Volume 59, Issue 3, May 2015
Index of content:
59(2015); http://dx.doi.org/10.1122/1.4913584View Description Hide Description
To distinguish it clearly from nonlinear viscoelasticity, we define “ideal thixotropy” as “a time-dependent viscous response to the history of the strain rate, with fading memory of that history,” endowing such fluids with memory but no elasticity. An “ideal thixotropic fluid” has instantaneous stress relaxation upon cessation of flow and no elastic recoil on removal of stress. We describe “nonideal thixotropic” fluids as those whose viscoelastic time scales governing stress relaxation are much shorter than those governing the thixotropic response. This ensures that a clear distinction can be maintained between “thixotropy” and “nonlinear viscoelasticity.” The stress tensor for an ideal thixotropic fluid can in general be expressed as a contraction product of a fourth rank viscosity tensor with the velocity gradient tensor, in which the viscosity tensor depends on the history of the flow. We show examples of constitutive equations that meet the definitions of ideal thixotropy or nonideal thixotropy. We also show examples of constitutive equations that have been designated as “thixotropic” by virtue of containing an equation for evolution of a “structure parameter,” but whose behavior is indistinguishable from that of ordinary nonlinear viscoelasticity, and so should not be considered thixotropic.
59(2015); http://dx.doi.org/10.1122/1.4913696View Description Hide Description
A model is presented to describe flow-induced crystallization in isotactic polypropylene at high shear rates. This model incorporates nonlinear viscoelasticity, compressibility, and nonisothermal process conditions due to shear heating and heat release due to crystallization. Flow-induced nucleation occurs with a rate coupled to the chain backbone stretch associated with the longest mode relaxation time of the polymer melt, obtained from a viscoelastic constitutive model. Flow-induced nuclei propagate in flow direction with a speed related to shear rate, thus forming shish, which increase the viscosity of the material. The viscosity change with formation of oriented fibrillar crystals (known as “shish”) is implemented in a phenomenological manner; shish act as a suspension of fibers with radius equivalent to the radius of the shish plus the attached entangled molecules? The model is implemented in a 2D finite element code and validated with experimental data obtained in a channel flow geometry. Quantitative agreement is observed in terms of pressure drop, apparent crystallinity, parent/daughter ratio, Hermans' orientation, and shear layer thickness. Moreover, simulations for lower flow rates are performed and the results are compared, in a qualitative sense, to experiments from literature.
Rheology of a dual crosslink self-healing gel: Theory and measurement using parallel-plate torsional rheometry59(2015); http://dx.doi.org/10.1122/1.4915275View Description Hide Description
Tough hydrogels can be synthesized by incorporating self-healing physical crosslinks in a chemically crosslinked gel network. Due to the breaking and reattachment of these physical crosslinks, these gels exhibit a rate-dependent behavior that can be different from a classical linear viscoelastic solid. In this work, we develop a theory to describe the linear mechanical response of a dual-crosslink gel in a parallel-plate torsional rheometer. Our theory is based on a newly developed finite strain constitutive model. We show that some of the parameters in the constitutive model can be determined by carrying oscillatory torsional experiments. For consistency, we also show that the torsion data in an oscillatory test can be predicted using our theory with parameters obtained from tension tests. Our theory provides a basis for interpreting and understanding the test data of these gels obtained from rheometry.
59(2015); http://dx.doi.org/10.1122/1.4915299View Description Hide Description
The more parameters in a rheological constitutive model, the better it tends to reproduce available data, though this does not mean that it is necessarily better justified. Good fits to data are only part of model selection. We develop a Bayesian inference approach that rigorously balances closeness to data against both the number of model parameters and their a priori uncertainty. The analysis reflects a basic principle: Models grounded in physics will enjoy greater generality and perform better away from where they are calibrated. In contrast, relatively empirical models can provide comparable fits, but their a priori uncertainty is penalized. We demonstrate the approach by computing the best-justified number of modes for a multimode Maxwell model (MMM) to describe the dynamic shear moduli , of a synthetic polymer network with transient crosslinks (polyvinyl alcohol with sodium tetra-borate). It is shown that a corresponding array of spring-pots, arranged as a parallel array of fractional-Maxwell model elements, is less credible. In contrast, for a biopolymer gluten dough we show that the MMM, irrespective of number of modes, is far less credible than a critical-gel/Rouse model (CGRM), which with its firmer physical basis provides a more credible model. This is true even though the MMM provides a closer fit to the data than the CGRM for the gluten system. Though quantitative, this formulation does not fully supplant user judgment. However, unlike most model fitting/selection approaches, it requires specific, quantifiable, and potentially debatable quantification of this judgment, and thus it provides a rigorous, repeatable assessment of model viability. Models are supported (or not) given numerical input, not vague assertions.
