Microstructures and rheology of micellar surfactant solution by Brownian dynamics simulation

In this paper, three-dimensional Brownian dynamics simulation has been conducted for dilute micellar surfactant solution under a steady shear flow. The rodlike micelle in surfactant solution is assumed as a rigid rod made up of lined-up beads. The Lennard–Jones potential and soft-sphere potential are employed and taken as the inter-bead potentials for end–end beads and interior–interior beads, respectively. The motion of the rodlike micelles is determined by solving the translational and rotational equations for each rod under hydrodynamic drag force, Brownian force and inter-rod potential force. Velocity Verlet algorithm has also been exerted in the simulation. The micellar network structure is formed at low shear rates and destroyed by high shear rates. The computed shear viscosities and the first normal stress coefficient represent shear thinning characteristics. The paper reveals the relation between rheology and microstructure of surfactant solution at different shear rates. The effect of surfactant solution concentration rested on the micellar structures and rheological properties has also been investigated.     

Thermomechanical response of a viscoelastic rod driven by a sinusoidal displacement

The forced vibrations of a rod of thermoviscoelastic material are studied. The rod is considered to be laterally insulated but not constrained, such that a one-dimensional analysis may be employed. Temperature dependence of the material properties and the resulting thermomechanical coupling effects are included. The vibrations are forced by the imposition of a sinusiodal displacement of known amplitude and frequency at one end of the rod. This problem corresponds to a dissipative material bonded to the surface of a relatively rigid, vibrating structure.Initial transient behavior is not considered. A steady-state response is found by means of a finite difference formulation. Material properties of a Lockheed solid propellant are used.The presence of critical frequencies, characterized by high stresses and temperatures, is found for small amplitudes of vibration. Nonlinearities and instabilities lead to a lack of one-to-one correspondence between stress and displacement boundary conditions. No relationship is found between the critical frequencies of the driven rod and the natural frequencies of a rod with an equivalent temperature profile.     

Viscoelastic properties of ultra-high viscosity alginates

Ultra-high viscosity alginates were extracted from the brown seaweeds Lessonia nigrescens (UHV_N, containing 61% mannuronate (M) and 2% guluronate (G)) and Lessonia trabeculata (UHV_T, containing 22% M and 78% G). The viscoelastic behavior of the aqueous solutions of these alginates was determined in shear flow in terms of the shear stress σ ₂₁, the first normal stress difference N ₁, and the shear viscosity η in isotonic NaCl solutions (0.154 mol/L) at T = 298 K in dependence of the shear rate [(g)\dot]\dot{\gamma} for solutions of varying concentrations and molar masses (3–10 × 10⁵ g/mol, homologous series was prepared by ultrasonic degradation). Data obtained in small-amplitude oscillatory shear (SAOS) experiments obey the Cox–Merz rule. For comparison, a commercial alginate with intermediate chemical composition was additionally characterized. Particulate substances which are omnipresent in most alginates influenced the determination of the material functions at low shear rates. We have calculated structure–property relationships for the prediction of the viscosity yield, e.g., η–M _w–c–[(g)\dot]\dot{\gamma} for the Newtonian and non-Newtonian region. For the highest molar masses and concentrations, the elasticity yield in terms of N ₁ could be determined. In addition, the extensional flow behavior of the alginates was measured using capillary breakup extensional rheometry. The results demonstrate that even samples with the same average molar mass but different molar mass distributions can be differentiated in contrast to shear flow or SAOS experiments.     

Contact problem for a plane crack under a normally incident antiplane shear wave

The contact-interaction problem for a stationary plane crack with friction between its edges under the action of a normal (to the crack plane) harmonic shear wave is addressed. Antiplane deformation conditions are considered. The distribution of contact forces and displacement discontinuity of crack edges are studied Published in Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 138–142, May 2007.     

