Volume 56, Issue 1, January 2012
Index of content:
A sequence of physical processes determined and quantified in large-amplitude oscillatory shear (LAOS): Application to theoretical nonlinear models56(2012); http://dx.doi.org/10.1122/1.3662962View Description Hide Description
The nonlinear yielding responses of three theoretical models, including the Bingham, a modified Bingham, and Giesekus models, to large-amplitude oscillatory shear are investigated under the framework proposed recently by Rogers et al. (2011). Under this framework, basis states are allowed to wax and wane throughout an oscillation, an approach that conflicts directly with the assumptions of all Fourier-like linear algebraic approaches. More physical yielding descriptions of the nonlinear waveforms are attained by viewing the responses as representing purely elastic to purely viscous sequences of physical processes. These interpretations are compared with, and contrasted with, results obtained from linear algebraic analysis methods: Fourier-transform rheology; and the Chebyshev description of the so-called elastic and viscous stress components σ′ and σ″. Further, we show that the discrepancies between the built-in model responses and parameters, and the interpretations of the Chebyshev and Fourier coefficients are directly related to misinterpretations of σ′ and σ″ as being the elastic and viscous stress contributions. We extend these ideas and discuss how every linear algebraic analysis is likely to conflate information from predominantly elastic and viscous processes when a material yields.
Rheology of surface-modified titania nanoparticles dispersed in PDMS melts: The significance of the power law56(2012); http://dx.doi.org/10.1122/1.3669646View Description Hide Description
We investigated the rheology of titanium dioxide (TiO2) nanoparticles with various surface modifications in neat and binary blends of polydimethylsiloxane(PDMS) homopolymers of different molecular weights (4 k–77 k). The dispersions for bare, octadecyl-(C18), and PDMS-grafted particles reflect different interaction forces. For bare particles, the relative viscosity decreases monotonically with increasing melt M w or increasing fraction of long chains (f), consistent with thicker adsorbed layers. The octadecyl(C18)-grafted dispersions show no dependence on melt M w or f, suggesting that the alkyl groups prevent polymeradsorption or bridging. Therefore, the van der Waals attractions are cut off at a separation on the order of twice the thickness of the C18 chains (≈5 nm), regardless of melt M w or f. The PDMS-grafted suspensions show an increase in relative viscosity with increasing melt M w or f, consistent with wetted polymer brushes for P < N and dewetted layers for P > N. The power law we developed previously fits the shear-rate dependent viscosities with a structural relaxation time that scales with the magnitude of the attraction, thereby reflecting the microscale dynamics.
The effect of interfacial slip on the dynamics of a drop in flow: Part I. Stretching, relaxation, and breakup56(2012); http://dx.doi.org/10.1122/1.3663379View Description Hide Description
Using a numerical method based on the boundary-integral technique, we assess the impact of interfacial slip on the dynamics of deformation and breakup of a single drop subjected to a uniaxial extensional flow under creeping-flow conditions. Interfacial slip is incorporated in our continuum development as a jump in the tangential velocity across the interface. This velocity jump is shown to reduce to the Navier-slip boundary condition to leading order and is characterized by a dimensionless slip coefficient , where is thickness of the diffuse interface between the liquids, is the viscosity of the interfacial region, is the viscosity of the suspending fluid, and is the drop radius. A key contribution of this paper is the development of a stable, boundary-integral formulation to incorporate interfacial slip into existing, no-slip boundary-integral frameworks for dropdeformation. Slip has a fourfold impact on the drop stretching, relaxation, and breakup phenomena. First, when the capillary number is small, the steady deformation of the drop with slip is smaller than the no-slip result, and the difference increases with the viscosity ratio and the capillary number. Slip thus leads to larger critical capillary numbers beyond which the drop stretches continuously in the extensional flow. Second, for capillary numbers greater than the critical value, we find that the shape of the deformeddrop for the same drop elongation is relatively insensitive to the slip coefficient, but the time required to reach this deformation is a strong function of the slip coefficient—slip slows down the deformation process. Third, the end-pinch mechanism of drop breakup leads to a different number and sizes of droplets with the inclusion of slip. Finally, slip causes the capillary-instability mechanism of drop breakup to produce larger drops at faster rates relative to the no-slip case. In addition to the above results, we also show that slip moderates the viscosity and normal stress differences in a sheared, dilute emulsion. Our study has important implications in the area of blending of immiscible polymers and indicates that the drop size distribution, which ultimately governs the material properties of the blend and composites prepared from it, is influenced strongly by interfacial slip.
56(2012); http://dx.doi.org/10.1122/1.3670732View Description Hide Description
The viscoelasticproperties of fluids are key to their performance in industries ranging from biotechnology to the automotive industry. Traditionally, fluid viscoelasticproperties are monitored with rheometers but these are expensive, require a skilled operator, function over a relatively limited frequency range and are not suitable for in situ monitoring. Piezoelectric cantilevers capable of in situ assessment of the rheological properties of relatively small fluid volumes have the potential to overcome many of these limitations and can be fabricated into low cost probes. Rheological assessment of test fluids using piezoelectric cantilevers is typically made through analysis of the cantilever’s resonant oscillation in the fluids. For accurate results, the damping of the cantilever should be low as quantified by a high quality factor Q. This can be difficult in fluids of high viscosity particularly for microscopic cantilevers. In this paper, a “mesoscale” piezoelectric bimorph cantilever was used. The mesoscale refers to a size regime intermediate between microscopic and macroscopic, in this work the cantilever used has dimensions of the order of millimeters. This mesoscale cantilever displayed a sufficiently high Q to probe the rheological properties of highly damping and elastic fluids in situ. The developed probe will be ideally suited to in-process monitoring of high value products such as those in the biotechnology industry.
