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Journal of RheologyVolume 48, Issue 1 (Jan-Feb 2004) |
Contents
An ellipsoidal drop model for single drop dynamics with non-Newtonian fluidsPier Luca Maffettonea) Francesco Greco AbstractA phenomenological model for the dynamics of a single drop immersed in an immiscible matrix is proposed with the two incompressible component liquids being in general viscoelastic. The model is formulated by assuming that the drop is always ellipsoidal, and the model parameters are determined once and for all in the small deformation limit. The model is thereafter applicable to whatever flow condition imposed at infinity, and for whatever intensity of the flow field. Predictions of steady state deformations, drop breakup, and drop relaxation display the effects of constitutive elasticity on drop dynamics. a) Author to whom all correspondence should be addressed. E-mail: pier.luca.maffettone@polito.it Structure scaling properties of confined nematic polymers in plane Couette cells: The weak flow limitM. Gregory Forest Qi Wang Hong Zhou Ruhai Zhou AbstractOne of the confounding issues in laminar flow processing of nematic polymers is the generation of molecular orientational structures on lengthscales that remain poorly characterized with respect to molecular and processing control parameters. For plane Couette flow within the Leslie-Ericksen continuum model, theoretical results since the 1970’s yield two fundamental predictions about the lengthscales of nematic distortion: a power law scaling behavior, Er-p, 1/4 ≤ p ≤ 1, where Er is the Ericksen number (ratio of viscous to elastic stresses); the exponent p varies according to whether the structure is a localized boundary layer or an extended structure. Until now, comparable results which incorporate molecular elasticity (i.e., distortions in the shape of the orientational distribution) have not been derived from mesoscopic Doi-Marrucci-Greco (DMG) tensor models. In this paper, we derive asymptotic, one-dimensional gap structures, along the flow-gradient direction, in “slow” Couette cells, which reflect self-consistent coupling between the primary flow, in-plane director (nematic) & order parameter (molecular) elasticity, and confinement conditions (plate speeds, gap height, and director anchoring angle). We then read off the small Deborah number, visco-elastic structure predictions: The flow is simple shear. The orientation structures consist of: 2 molecular-elasticity boundary layers with the Marrucci scaling Er-1/2, which are amplified by tilted plate anchoring; and a non-uniform, director-dominated structure that spans the entire gap, with Er-1 average length scale, present for any anchoring angle. We close with direct numerical simulations of the DMG steady, flow-nematic boundary-value problem, first to benchmark the small Deborah number structure formulas, and then to document onset of new flow-orientation structures as the asymptotic expansions become disordered. A new technique for reconstructing instantaneous velocity profiles from viscometric tests: Application to pasty materialsJ. C. Baudeza), S. Rodtsb), X. Chateaub), and P. Coussotb) a) Cemagref, Domaine des Palaquins b) Laboratoire des Matériaux et des Structures
du Génie Civil AbstractWe present a new technique for reconstructing the instantaneous velocity profiles during creep, dynamic or ramp tests under controlled stress in wide-gap Couette flows, from a series of similar tests under smaller stress amplitudes. This approach is based on a rigourous theory and, since it requires that the fluid does not flow close to the outer cylinder, is particularly suitable for yield stress fluids. The interest of this reconstruction technique is that it is simpler than direct techniques (NMR, Light Scattering, PIV, etc.) and has almost no limitations in time and space resolution. Thus one can obtain the velocity profiles under steady-state and transient flows. We show that for a commercial hair gel the velocity profile obtained with this technique is in excellent agreement with that found from MRI-rheometry within the range of measurement [4 decades of velocity]. From other tests with a mustard and a kaolin-water suspension we demonstrate that the “viscosity bifurcation” effect observed with various pasty materials [Coussot et al., Phys. Rev. Lett., 2002a] is directly associated with an abrupt change in the slope of the velocity profiles at the interface between the sheared and the unsheared regions. We also show that the effect of wall slip on the reconstructed velocity profile is to shift the level of the unsheared region to a virtual, constant, finite, velocity level. Microrheology of model quasi-hard-sphere dispersionsI. S. Sohn and R. Rajagopalana) Department of Chemical Engineering AbstractWe examine if a microrheological interpretation of probe diffusion in model dispersions dominated by excluded-volume interactions and hydrodynamics