A comparison of three different methods for measuring both normal stress differences of viscoelastic liquids in torsional rheometers

A novel pressure sensor plate (normal stress sensor (NSS) from RheoSense, Inc.) was adapted to an Advanced Rheometrics Expansion System rheometer in order to measure the radial pressure profile for a standard viscoelastic fluid, a poly(isobutylene) solution, during cone–plate and parallel-plate shearing flows at room temperature. We observed in our previous experimental work that use of the NSS in cone-and-plate shearing flow is suitable for determining the first and second normal stress differences N ₁ and N ₂ of various complex fluids. This is true, in part, because the uniformity of the shear rate at small cone angles ensures the existence of a simple linear relationship between the pressure [i.e., the vertical diagonal component of the total stress tensor (Π₂₂)] and the logarithm of the radial position r (Christiansen and coworkers, Magda et al.). However, both normal stress differences can also be calculated from the radial pressure distribution measured in parallel-plate torsional flows. This approach has rarely been attempted, perhaps because of the additional complication that the shear rate value increases linearly with radial position. In this work, three different methods are used to investigate N ₁ and N ₂ as a function of shear rate in steady shear flow. These methods are: (1) pressure distribution cone–plate (PDCP) method, (2) pressure distribution parallel-plate (PDPP) method, and (3) total force cone–plate parallel-plate (TFCPPP) method. Good agreement was obtained between N ₁ and N ₂ values obtained from the PDCP and PDPP methods. However, the measured N ₁ values were 10–15% below the certified values for the standard poly(isobutylene) solution at higher shear rates. The TFCPPP method yielded N ₁ values that were in better agreement with the certified values but gave positive N ₂ values at most shear rates, in striking disagreement with published results for the standard poly(isobutylene) solution.

On Shear and Torsion Factors in the Theory of Linearly Elastic Rods

Lower bounds for the factors entering the standard notions of shear and torsion stiffness for a linearly elastic rod are established in a new and simple way. The proofs are based on the following criterion to identify the stiffness parameters entering rod theory: the rod’s stored-energy density per unit length expressed in terms of force and moment resultants should equal the stored-energy density per unit length expressed in terms of stress components of a Saint-Venant cylinder subject to either flexure or torsion, according to the case. It is shown that the shear factor is always greater than one, whatever the cross section, a fact that is customarily stated without proof in textbooks of structure mechanics; and that the torsion factor is also greater than one, except when the cross section is a circle or a circular annulus, a fact that is usually proved making use of Saint-Venant’s solution in terms of displacement components.     

On Constructing the Unique Solution for the Necking in a Hyper-Elastic Rod

In this paper, a novel approach which considers gradient effects and uses non-deforming boundary conditions is adopted to construct the unique solution for necking in a hyper-elastic rod. We study the problem of the large axially symmetric deformations of a rod composed of an incompressible Ogden’s hyper-elastic material subject to a tensile stress (or a given displacement) when its two ends are fixed to rigid bodies. The attention is on the class of energy functions for which the stress–strain curve in the case of the uniaxial tension has a peak and valley combination. A phase-plane analysis is introduced to study the qualitative behaviour of the solutions. Then, by using the non-deforming conditions at two ends, the solutions corresponding to trajectories in different phase planes are obtained. It turns out that the non-deforming conditions play an important role in selecting the solutions. Further, by converting the problem into a displacement-controlled problem, the unique solution is obtained. The engineering strain and engineering stress curve plotted from our solution exhibits two interesting phenomena: (i) After the stress reaches the peak value there is a sudden stress drop; (ii) Afterwards it is followed by a stress plateau. Some mathematical explanations on these two phenomena are then given.     

A Generalized Piezoelectric Bernoulli–Navier Anisotropic Rod Model

We apply the asymptotic analysis procedure to the three-dimensional static equations of piezoelectricity, for a linear nonhomogeneous anisotropic thin rod. We prove the weak convergence of the rod mechanical displacement vectors and the rod electric potentials, when the diameter of the rod cross-section tends to zero. This weak limit is the solution of a new piezoelectric anisotropic nonhomogeneous rod model, which is a system of coupled equations, with generalized Bernoulli–Navier equilibrium equations and reduced Maxwell–Gauss equations.     

