Linear Viscoelastic Liquids Research Articles

Retarded hydrodynamic fluctuations effects on the light scattering spectrum and elastic moduli of a linear viscoelastic liquid

Fluctuating hydrodynamics (FH) is one of the theories that describes the dynamics of the fluctuations for fluids at mesoscopic scales. However, it is only valid for Markovian processes. Here we extend this approach for a viscoelastic liquid by using a generalized Langevin equation (GLE). We obyain general analytic expressions for the density fluctuations correlation function, the dynamic structure factor and the light scattering spectrum. In particular, we calculate the intermediate scattering function when the time memory and the noise correlation function are power-laws. We find that the difference in values of this quantity as functions of the viscoelasticity may be ∼62% and might be measurable.

Fractional Time Fluctuations in Viscoelasticity: A Comparative Study of Correlations and Elastic Moduli.

We calculate the transverse velocity fluctuations correlation function of a linear and homogeneous viscoelastic liquid by using a generalized Langevin equation (GLE) approach. We consider a long-ranged (power-law) viscoelastic memory and a noise with a long-range (power-law) auto-correlation. We first evaluate the transverse velocity fluctuations correlation function for conventional time derivatives and then introduce time fractional derivatives in their equations of motion and calculate the corresponding fractional correlation function. We find that the magnitude of the fractional correlation is always lower than the non-fractional one and decays more rapidly. The relationship between the fractional loss modulus and is also calculated analytically. The difference between the values of for two specific viscoelastic fluids is quantified. Our model calculation shows that the fractional effects on this measurable quantity may be three times as large as compared with its non-fractional value. The fact that the dynamic shear modulus is related to the light scattering spectrum suggests that the measurement of this property might be used as a suitable test to assess the effects of temporal fractional derivatives on a measurable property. Finally, we summarize the main results of our approach and emphasize that the eventual validity of our model calculations can only come from experimentation.

Rheological Characterization of Ethanolamine Gel Propellants

Ethanolamine is considered to be an environmentally friendly propellant system because it has low toxicity and is noncarcinogenic in nature. In this article, efforts are made to formulate and prepare ethanolamine gel systems, using pure agarose and hybrids of paired gelling agents (agarose + polyvinylpyrrolidine (PVP), agarose + SiO2, and PVP + SiO2), that exhibit a measurable yield stress, thixotropic behavior under shear rate ranges of 1–1,000 s−1 and a viscoelastic nature. To achieve these goals, multiple rheological experiments (including flow and dynamic studies) are performed. In this article, results are presented from experiments measuring the apparent viscosity, yield stress, thixotropy, dynamic strain, frequency sweep, and tan δ behaviors, as well as the effects of the test temperature, in the gel systems. The results show that the formulated ethanolamine gels are thixotropic in nature with yield stress between 30 and 60 Pa. The apparent viscosity of the gel decreases as the test temperature increases, and the apparent activation energy is the lowest for the ethanolamine-(PVP + SiO2) gel system. The dynamic rheology study shows that the type of gellant, choice of hybrid gelling materials and their concentration, applied frequencies, and strain all vitally affect the viscoelastic properties of the ethanolamine gel systems. In the frequency sweep experiment, the ethanolamine gels to which agarose, agarose + PVP, and agarose + SiO2 were added behave like linear frequency-dependent viscoelastic liquids, whereas the ethanolamine gel to which PVP + SiO2 was added behaves like a nearly frequency-independent viscoelastic solid. The variation in the tan δ of these gelled propellants as a function of frequency is also discussed.

Time periodic electroosmosis of linear viscoelastic liquids over patterned charged surfaces in microfluidic channels

In the present study, we aim to highlight the interactions between fluid rheology and interfacial electrokinetic phenomenon pertaining to time periodic electroosmotic flows of viscoelastic fluids, obeying linearized Maxwell model, over charge-modulated substrates. We successfully demonstrate that by altering the forcing frequency, fluid rheology, and charge-patterning characteristics, one may obtain drastically altered flow fields and hence mixing characteristics. Accordingly, we suggest that one may explore the paradigm of enhanced microfluidic mixing by exploiting the fluid rheology, supplementing the traditionally used methods such as topographical and geometrical modifications.

