Rheologica Acta最新文献

An overarching challenge in rheology is to develop constitutive models for complex fluids for which we lack accurate first principles theory. A further challenge is that most experiments probing dynamical structure and rheology do so only in very simple flow fields that are not characteristic of the complex deformation histories experienced by material in a processing application. A recently developed experimental methodology holds potential to overcome this challenge by incorporating a fluidic four-roll mill (FFoRM) into scanning small-angle X-ray scattering instrumentation (sSAXS) (Corona, P. T. et al. Sci. Rep. 8, 15559 (2018); Corona, P. T. et al. Phys. Rev. Mater 6, 045603 (2022)) to rapidly generate large data sets of scattering intensity for complex fluids along diverse Lagrangian flow histories. To exploit this uniquely rich FFoRM-sSAXS data, we propose a machine learning framework, Scattering-Informed Microstructure Prediction under Lagrangian Evolution (SIMPLE), which uses FFoRM-sSAXS data to learn an evolution equation for the scattering intensity and an associated tensorial differential constitutive equation for the stress. The framework incorporates material frame indifference and invariance to arbitrary rotations by data preprocessing. We use autoencoders to find an efficient reduced order model for the scattering intensity and neural network ordinary differential equations to predict the time evolution of the model coordinates. The framework is validated on a synthetic FFoRM-sSAXS data set for a dilute rigid rod suspension. The model accurately predicts microstructural evolution and rheology for flows that differ significantly from those used in training. SIMPLE is compatible with but does not require material-specific constraints or assumptions.

Developing constitutive models that can describe a complex fluid’s response to an applied stimulus has been one of the critical pursuits of rheologists. The complexity of the models typically goes hand-in-hand with that of the observed behaviors and can quickly become prohibitive depending on the choice of materials and/or flow protocols. Therefore, reducing the number of fitting parameters by seeking compact representations of those constitutive models can obviate extra experimentation to confine the parameter space. To this end, fractional derivatives in which the differential response of matter accepts non-integer orders have shown promise. Here, we develop neural networks that are informed by a series of different fractional constitutive models. These fractional rheology-informed neural networks (RhINNs) are then used to recover the relevant parameters (fractional derivative orders) of three fractional viscoelastic constitutive models, i.e., fractional Maxwell, Kelvin-Voigt, and Zener models. We find that for all three studied models, RhINNs recover the observed behavior accurately, although in some cases, the fractional derivative order is recovered with significant deviations from what is known as ground truth. This suggests that extra fractional elements are redundant when the material response is relatively simple. Therefore, choosing a fractional constitutive model for a given material response is contingent upon the response complexity, as fractional elements embody a wide range of transient material behaviors.

Extrusion molding is an important method in the polymer processing industry. The stress concentration of polymer melts can easily occur at the contraction channel, especially at the contraction exit during extrusion molding, which causes volume defects in the final parts. To eliminate or minimize volume defects, this study examined the effects of contraction profiles and contraction lengths on the rheological behaviors of polystyrene melts based on numerical methods and algorithms in the current study. The contraction profiles included abrupt contraction, V-shaped contraction, hyperbolic contraction, and elliptic contraction geometries at different contraction lengths. A single-mode Rolie-Poly model was employed to describe the stress–strain relationship of polystyrene melt. Additionally, the finite volume method and SIMPLE algorithm were used to discretize and solve the governing equations of the fluid in a 4:1 contraction flow. Numerical simulations of the principal stress difference (PSD), stretch ratio, and velocity of polystyrene melt in the aforementioned contraction geometries were implemented. The numerical results indicate that contraction profiles and contraction length are two major factors affecting the rheological behaviors of polystyrene melts in contraction flows based on the same contraction ratio and flow rate. V-shaped contraction, hyperbolic contraction, and elliptic contraction geometries can reduce stress concentration compared to abrupt contraction. Thus, during extrusion molding, it is better to use the elliptic contraction profile with adequate contraction length to eliminate or minimize defects in parts caused by stress concentration at the sharp edge exit.

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The elongational rheology of blends of a polystyrene (PS) Pom-Pom with two linear polystyrenes was recently reported by Hirschberg et al. (J. Rheol. 2023, 67:403–415). The Pom-Pom PS280k-2x22-22k with a self-entangled backbone (M_w,bb = 280 kg/mol) and 22 entangled sidearms (M_w,a = 22 kg/mol) at each of the two branch points was blended at weight fractions from 75 to 2 wt% with two linear polystyrenes (PS) having M_w of 43 kg/mol (PS43k) and 90 kg/mol (PS90k), respectively. While the pure Pom-Pom shows strong strain hardening in elongational flow (SHF > 100), strain hardening (SHF > 10) is still observed in Pom-Pom/linear blends containing only 2 wt% of Pom-Pom. The elongational start-up viscosities of the blends with Pom-Pom weight fractions above 10 wt% are well described by the Molecular Stress Function (MSF) model, however, requiring two nonlinear fit parameters. Here we show that quantitative and parameter-free modeling of the elongational viscosity data is possible by the Hierarchical Multi-mode Molecular Stress Function (HMMSF) model based on the concepts of hierarchical relaxation and dynamic dilution. In addition, we investigated the elongational viscosity of a blend consisting of 20 wt% Pom-Pom PS280k-2x22-22k and 80 wt% of a PS star with 11 arms of M_w,a = 25 kg/mol having a similar span molecular weight as PS43k and similar M_w,a as the Pom-Pom. This work might open up possibilities toward polymer upcycling of less-defined polymers by adding a polymer with optimized topology to gain the intended strain hardening, e.g., for film blowing applications.