Rheo-PIV of a shear-banding wormlike micellar solution under large amplitude oscillatory shear

We explore the behavior of a wormlike micellar solution under both steady and large amplitude oscillatory shear (LAOS) in a cone–plate geometry through simultaneous bulk rheometry and localized velocimetric measurements. First, particle image velocimetry is used to show that the shear-banded profiles observed in steady shear are in qualitative agreement with previous results for flow in the cone–plate geometry. Then under LAOS, we observe the onset of shear-banded flow in the fluid as it is progressively deformed into the non-linear regime—this onset closely coincides with the appearance of higher harmonics in the periodic stress signal measured by the rheometer. These harmonics are quantified using the higher-order elastic and viscous Chebyshev coefficients e _n and v _n , which are shown to grow as the banding behavior becomes more pronounced. The high resolution of the velocimetric imaging system enables spatiotemporal variations in the structure of the banded flow to be observed in great detail. Specifically, we observe that at large strain amplitudes (γ ₀ ≥ 1), the fluid exhibits a three-banded velocity profile with a high shear rate band located in-between two lower shear rate bands adjacent to each wall. This band persists over the full cycle of the oscillation, resulting in no phase lag being observed between the appearance of the band and the driving strain amplitude. In addition to the kinematic measurements of shear banding, the methods used to prevent wall slip and edge irregularities are discussed in detail, and these methods are shown to have a measurable effect on the stability boundaries of the shear-banded flow.     

Shear banding during nonlinear creep with a solution of monodisperse polystyrene

Creep experiments with a solution of polystyrene (M _w = 2.6 MDa, 16 vol.%, 25 °C) in diethyl phthalate are reported for stresses between 100 and 2,500 Pa (≈ 3G _N ⁰/4). The aim was to look for a flow transition as reported for strongly entangled poly(isobutylene) solutions. The experiments with the polystyrene solution were repeated for cone angles of 2, 4, and 6° (radius 15 mm) and showed no dependence on cone angle. The Cox–Merz rule was not fulfilled for stresses beyond about 800 Pa. The tangential observation with a CCD camera showed that the edge took a concave shape because of the second normal stress difference. Beyond 1,000 Pa, the concave edge develops into a crevice, thus substantially reducing the effective cross-section. This leads to runaway in a constant torque experiment. At p ₂₁ = 800 Pa, head-on particle tracking confirms that the originally linear velocity profile takes a gooseneck shape, thus revealing shear banding. When the creep stress is stepped down to 100 Pa, this velocity profile evolves back to a linear one. The conclusion from this work is that even if nonlinear creep experiments are reproducible and a steady state is reached, this does not mean that the flow field is homogeneous. This paper was presented at Annual European Rheology Conference (AERC) held in Hersonisos, Crete, Greece, April 27–29, 2006.     

Analyzing the influence of compressibility on the rapid pressure–strain rate correlation in turbulent shear flows

The influence of compressibility on the rapid pressure–strain rate tensor is investigated using the Green’s function for the wave equation governing pressure fluctuations in compressible homogeneous shear flow. The solution for the Green’s function is obtained as a combination of parabolic cylinder functions; it is oscillatory with monotonically increasing frequency and decreasing amplitude at large times, and anisotropic in wave-vector space. The Green’s function depends explicitly on the turbulent Mach number M _t , given by the root mean square turbulent velocity fluctuations divided by the speed of sound, and the gradient Mach number M _g , which is the mean shear rate times the transverse integral scale of the turbulence divided by the speed of sound. Assuming a form for the temporal decorrelation of velocity fluctuations brought about by the turbulence, the rapid pressure–strain rate tensor is expressed exactly in terms of the energy (or Reynolds stress) spectrum tensor and the time integral of the Green’s function times a decaying exponential. A model for the energy spectrum tensor linear in Reynolds stress anisotropies and in mean shear is assumed for closure. The expression for the rapid pressure–strain correlation is evaluated using parameters applicable to a mixing layer and a boundary layer. It is found that for the same range of M _t there is a large reduction of the pressure–strain correlation in the mixing layer but not in the boundary layer. Implications for compressible turbulence modeling are also explored.      