Rheological Characterization of Monomethylhydrazine Gels

In this paper, viscometry, yield stress, and small shear strain oscillation experiments on monomethylhydrazine gels are presented. The goal is to define a gel formulation with a measurable yield stress under low-shear conditions and shear-thinning behavior at shear rates representative of typical rocket injectors. Hydroxypropylcellulose, fumed silica, and a hybrid of the two materials are investigated as gelling agents for monomethylhydrazine. The two gel formulations that included hydroxypropylcellulose exhibited similar shear-thinning behavior with power-law flow indices of to 0.2. The pure fumed silica gel samples exhibited highly shear-thinning behavior with negative power-law flow indices indicative of thixotropic behavior. Tests performed after a preshear cycle showed shear-thinning power-law flow indices of . Unlike the pure hydroxypropylcellulose and hybrid gels, the fumed silica gel exhibited a well-defined, measureable yield stress. Small-strain oscillatory experiments showed that hydroxypropylcellulose and hybrid gels behave like linear viscoelastic liquids below a critical strain value, whereas the fumed silica gel behaves like a viscoelastic solid with a distinguishable yield stress. The phase angle of these gelled propellants is also discussed as a function of frequency, as are the implications of these results to the physical processes of interest.

Solvability of initial boundary value problems for equations describing motions of linear viscoelastic fluids

The nonlinear parabolic equations describing motion of incompressible media are investigated. The rheological equations of most general type are considered. The deviator of the stress tensor is expressed as a nonlinear continuous positive definite operator applied to the rate of strain tensor. The global‐in‐time estimate of solution of initial boundary value problem is obtained. This estimate is valid for systems of equations of any non‐Newtonian fluid. Solvability of initial boundary value problems for such equations is proved under some additional hypothesis. The application of this theory makes it possible to prove the existence of global‐in‐time solutions of two‐dimensional initial boundary value problems for generalized linear viscoelastic liquids, that is, for liquids with linear integral rheological equation, and for third‐grade liquids.

Measurement of the temperature rise in non-Newtonian oscillatory pipe flows

An experimental investigation of the temperature increase due to viscous dissipation in an oscillating pipe flow is presented. An oscillating pipe of circular section, acting as an extrusion die, was placed at the last stage of a polymer extrusion process and the increase in the temperature of the fluid, due to the superimposed oscillation, was measured. Thermocouples and a temperature control system were mounted on the walls of the oscillating section. Experimental results were obtained following the conditions suggested by Casulli et al. [J. Polym. Eng. Sci. 30 (1990) 1551]. Commercially available low density polyethylene was chosen as the experimental fluid. Results were obtained for the case when the imposed oscillatory motion was parallel to the axial direction of the flow. The bulk temperature of the fluid at the exit of the oscillating section was found to increase with the oscillating frequency and amplitude. If the dimensionless temperature increase is plotted as a function of the characteristic oscillation speed, the experimental results collapse into a single curve. In order to justify the experimental measurements, a theoretical analysis was performed for two simple non-Newtonian fluid models: linear viscoelastic and power-law liquids. Analytic expressions for the velocity and temperature fields were obtained. These models predicted an increase of the bulk temperature with the speed of oscillation in agreement with the experimental results. The direct comparison of the measurements and the predictions showed good order-of-magnitude agreement. We found that the temperature increase predicted using a linear viscoelastic model agrees well with the experiments for low oscillation speeds. For the case of large oscillation speeds, the prediction based on a power-law model resulted in a better agreement than the viscoelastic model prediction.

The equation of bubble dynamics in a compressible linear viscoelastic liquid

Several forms of the equation describing the radial motion of a spherical bubble in a compressible linear viscoelastic liquid are derived. The relative merits of these equations are discussed by using a three-parameter linear Oldroyd model to describe the non-Newtonian properties of the liquid.

Mechanical Behaviour of Linear Viscoelastic Liquids

AbstractThe mechanical properties of some amorphous materials can be described in terms of a modified anelastic element (MAE). The characteristics of this element, developed in a previous publication, are extended in order to describe the mechanical behaviour of linear viscoelastic liquids. This treatment leads to the modified standard linear liquid (MSLL). Through this phenomenological model the quasi‐static and dynamic moduli or compliances of viscoelastic liquids can be analytically expressed as a function of time or frequency. The parameters involved in the equations – γ, t0 or ω0, and η0 – are related to the width and the mean characteristic time of the relaxation or retardation spectrum and to the zero‐shear‐rate viscosity of the specimen. A procedure to determine the parameters of the MSLL from dynamical properties is proposed. It is applied to measurements in molten polypropylene (PP) given in the literature, and the results are discussed. Moreover, since the shape of the spectrum associated to the MSLL is quite similar to the well‐known log‐normal distribution function, also a comparison is done.

