channel aspect ratios and the maximum error reduces to only about 1% when the aspect ratio is 5. The developed model reveals that the mixing length for a viscoelastic fluid may be by far larger than that for a Newtonian fluid. Moreover, the Taylor dispersion coefficient for electroosmotic flow of viscoelastic fluids, which its determination is a main part of the analysis, is found to be an increasing function of both the elasticity level and the EDL thickness. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4533–4541, 2015

Electromechanical performance of a viscoelastic dielectric elastomer balloon

In this paper, we present a theoretical study about the effect of viscoelasticity on the electromechanical performance of a dielectric elastomer (DE) balloon. The thermodynamic dissipative model is given and the equation of motion is deduced by a free-energy method. It is found that when the balloon is only subject to the pressure or a static voltage, it may reach a state of equilibrium after the viscoelastic relaxation. When the static voltage exceeds a certain value, the balloon will never reach the equilibrium and be in failure eventually. When the voltage is sinusoidal, the balloon will resonate at multiple frequencies. The study result indicates that the natural frequency is independent on the viscoelasticity. However, the presence of viscoelasticity can reduce the amplitude and increase the mean stretch of the DE.

Thermal convection of dusty compressible Rivlin-Ericksen viscoelastic fluid with hall currents

An investigation is made on the effect of Hall currents and suspended particles on the hydromagnetic stability of a compressible, electrically conducting Rivlin-Ericksen elastico-viscous fluid. The perturbation equations are analyzed in terms of normal modes after linearizing the relevant set of hydromagnetic equations. A dispersion relation governing the effects of viscoelasticity, magnetic field, Hall currents, compressibility and suspended particles is derived. For the stationary convection Rivlin-Ericksen fluid behaves like an ordinary Newtonian fluid due to the vanishing of the viscoelastic parameter. Compressibility and magnetic field are found to have a stabilizing effect on the system whereas Hall currents and suspended particles hasten the onset of thermal instability. These analytic results are confirmed numerically and the effects of various parameters on the stability parameter are depicted graphically. The critical Rayleigh numbers and the wavenumbers of the associated disturbances for the onset of instability as stationary convection are obtained and the behavior of various parameters on critical thermal Rayleigh numbers has been depicted graphically. It has been observed that oscillatory modes are introduced due to the presence of viscoelasticity, suspended particles and Hall currents which were not existing in the absence of these parameters.

Time-evolution K–L analysis of coherent structures based on DNS of turbulent Newtonian and viscoelastic flows

The turbulent dynamics corresponding to direct numerical simulation (DNS) data of Newtonian and viscoelastic turbulent channel flows is analyzed here through a projection of a time sequence of velocity fields into a set of Karhunen–Loeve (K–L) modes, large enough to contain, on the average, more than 90% of the fluctuating turbulence kinetic energy. Previous calculations of the K–L eigenstructure have demonstrated a dramatic decrease in the K–L dimensionality accompanying the presence of viscoelasticity in turbulent channel flows. Projection of turbulent velocity information into the most energetic K–L modes allows for a significant data reduction, most suitable for the study of the time-evolution dynamics. We exploit this feature here in analyzing the time series of the projection coefficients of the velocity field into K–L modes to gain further quantitative insights into the behavior of the overall flow dynamics. The presence of viscoelasticity induces significant changes to the turbulence dynamics as compared to the Newtonian one obtained at the same friction Reynolds number. Namely, it cuts in half the representational entropy constructed from the projection coefficients whereas it doubles the fluctuating kinetic energy. Moreover, dynamic correlation analysis of pairs of K–L coefficients showed a systematic increase in the time scales characterizing dynamic turbulent events with viscoelasticity. These correlations have distinct pulse behavior characteristic of intermittence and quasiperiodicity. Correlations between K–L modes corresponding to different wavenumbers along the principal flow direction depend sensitively on the velocity of the moving frame of reference with respect to which they are calculated, and resonate at characteristic velocities corresponding to the convective velocities of the coherent structures to which the two modes contribute. Based on that, we propose a new two-dimensional analysis of those correlations with respect to both the time and the moving frame velocity in order to detect coherent flow structures and their mean convective velocity. Those show considerable differences when they are calculated with and without the presence of viscoelasticity.