Resonant vibrations of a hinged viscoelastic rectangular plate

The paper examines the effect of dissipative heating on the performance of a sensor in a hinged thermoviscoelastic rectangular plate undergoing resonant flexural vibrations. The thermoviscoelastic behavior of materials is described using the concept of complex characteristics. The coupling of the electromechanical and thermal fields is taken into account. The nonlinear problem is solved by the variational and Bubnov–Galerkin methods. The effect of the dissipative-heating temperature and the dimensions of the sensor on its performance during resonant vibrations of the plate is analyzed.     

The normal stress behaviour of suspensions with viscoelastic matrix fluids

 We investigate the variations in the shear stress and the first and second normal stress differences of suspensions formulated with viscoelastic fluids as the suspending medium. The test materials comprise two different silicone oils for the matrix fluids and glass spheres of two different mean diameters spanning a range of volume fractions between 5 and 25%. In agreement with previous investigations, the shear stress–shear rate functions of the viscoelastic suspensions were found to be of the same form as the viscometric functions of their matrix fluids, but progressively shifted along the shear rate axis to lower shear rates with increasing solid fraction. The normal stress differences in all of the suspensions examined can be conveniently represented as functions of the shear stress in the fluid. When plotted in this form, the first normal stress difference, as measured with a cone and plate rheometer, is positive in magnitude but strongly decreases with increasing solid fraction. The contributions of the first and the second normal stress differences are separated by using normal force measurements with parallel plate fixtures in conjunction with the cone-and-plate observations. In this way it is possible for the first time to quantify successfully the variations in the second normal stress difference of viscoelastic suspensions for solid fractions of up to 25 vol.%. In contrast to measurements of the first normal stress difference, the second normal stress difference is negative with a magnitude that increases with increasing solid content. The changes in the first and second normal stress differences are also strongly correlated to each other: The relative increase in the second normal stress difference is equal to the relative decrease of the first normal stress difference at the same solid fraction. The variations of the first as well as of the second normal stress difference are represented by power law functions of the shear stress with an unique power law exponent that is independent of the solid fraction. The well known edge effects that arise in cone-and-plate as well as parallel-plate rheometry and limit the accessible measuring range in highly viscoelastic materials to low shear rates could be partially suppressed by utilizing a custom- designed guard-ring arrangement. A procedure to correct the guard-ring influence on torque and normal force measurements is also presented. Received: 20 December 2000 Accepted: 7 May 2001     

Forced oscillations of a layer of a viscoelastic material under the action of a convective pressure wave

The longitudinal and transverse components of deformation of the surface of a flat layer of a viscoelastic material glued onto a solid base under the action of a traveling pressure wave are determined. The coating compliance is described by two components corresponding to two components of surface displacement. The dimensionless compliance components depend only on the viscoelastic properties of the material, the ratio of the wave length to the layer thickness λ/H, and the ratio of the wave velocity to the velocity of propagation of shear oscillations V/C _t ⁰ . Data on the dynamic compliance are presented for 0.3 < λ/H < 30 and 0.1 < V/C _t ⁰ < 10. The compliance is demonstrated to be determined by its absolute value and by the phase lag of strain from pressure. The effect of viscous losses in the material and compressibility of the latter on the dynamic compliance is analyzed. An anomalous behavior of the compliance with the wave velocity being greater than a certain critical value is explained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 90–97, March–April, 2007.     

A comparison of PIV measurements of canopy turbulence performed in the field and in a wind tunnel model