59(2015); http://dx.doi.org/10.1122/1.4916531View Description Hide Description
The solidification of waxy components during the cool down of waxy crude oils in pipelines may provide complex yield stress fluid behavior with time-dependent characteristics, which has a critical impact for predicting flow restart after pipeline shut-in. Here, from a previous set of data at a local scale with the help of Magnetic Resonance Imaging and a new full set of data for various flow and temperature histories, we give a general picture of the rheological behavior of waxy crude oils. The tests include start flow tests at different velocities or creep tests at different stress levels, abrupt changes of velocity level, steady flow, after cooling under static or flowing conditions. We show that when the fluid has been cooled at rest it forms a structure that irreversibly collapses during the startup flow. Under these conditions, the evolution of the apparent viscosity mainly depends on the deformation undergone by the fluid for low or moderate deformation and starts to significantly depend on the shear rate for larger values. Even the (apparent) flow curve of statically cooled waxy crude oils was observed to be dependent on the flow history, more specifically on the maximum shear rate experienced by the material. After being sufficiently sheared, i.e., achieving an equilibrium state, the rheological behavior is that of a simple liquid for shear rates lower than the maximum historical one. A model is proposed to represent those trends experimentally observed. In contrast with most previous works in that field, the model is built without any a priori assumption based on classical behavior of a class of fluids. Finally, it is shown that this model predicts the flow characteristics of these materials under more complex flow histories (sweep tests, sudden shear rate decrease) much better than the so far most often used (Houska) model.
Estimating the viscosity of a highly viscous liquid droplet through the relaxation time of a dry spot59(2015); http://dx.doi.org/10.1122/1.4917240View Description Hide Description
We discuss in this paper a technique which enables the estimation of the viscosity of microscopic droplets, with application to particles suspended in the atmosphere. The principle of this technique is to deposit a droplet of material approximately 30–100 μm in diameter on a substrate and poke it with a sharp needle hence generating a hole. The amount of sample needed to perform such measurement allows the viscosity of small sample volumes (less than a microliter), such as those generated from atmospheric sampling, to be determined. We show here that the time required for the droplet to relax to its equilibrium shape can be related to the viscosity. We hereby present two mathematical models based on the lubrication approximation which are able to capture the droplet relaxation dynamics. One model is fully transient and resolves the dynamics of the wetting front using a disjoining pressure approach. The other is quasistatic and requires a relationship between the contact line velocity and the contact angle. Comparing the computed relaxation time to that measured experimentally enables the approximate evaluation of the viscosity. The mathematical models are first tested against data from the literature for the closure of a hole in a continuous thin film and then demonstrated for droplets of the polybutene oil N450000 (trade name Cannon Standard Oil), a high-viscosity standard, which serve as a benchmark sample since it is precisely characterized. We also present here viscosity estimates for droplets consisting of secondary organic material and water which are present over forested region yet remain very poorly understood for a lack of adequate characterization technique.
59(2015); http://dx.doi.org/10.1122/1.4917342View Description Hide Description
This work studies how stepwise extension of various well-entangled polymer melts produce mechanical/structural breakdowns during stress relaxation. Depending on how stepwise extension is imposed on five different styrene-butadiene random copolymers, two different forms of specimen failure are observed. When a step extension is produced with a low Hencky rate or to a low strain below some thresholds, the sample breaks up rather sharply after an appreciable period of induction during which the stress relaxes quiescently. After step extension, the sample draws and undergoes unsustainable necking due to shear yielding, if the step extension is produced with a Hencky rate higher than the Rouse relaxation rate and the magnitude is beyond a Hencky strain of 1.5. Moreover, introduction of long-chain branching suppresses the elastic breakup, postponing it to Hencky strains beyond 2.5. The clearly identifiable characteristics of the elastic yielding may be understood in terms of some speculative interpretations. More convincing explanations have yet to come from future computer experiments that hopefully the present work is able to motivate.
Internal viscoelastic flows for fluids with exponential type pressure-dependent viscosity and relaxation time59(2015); http://dx.doi.org/10.1122/1.4917541View Description Hide Description
The isothermal steady-state and pressure-driven flows in a straight channel and a circular tube, of an incompressible viscoelastic fluid which follows the Maxwell constitutive model, are considered. Under the assumption that both the shear viscosity and the single relaxation time of the fluid vary exponentially with pressure, the governing equations are solved analytically using a regular perturbation scheme with small parameter the dimensionless pressure-viscosity coefficient. The solution is found up to sixth order in the small parameter, revealing a two-dimensional (2D) flow field and the dependence of the primary flow variables on the geometrical aspect ratio, the pressure-viscosity coefficient, and the Weissenberg and Reynolds numbers. It is demonstrated that the pressure-dependent viscosity and relaxation time enhance the pressure gradient along the main flow direction, generate another along the wall-normal direction, and cause vertical motion of the fluid. Viscoelastic extra-stresses, which affect significantly the average pressure difference, required to drive the flow and the shear stress at the wall, are also predicted. Moreover, the mean Darcy friction factor shows a substantial deviation from the average pressure difference, as the fluid elasticity increases. For the Newtonian fluid, the effect of the pressure-dependent viscosity on the velocity components is minor, but substantial on the pressure and shear-stress profiles. Most of these features are predicted for the first time, and they are due to the fact that the flow field is fully 2D, indicating the complex nature of fluids with pressure-dependent viscosity and relaxation time.