captures the underlying viscoelastic relaxation mechanisms reasonably accurately. Standard dynamic light scattering is used to measure mean-squared displacements (MSD) of visible probe particles in a refractive-index-matched model hard-sphere dispersion (poly(methyl methacrylate) particles in cycloheptyl alcohol). The loss and storage moduli of the dispersion are extracted as functions of frequency w from the measured MSDs. We suggest a semi-empirical modification of the generalized Stokes-Einstein relation to convert the MSD to the viscoelastic modulus G*(w). The results show a volume-fraction-dependent plateau G¥ at high frequencies in the storage modulus consistent with the domination of lubrication stresses. Viscoelasticity sets in at volume fractions f above 0.2, and for 0.2 < f < 0.45 the ratio of the mean viscoelastic relaxation time <t> to the Péclet time tp remains constant as had been observed previously for index-matched silica dispersions, but the microrheological measurements show a narrower spectrum of relaxation times. Master curves could be constructed for G*(w)/G¥ as sole functions of frequencies scaled with tp in the above volume-fraction range. The microrheological method used provides moduli over a large range of frequencies from single measurements and avoids the need for time-temperature superposition to reach high frequencies. The effects of fast relaxation phenomena caused by soft surface layers and the deviations from hydrodynamic interactions expected for ideal hard-sphere systems can also be examined. aa) Author to whom all correspondence should be addressed. E-mail: raj@che.ufi.edu On the polymer entropic force singularity and its relation to extensional stress relaxation and filament recoilEric S. G. Shaqfeha), Gareth H. McKinleyb), Nathanael Wooc), D. A. Nguyend), and Tam Sridhard) a) Departments of Chemical and Mechanical Engineering b) Department of Mechanical Engineering c) Scientific Computing and Computational Math Program d) Department of Chemical Engineering AbstractWe examine the use of transient extensional rheology as a means of examining worm-like and freely-jointed chain behavior of polymers in dilute solution at high extension. We demonstrate theoretically that both chain types follow different power-law stress decay functions for short times after cessation of strong extensional flow. The different power laws are universal for different strain and strain-rate histories and, moreover, are signatures of the singularities in the entropic-spring force laws that develop close to full extension. We also demonstrate that these power law exponents are directly related to the inertialess elastic recoil of an extensionally stretched filament of polymer solution. Finally, these theoretical predictions are compared to experimental results for the relaxation of stress following extension for monodisperse polystyrene solutions. When modeled as freely-jointed chains, we find excellent agreement with the theoretical predictions. Structural effects on the viscoelasticity of PDMS networks close to the sol-gel thresholdT. Tixier, Ph. Tordjemana), and G. Cohen-Solal P. H. Mutin AbstractPolydimethylsiloxane (PDMS) networks were obtained by hydrosilation of a difunctional vinylterminated PDMS prepolymer with three crosslinkers of different functionality and molecular weight. These samples were studied using dynamic viscoelastic experiments as a function of time and frequency. Critical parameters were determined close to and above the sol-gel threshold. Rheological master curves could be built for the three PDMS networks above the gel point. The results obtained suggest that the critical exponents are not universal and depend on the chemical structure of the incipient networks. a) Author to whom correspondence should be addressed. E-mail: tordjema@lain.univ-montp2.fr The effect of (2-hydroxypropyl)-β-cyclodextrinon rheology of hydrophobically end-capped poly(ethylene glycol) aqueous solutionsJiří Horskýa), Jana Mikešová, and Otakar
Quadrat Jaromír Šňupárek Abstract(2-Hydroxypropyl)-β-cyclodextrin (HPBCD), a modified cyclic oligosaccharide, changes the flow behavior of aqueous solutions of a model telechelic associative polymer, hydrophobically end-capped poly(ethylene glycol) (ODU-12), because the inclusion complexation of HPBCD and octadecyl end-capping groups interferes with aggregation of the polymer end groups. The HPBCD-induced decrease in the high-frequency modulus can be well described assuming a 1:1 binding isotherm, but cannot fully explain the decrease in the low shear rate Newtonian viscosity, because HPBCD also strongly decreases the relaxation time. Consequently, besides decreasing low shear rate Newtonian viscosity, HPBCD also extends the Newtonian behavior to higher shear rates as predicted by the free-path version of the transient network theory [ Marrucci et al. Macromolecules 26, 6483-6488 (1993)]. a) Author to whom correspondence