New insights into the viscoelasticity of glass

The behaviour of a linear viscoelastic liquid with finite compressibility is investigated theoretically and numerically. Some conditions for the generalized Maxwell model to give a consistent description of the different features of its phenomenology are given. Creep-recovery experiments are shown to be very valuable in evaluating the long-term part of the relaxation and the compressibility effect. These effects are investigated numerically in the case of soda-lime-silica glass in the transformation range. The possibility of modelling the stress relaxation in this material with the Kohlrausch-Williams-Watt function is questioned.

Enhancement of the drainage of non-Newtonian liquid films by oscillation

The flow of thin liquid films down an oscillating vertical surface is investigated both theoretically and experimentally for Newtonian and non-Newtonian liquids. The effects of the oscillation are explored analytically for Newtonian and linear viscoelastic liquids, and numerically for a generalized Newtonian liquid. The oscillatory motion has no net effect on the drainage of Newtonian and linear viscoelastic liquids, but enhancement is predicted for shear-dependent liquids. A gravimetric experiment is developed to check the theoretical predictions. The experiment enables the mass of liquid remaining on an oscillating glass tile to be monitored as a function of time. Good quantitative agreement between theory and experiments is shown for Newtonian liquids. For shear-thinning non-Newtonian liquids the experiments confirm that the predicted enhancement in the drainage occurs, in qualitative agreement with theory.

Back to the thermodynamic admissibility of creep-relaxation functions in linear viscoelasticity

The recent discussion on admissibility criteria for the kernels of linear viscoelastic liquids is completed by the results for viscoelastic solids. The necessary and sufficient conditions of thermodynamic admissibility are established. The class of thermodynamically admissible creep-relaxation functions is proved to be wider than it is usually supposed, including as well numerous nonmonotone and even locally negative functions. These nontraditional viscoelasticity kernels find applications in physics of heterogeneous materials, like for instance in mechanics and theology of composites.

Evaluation of unsteady Couette‐flow measurement under the influence of fluid inertia

The use of modern viscometers ensures that the inertia of the measuring device in unsteady rheometry is taken into account. This is made possible by appropriate viscometer design, or by considering the transmission function during the recording of data. On the other hand the inertia of the fluid in general is neglected in the evaluation of experiments. This leads to errors in the determination of material functions for liquids with low‐shear viscosities, such as dilute polymer solutions. For shear oscillatory experiments evaluation methods are presented for cylindrical and plane Couette flow which yield the complex viscosity of linear viscoelasticity taking into account fluid inertia. For cessation or inception of steady‐shear flow one has to assume a specific constitutive equation for linear viscoelastic liquids in order to develop a correct evaluation method. Relations are presented for Maxwell and Jeffreys fluids. For more complicated models a numerical evaluation method is outlined.

Heat and temperature effects on the light scattered from a viscoelastic liquid

A thermodynamic description of effects of relaxation processes in a viscoelastic-medium is presented. By using extended irreversible thermodynamics we calculate the isotropic light scattering spectrum of a linear viscoelastic liquid. We calculate the modifications on the longitudinal stress modulus produced by a relaxing heat flux. The implications of our approach are discussed and comparison with other work is also made.

Deformation Hardening and Thinning in Both Elongation and Shear of a Low Density Polyethylene Melt

Polymer melts show “thinning” in shear deformation and “hardening” in simple elongation; the latter phenomenon is especially pronounced for melts of branched polyethylene (LDPE). Elongation hardening and shear thinning are closely connected with the deformation histories in simple elongational and simple shear flows. These flows are used for material characterization, and they are adequate for purely viscous and purely linear viscoelastic liquids. For elastic liquids with slowly fading memory, however, the first principal stretch rate λ̇1(t) turns out to be a better reference than the components of the strain rate tensor, and λ̇1(t) is very different for the two conventional test modes, viz. simple elongation and simple shear. For a more relevant comparison of the rheological behavior in elongation and shear, we therefore deformed a LDPE melt at 150°C such that λ̇1(t) was the same in both test modes. The LDPE melt investigated showed hardening in elongation as well as in shear when λ̇1 increased exponentially with time, and the melt response was thinning in both elongation and shear when λ̇1 was kept constant, except for small total strains and strain rates at which the melt exhibited linear viscoelasticity.