Budgets of Reynolds stress, kinetic energy and streamwise enstrophy in viscoelastic turbulent channel flow

The budgets of the Reynolds stress, turbulent kinetic energy and streamwise enstrophy are evaluated through direct numerical simulations for the turbulent channel flow of a viscoelastic polymer solution modeled with the Finitely Extensible Nonlinear Elastic with the Peterlin approximation (FENE-P) constitutive equation. The influence of viscoelasticity on the budgets is examined through a comparison of the Newtonian and the viscoelastic budgets obtained for the same constant pressure drop across the channel. It is observed that as the extensional viscosity of the polymer solution increases there is a consistent decrease in the production of Reynolds stress in all components, as well as in the other terms in the budgets. In particular, the effect of the flow elasticity, which is associated with the reduction in the intensity of the velocity-pressure gradient correlations, potentially leads to a redistribution of the turbulent kinetic energy among the streamwise, the wall-normal and the spanwise directions. In this work, we also show that in the presence of viscoelasticity there is a significant reduction in all components of the production of streamwise enstrophy. This is consistent with a proposed mechanism for polymer-induced drag reduction through the inhibition of vortex stretching by the high extensional viscosity of the polymer solution.

SIMULATION OF THE PHASE OF ESTABLISHMENT OF THE RHEOMETRIC FLOW OF A VISCOELASTIC FLUID

The flow between two plates in the phase of establishment for the case of a viscoelastic fluid in comparison with a Newtonian fluid is investigated numerically and analytically. The quantitative and qualitative features of the flow are analyzed. It is noted that in a number of cases this flow has wave features, and it is determined that the presence of viscoelasticity usually increases the time of establishment of the flow. It is pointed out that some of the revealed features of the flow can be used in experimental investigations of non‐Newtonian fluids.

On Non‐Newtonian Flow Past a Cylinder in a Confined Flow

Consideration is given to the effect of viscoelasticity on the flow of non‐Newtonian liquids past a cylinder contained in a confined geometry. Both flow visualization and force measurements are discussed. It is shown that the proximity of a bounding wall near the cylinder results in a force on the cylinder at right angles to the mean flow direction and toward the wall. Over the range of flow conditions available, the total drag on the cylinder is reduced by the presence of viscoelasticity. This conclusion is shown to be true for ‘constant‐viscosity’ elastic liquids and also for those that exhibit substantial ‘shear thinning.’ To facilitate this, experiments are carried out on Newtonian liquids, Boger liquids, aqueous solutions of polyacrylamide, and aqueous solutions of Xanthan gum. Attempts to simulate numerically the flow in the cylinder problem using modern finite‐element techniques are shown to lead to qualitative agreement with the experimental observations.

Increased dynamic stiffness of trabeculae carneae from senescent rats.

Dynamic stiffness was measured in both adult and senescent Wistar rats using sinusoidal length perturbations from 17 to 40 Hz, superimposed on isometric contractions at low and below Lmax. The slope of the stiffness-tension relationship was found to be increased in senescent muscles of both sexes and at two different temperatures. The age dependence of the slope was independent of resting muscle length. The slope also exhibited frequency dependence and hysteresis that indicates the presence of viscoelasticity during activation. No age dependence was seen in peak active tension, peak dT/dt, or resting stiffness. The findings of this study, taken together with other studies that have shown a decreased shortening ability in the senescent muscle, explain in part the maintenance of active tension development in the face of decreased shortening ability associated with the senescent muscle.

Drag Reducing Properties of Polyphosphates

It is well known that small amounts of certain polymers of high molecular weight can substantially reduce the frictional losses in liquids during turbulent flow1,2. In capillaries3 the reduction can reach 50% or more at concentrations well below 100 parts per million by weight (p.p.m.w.). This effect has been observed with a wide range of organic materials, both of natural and synthetic origins. Although there is no completely satisfactory explanation for this phenomenon, there are a number of characteristics which most good drag reducing agents seem to have in common—for example, the presence of pronounced viscoelasticity even at very low concentrations, a few hundredths of a per cent4. As a result the presence of viscoelasticity may indicate potential drag reducing ability. In this connection a series of solutions was recently tested in our laboratory and it was observed that a dilute solution of potassium polyphosphate was highly viscoelastic. The solution exhibited a large recoil on cessation of stirring even at very low stirring rates. Furthermore, the shear viscosity showed a strong reversible dependence on shear rate. Consequently, it was decided to test for drag reducing ability.