Particle image velocimetry (PIV) has been used to compare between turbulence characteristics just within and above a mature corn canopy and those of a model canopy setup in a wind tunnel (WT). The laboratory normalized mean velocity profile is adjusted using variable mesh screens to match the normalized mean shear of the corn field (CF) data. The smallest resolved scale in the field is about 15 times the Kolmogorov length scale (η_CF ≈ 0.4 mm), whereas in the WT it is 5 times η_WT (η_WT ≈ 0.15 mm). In both cases, the mean velocity and turbulence statistics are consistent with those measured using single point sensors. However, the profiles of normalized Reynolds shear stress in the field and the laboratory differ. Turbulent spectral densities calculated from PIV spatial and time series in the field display an inertial range spanning three decades. In the laboratory due to lower Reynolds numbers, the inertial range shrinks to two decades. Quadrant-Hole analysis is applied to Reynolds shear stress, vorticity magnitude and dissipation rates. In quadrants 1–3, the WT and field conditionally sampled stresses show similar trends. However, a conflicting trend is found in the sweep quadrant. The analysis confirms that sweep and ejections dominate the momentum flux and dissipation rate.The content of this paper, entitled “Applying PIV for Measuring Turbulence just within and above a Corn Canopy,” was presented at the 6th International Symposium on Particle Image Velocimetry at Pasadena, CA, USA, September 21–23, 2005.     

Stress and strain controlled rheometry on a concentrated lyotropic lamellar phase of AOT/Water/Iso-octane

We present the results of extensive strain- and stress-controlled rheometry performed on an AOT–water–iso-octane system, which forms lamellar structures with a high density of topological defects. In spite of different time-scales, both measurement methods, strain- and stress-controlled, are shown to be controlled by the level of strain experienced by the material. In both cases, after a complex transition, an apparent steady state is reached. Whereas both apparent steady states are identical for intermediate shear rate and shear stress following a power law, these are found to differ once the lower values of applied shear rate and shear stress are considered. The origin of this difference is discussed in terms of supplied energy to the sheared sample. I. Pignot-Paintrand is affiliated with The Université Joseph Fourier and member of the Institut de Chimie Moléculaire de Grenoble     

Basic equations of the theory of thermoviscoelastic plates with distributed sensors and actuators

The basic equations of the theory of thermoviscoelastic thin-walled plates with piezoelectric sensors and actuators under monoharmonic mechanical and electric loading are derived using the Kirchhoff–Love hypotheses. The thermomechanical behavior of passive and piezoactive materials is described using the concept of complex characteristics. Methods of solving nonlinear problems of active damping of thermomechanical vibrations of plates with sensors and actuators are considered. The effect of dissipative heating on the damping of axisymmetric vibrations of a thermoviscoelastic solid circular plate is analyzed as an example     

Applicability of normal and shear stress cells embedded in cohesionless materials

A normal stress cell and a shear stress cell have been designed and tested under very varied conditions including permanent strain. Results pooled from nine different tests with the cells embedded in cohesionless materials (sand and wheat) showed that the coefficient of variation of the normal stress-cell sensitivity was 0.04, while it was 0.10 for the shear cell. The agreement between predicted and measured sensitivity was considered to be good for the normal stress cell and reasonably good for the shear stress cell. The shear cell showed a systematic dependence, within acceptable limits, of the total stress state in the surrounding material. A qualitative explanation of this phenomenon is given. Paper was presented at the SEM VI International Congress on Experimental Mechanics held in Portland, OR in June 6–10, 1988.     

Asymptotic Profiles for the Blasius and Sakiadis flows in a Darcy–Brinkman Isotropic Porous Medium Either with Uniform Suction or with Zero Transverse Velocity

The Blasius and Sakiadis flows with uniform suction or with zero transverse velocity, at the asymptotic state, in a Darcy–Brinkman porous medium are investigated in this note. Exact analytical solutions are derived for velocity as well as for the integral quantities. It is found that both the dimensional and non-dimensional displacement thickness, momentum thickness, energy thickness and the absolute wall shear stress are identical in both Blasius and Sakiadis flows at the asymptotic state.     

Resonant vibrations of a clamped thermoviscoelastic rectangular plate with sensors and actuators

The paper discusses the active damping of the resonant flexural vibrations of a clamped thermoviscoelastic rectangular plate with distributed piezoelectric sensors and actuators. The thermoviscoelastic behavior of the passive and active materials is described using the concept of complex characteristics. The interaction of the mechanical and thermal fields is taken into account. The Bubnov–Galerkin method is used. The effect of self-heating, the dimensions of the piezoelectric inclusions, and the feedback factor on the effectiveness of active damping of the resonance vibrations of the plate is studied