should be addressed. E-mail: horsky@imc.cas.cz Elongational behavior of gelled propellant simulantsA. L. Yarina), E. Zussmana), A. Therona), S. Rahimib), Z. Sobeb), and D. Hasanb) a) Faculty of Mechanical Engineering b) Rafael, Manor Propulsion and Explosive Systems Division AbstractAn elongational rheometer is used to study the rheological behavior of gelled propellant simulants in uniaxial elongational flow. In simple shear such fluids typically exhibit a shear thinning behavior which could be described by a power-law constitutive equation. Knowledge of the elongational behavior of these fluids is important for understanding the processes of their atomization and spray formation. The results of the present work demonstrated that the 3D power-law model permits description of uniaxial elongation of these fluids as well. Moreover, the values of the rheological parameters of the tested fluids measured in simple shear and in uniaxial elongation agree fairly closely. Therefore the elongational behavior of gelled propellant simulants can be inferred from their shear behavior. Thermodynamic admissibility of the reptation modelScott T. Milner ExxonMobil Research and Engineering AbstractIn a recent paper, Ottinger and Beris assert that the celebrated Doi-Edwards (DE) model for entangled polymer dynamics is incompatible with the so-called “GENERIC” form of non-equilibrium thermodynamics. Simply put, they claim that the DE model for tube dynamics is inconsistent with the principle of virtual work. I show that with the correct choice of effective Hamiltonian, namely the full tube configurational entropy, the DE stress tensor does in fact result from a virtual work argument. Dynamic transitions and oscillatory melting of a two-dimensional crystal subjected to shear flowEdward J. Stancika), Anne L. Hawkinsona), Jan Vermantb), and Gerald G. Fullera,c) a) Department of Chemical Engineering b) Department of Chemical Engineering AbstractThe effect of a delicate balance of forces on the interparticle dynamics and structure of monodisperse spherical polystyrene particles suspended at the interface between decane and water was observed as shear flow was applied to the system. A strong dipole-dipole repulsion, due to ionizable surface sulfate groups, induces the particles to arrange themselves on a hexagonal lattice under quiescent conditions. The application of a shear flow to the interface, however, forces the lattice into a new semi-ordered, anisotropic state over which great control is exerted by particle concentration and applied shear rate. At low particle concentrations or high shear rates, the forces applied by the flow dominate the system and cause strings of particles to align in the flow direction to facilitate their movement past each other. A remarkable contrast to this behavior is seen at high concentrations or low shear rates, where the interparticle forces gain importance and tend to more strongly keep the particles in their lattice positions. Consequently, domains of particles are forced to rotate in the flow. The transition between these two regimes and the nature of this rotation, including an associated cyclic melting and crystallization of the lattice, is discussed. c) Author to whom all correspondence should be addressed. E-mail: ggf@stanford.edu Tensorial constitutive models for disordered foams, dense emulsions, and other soft nonergodic materialsM. E. Cates P. Sollich AbstractIn recent years, the paradigm of ‘soft glassy matter’ has been used to describe diverse nonergodic materials exhibiting strong local disorder and slow mesoscopic rearrangement. As so far formulated, however, the resulting ‘soft glassy rheology’ (SGR) model treats the shear stress in isolation, effectively ‘scalarizing’ the stress and strain rate tensors. Here we offer generalizations of the SGR model that combine its nontrivial aging and yield properties with a tensorial structure that can be specifically adapted, for example, to the description of fluid film assemblies or disordered foams. The Newtonian viscosity of concentrated stabilized dispersions: Comparisons with the hard sphere fluidD. M. Heyesa) H. Sigurgeirsson AbstractThe Newtonian shear viscosity, hs, of near-hard-sphere colloidal particle liquids from many sources at various packing fractions is compared with that of the pure hard sphere fluid which can be calculated essentially exactly by Molecular Dynamics, MD, computer simulations. The experimental relative viscosities for the colloidal systems, hs/h0 where h0 is the viscosity of the solvent, generally lie in between two curves formed from the hard sphere data, namely, hs/hB as an upper bound and the inverse self-diffusion coefficient, DB/D, as the lower bound, where hB and DB are the Boltzmann transport coefficients accurate at low densities. Brownian Dynamics simulation values of hs/h0 and D0/DL where DL is the long-time self-diffusion coefficient are close to this lower bound