56(2012); http://dx.doi.org/10.1122/1.3671401View Description Hide Description
Rheological measurements offer a unique means of interrogating the physics of amorphous solids, including crosslinked rubbers and polymericglasses. Here, we present several vignettes to demonstrate the ability of both classical and novel rheological experiments to resolve important questions in condensed matter physics. First, results from torque and normal force measurements aimed at understanding the thermodynamics and mechanics of polymer networks in both dry and swollen states are presented. In particular, we examine the validity of the Frenkel–Flory–Rehner theory of rubber network swelling. Torsion and normal force measurements are also described for a series of polymericglasses that exhibit similar shear moduli but, surprisingly, very different normal force responses, with one set of materials showing extreme deviations from neo-Hookean behavior and the other being close to neo-Hookean. We then describe the use of a novel torsional dilatometer, which allows simultaneous measurement of mechanical properties and volume recovery, to investigate the aging and rejuvenation behaviors of glassypolymers. Also, the temperature dependence of dynamics is probed in glassypolymers that have been aged into equilibrium below the nominal glass transition temperature and evidence is presented that time-scale divergence may not be a true signature of the glass transition itself. Finally, we describe a reduction in scale of the classical membrane inflation test to allow measurement of the biaxial creep compliance of nanometer thick polymeric films using an atomic force microscope. In each instance, emphasis is placed on how the measurements are designed to interrogate the physics of interest in the materials investigatedx.
The matching of a “one-dimensional” numerical simulation and experiment results for low viscosity Newtonian and non-Newtonian fluids during fast filament stretching and subsequent break-up56(2012); http://dx.doi.org/10.1122/1.3669647View Description Hide Description
This paper develops a model for fast filament stretching, thinning, and break-up for Newtonian and non-Newtonian fluids, and the results are compared against experimental data where fast filament relaxation occurs. A 1D approximation was coupled with the arbitrary Lagrangian Eulerian (ALE) formulation to perform simulations that captured both filament thinning and break-up. The modeling accounts for both the initial polymer stretching processes from the precise movement of the two moving pistons and also the subsequent thinning when the pistons are at rest. The simulations were first validated for a low viscosity Newtonian fluid matched to experimental data obtained from a recently developed apparatus, the Cambridge Trimaster. A non-Newtonian polymer fluid, with high frequency linear viscoelastic behavior characterized using a piezoaxial vibrator rheometer, was modeled using both an Oldroyd-B and FENE-CR single-mode constitutive models. The simulations of the filament deformation were compared with experiment. The simulations showed a generally reasonable agreement with both the stretch and subsequent relaxation experimental responses, although the mono mode models used in this paper were unable to capture all of the details for the experimental time evolution relaxation profile of the central filament diameter.
Elimination of inertia from a Generalized Langevin Equation: Applications to microbead rheology modeling and data analysis56(2012); http://dx.doi.org/10.1122/1.3675625View Description Hide Description
Viscoelastic properties of condensed soft matter can be estimated by following the trajectory of an embedded micron-sized particle in a method called passive microbead rheology. Data analysis of passive microbead rheology is usually based on formulas that relate bead displacement statistics to the dynamic modulus of the material in the frequency-domain. Therefore, methods of analysis require conversion of the data to the frequency-domain using numerical Fourier transform routines. These methods are known to introduce errors associated with frequency discretization and finite window size. Time-domain data analysis methods based on a single bead trajectory were introduced by Fricks et al. [SIAM J. Appl. Math. 69, 1277–1308 (2009)] as an alternative to the frequency-domain formulas. We have expanded these ideas with the aim of performing Monte Carlo simulations on synthetic data to evaluate and compare analysis algorithms for systems in which particles are trapped in linear or nonlinear traps. Brownian dynamics simulations were used to generate trajectories of beads embedded in viscoelastic materials having a discrete relaxation spectrum, with multiple relaxation times. We show that by including a small purely dissipative element in the memory function of the generalized Langevin equation (GLE), we can eliminate inertia-related fast variables directly from the GLE to find an inertia-less GLE, avoiding the singularity reported by McKinley et al. [J. Rheol. 53, 1487–1506 (2009)]. Using the inertia-less GLE, the computational cost of the simulations is reduced by nearly 5 orders of magnitude. We also show that, in real systems, this purely dissipative element can arise from fluid inertia, since for the bead the Basset force acts dissipative at high frequencies.
56(2012); http://dx.doi.org/10.1122/1.3675605View Description Hide Description
The Herschel–Bulkley rheological fluid model includes terms representing viscosity and plasticity. In this classical model, below the yield stress the material is strictly rigid. Complementing this model by including elastic behavior below the yield stress leads to a description of an elastoviscoplastic (EVP) material such as an emulsion or a liquid foam. We include this modification in a completely tensorial description of cylindrical Couetteshear flows. Both the EVP model parameters, at the scale of a representative volume element, and the predictions (velocity, strain and stress fields) can be readily compared with experiments. We perform a detailed study of the effect of the main parameters, especially the yield strain. We discuss the role of the curvature of the cylindrical Couette geometry in the appearance of localization; we determine the value of the localization length and provide an approximate analytical expression. We then show that, in this tensorial EVP model of cylindrical Couetteshear flow, the normal stress difference strongly influences the velocity profiles, which can be smooth or nonsmooth according to the initial conditions on the stress. This feature could explain several open questions regarding experimental measurements on Couette flows for various EVP materials such as emulsions or liquid foams, including the nonreproducibility that has been reported in flows of foams. We then discuss the suitability of Couette flows as a way to measure rheological properties of EVP materials.