Reflection of an obliquely incident S H plane wave at a plane interface between an elastic solid and a viscoelastic liquid

The results of numerical calculations are presented for the reflection coefficient of the shear horizontal (SH) plane waves incident on an elastic solid–viscoelastic liquid interface. The linear viscoelastic Maxwell liquid with one relaxation time is considered. The modulus and phase of the reflection coefficient as a function of incidence angle and frequency are determined numerically for typical parameters of the considered media. The validity of an approximate expression for the reflection coefficient is analyzed. Some new properties of the reflected SH wave are considered and discussed.

A continuum mechanics theory of depolarized and polarized Rayleigh-Brillouin light scattering spectra of supercooled liquids

On the basis of a constitutive equation appropriate for linear viscoelastic liquids, a continuum mechanics theory has been developed to consistently describe the polarized and depolarized light scattering spectra of viscoelastic liquids consisting of anisotropic molecules. The theory introduces the effect of the translation-rotational coupling in the hydrodynamic equations. It is shown that such a coupling results in reducing of the dynamic shear viscosity, the reduction of the dynamic shear viscosity thus makes the bulk viscosity dominant in determining the isotropic light scattering spectrum. The results are useful for interpreting the dynamic light scattering spectra of viscous and supercooled liquids.

Rheology of Ternary Mixtures of Styrene‐Butadiene Diblock Copolymer, Homopolybutadiene, and n‐Tetradecane

The effects of adding low‐molecular‐weight homopolybutadiene (hB) into solutions of a styrene‐butadiene (SB) diblock copolymer in n‐tetradecane (C14) on their rheology and microdomain structure are examined. In solutions of SB in C14, SB molecules form micelles with precipitated S blocks as the rigid cores and soluble B blocks as the cilia. These micelles form a macrolattice. The macrolattice is stabilized by a thermodynamic force that tends to keep the local concentration of B segments in the matrix phase as uniform as possible. Such a micellar solution having a macrolattice exhibits nonlinear dynamic behavior as well as plastic flow in steady shear. When hB is added to the solution, the solution loses its plasticity and becomes a linear viscoelastic liquid and the macrolattice becomes disordered. The mechanism of such a transition may be a result of the fact that the added hB acts as a buffer to compensate for the local concentration change induced by the lattice deformation and makes the macrolattice unstable. Solutions of SB in pure hB (with concentration below 35 wt % SB) are no longer plastic but linear viscoelastic. The solutions exhibit some slow relaxation processes, which are often called the second plateau. The mechanism of the SB in hB solutions that exhibit the second plateau is also discussed.

Slow nonstationary motions of viscoelastic liquids

The theory of linear viscoelastic liquids is developed by analogy with the theory of linear hereditary media in electrodynamics [1]. In a simplified description of the reduction of turbulent friction resistance in viscoelastic polymer solutions an important place is occupied by the problem of a plane moving parallel to itself [2–10]. Thus, in order to determine the damping of turbulence near a wall according to the Van Drist model, harmonic oscillations of a plate are considered [2]. In the Einstein-Lee model and the Dankwerts-Hanratty model the solution of the problem of flow near a suddenly starting plane is used. In the present study, using a linear approximation, we solve the problem of the frictional resistance of an unbounded plate moving in an arbitrary manner along the boundary of a half-space occupied by a viscoelastic liquid of general type. We find the consequences of the causality of the initial determining equations of the liquid and show that the resistance in viscoelastic liquids is less than in a viscous liquid. We give the results of calculations for the simplest models of a liquid.

ChemInform Abstract: STRESS RELAXATION MODULUS OF A COMMERCIAL GLASS

AbstractDer Spannungsrelaxationsmodul unter Kompression wurde an einem Behälterglas (71 Gew.% S102, 15 Na2O; 4,5 MgO; 8 CaO; 1,5 Al2O3) untersucht.