which indicates that Brownian motion alone without hydrodynamic interactions underestimates the viscosity of the system. Hydrodynamic effects increase the viscosity closer to the pure hard sphere curve obtained by MD. The ratio, D0/DL obtained from the experimental data increases slightly more rapidly than hs/h0 at high packing fractions. There is a near-linear relationship between the inverse viscosity (‘fluidity’) and self-diffusion coefficient with inverse packing fraction for the hard sphere fluid, the former proposed by Dymond (1974). This analytic form accounts reasonably well for the corresponding quantities of the colloidal systems as well. We analysed the values of the relative viscosities at 50 % packing fraction. We conclude that the value is ~ 40 for the pure hard sphere fluid itself from recent Molecular Dynamics simulations by of Sigurgeirsson and Heyes (2003), and probably ~ 25 ± 5 from experiments on real near-hard sphere colloids (although the experimental scatter is quite large), and ~ 10 by Brownian Dynamics computer simulations. For the long time self-diffusion coefficient the ratio is ~ 40 ± 10 for experimental colloidal systems, and ~ 10 from simulation by Molecular Dynamics and Brownian Dynamics. The infinite frequency shear viscosity has a ratio ~ 10 and the short-time self-diffusion coefficient ratio is ~ 4, both of which are somewhat lower than their ‘long time’ counterparts. The shear viscosity at finite shear rates in the second Newtonian plateau typically lies in between the values of the Newtonian viscosity and the infinite frequency viscosity (i.e., ~ 15±5). a) Author to whom all correspondence should be addressed. E-mail: d.heyes@surrey.ac.uk Interfacial elasticity and coalescence suppression in compatibilized polymer blendsEllen Van Hemelrijcka), Peter Van Puyveldela,d), Sachin Velankarb,c), Christopher W. Macoskob), and Paula Moldenaersa) a) K. U. Leuven, Department of Chemical
Engineering b) Department of Chemical Engineering and
Materials Science AbstractShear-induced coalescence was studied in immiscible blends of polydimethylsiloxane (PDMS) and polyisoprene (PI) with a droplet-matrix morphology, using both rheology and scanning electron microscopy. Dynamic moduli of the blends compatibilized with different amounts of a PDMS-PI diblock were measured. The experimental results indicate that the blend response is characterized by two relaxation mechanisms. The general Palierne model with an interfacial shear modulus was used to analyze the data, since this model can describe the dynamic response of polymer blends in which interfacial tension gradients induce an extra relaxation mechanism besides droplet relaxation. Scanning electron microscopy was used to investigate the droplet size evolution in the blends during coalescence. For systems with a high amount of compatibilizer, it is shown that coalescence is completely suppressed under the conditions studied here. c)
Present address: Department of Chemical and Petrochemical Engineering,
University of Pittsburgh, Pittsburgh, PA 15261, USA Understanding the complex rheological behavior of PEO-PPO-PEO copolymers in aqueous solutionJean-Pierre Habasa,c), Emmanuel Paviea), Alain Lappb), and Jean Peyrelassea) a) Laboratoire de Physico-Chimie des Polymêres b) Laboratoire Léon
Brillouin, CEA Saclay AbstractThe viscoelastic properties of a 4-branched poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) copolymer in aqueous solutions have been studied in all parts of its phase diagram. In the unimer zone, the solution behaves like a Maxwellian fluid. The formation of micelles induces the presence of a secondary relaxation process on the dynamic mechanical response of the system. When the micelles condense into a crystalline body centered structure, the solution exhibits rheological properties similar to the behavior of an entangled polymer. The crystal’s terminal relaxation time t is strongly dependent on the value of the stress used in the dynamic mechanical test. Stress-time relationships can also be observed with yield stress measurements. First of all, the structural origin of these phenomena has been explored. The relevance of several already proposed mechanisms has been analyzed and discrepancies between rheological results and SANS experiments discussed. We have been able to demonstrate that the evolution of the crystalline phase’s terminal relaxation time with stress can be described with an approach derived from Eyring’s theory. Moreover, this rheological relaxation time has been interpreted as being characteristic of a micelle’s diffusion in a crystalline structure. Finally, the values of the diffusion length and the intermicellar energy have been calculated and compared to already existing theories. c) Author to whom correspondence should be addressed. E-mail: jean-pierre.habas@univ-pau.fr |
Please e-mail suggestions and comments to albertco@umche.maine.edu. Updated 25 January 2004 |