Graphical Abstract

Conductive polypyrrole nanotubes were synthesized with a two-step one-pot synthesis. During synthesis, the nanotubes were decorated with magnetite nanoparticles at different concentrations granting them magnetic properties. The characterization of the tubes revealed differences from the theoretical reactions. A bidisperse magnetorheological fluid (MRF) was prepared by mixing the composite polypyrrole nanotubes/magnetite nanoparticles with commercial carbonyl iron spherical microparticles in silicone oil. The rheological properties of the bidisperse system were studied under the presence of magnetic field at room and elevated temperature. An enhancement of the MR effect with the presence of the nanotubes was observed when compared with a standard MRF consisted only of magnetic microparticles. Due to the faster magnetic saturation of the nanotubes, this enhancement is exceptionally high at low magnetic fields. The stability of the system is studied under dynamic conditions where it is revealed that the nanotubes keep the standard particles well dispersed with the sedimentation improving by more than 50%.

This study introduces the Constitutive Neural Network (ConNN) model, a machine learning algorithm that accurately predicts the temporal response of complex fluids under specific deformations. The ConNN model utilizes a recurrent neural network architecture to capture the time dependent stress responses, and the recurrent units are specifically designed to reflect the characteristics of complex fluids (fading memory, finite elastic deformation, and relaxation spectrum), without presuming any equation of motion of the fluid. We demonstrate that the ConNN model can effectively replicate the temporal data generated by the Giesekus model and the Thixotropic-Elasto-Visco-Plastic (TEVP) fluid model under varying shear rates. To test the performance of the trained model, we subject it to an oscillatory shear flow, with periodic reversals in flow direction, which has not been trained on. The ConNN model successfully replicates the shear moduli of the original models, and the trained values of the recurrent parameters match the physical prediction of the original models. However, we do observe a slight deviation in the normal stresses, indicating that further improvements are necessary to achieve more rigorous physical symmetry and improve the model prediction.

Strain hardening of polymer melts is able to improve the uniformity of items in processing operations with elongational deformation. Of particular interest in this aspect is the dependence of strain hardening on elongational rate. In its first part, the paper presents a review on melt strain hardening obtained in uniaxial extensional experiments. Its dependence on elongational rate is of particular interest insofar as besides non-strain-hardening polymers, strain hardening increasing or decreasing with rate can be found. Results on linear polymers like polystyrene (PS), polypropylene (PP), high-density polyethylene (HDPE), and linear low-density polylethylene (LLDPE) in dependence on molecular parameters are discussed, as well as those of various blends. Particularly interesting are the strain-hardening features of certain HDPEs and LLDPEs, which could be understood by the assumption of a non-homogeneous chemical structure of the samples. Blends of various compositions of a linear and a long-chain branched PP throw light on the complex relation between branching structure and rate dependence of strain hardening. In the second part of the paper, the different strain-hardening behavior of linear polymers is interpreted by assessing the Rouse times as decisive physical quantity. For blends of certain linear species like HDPE and PP and those of linear with long-chain branched polymers, the existence of separate phases in the molten state is postulated. The assumptions are discussed in the light of the various studies on miscibility of linear and branched polyolefins from the literature.

Graphical Abstract

The rheological behavior of shear thickening fluid suspensions synthesized using three dispersion liquids, namely polyethylene glycol, glycerin, and diethylene glycol, having different numbers of hydroxyl groups at the ends of the chain and distinct chain lengths, was researched. The primary objective of this study is to investigate the effects of the length of the chain molecular, the number of –OH groups at the ends of the chain, and the density of dispersion liquids on the rheological behavior. Evaluations were made by taking into account the thickening ratio which expresses the maximum change in the viscosity of the fluid relative to the initial viscosity and the thickening period which states the difference between the shear rate at which the maximum viscosity is obtained and the critical shear rate. As a result of the evaluation made by considering these parameters, the rheological performance of shear thickening fluid suspensions synthesized with liquids having longer molecular chain lengths, higher –OH number, and higher density came to the fore. Samples synthesized with glycerin, which have more hydroxyl groups at the molecular chain ends, provided a more stable distribution by making stronger hydrogen bonds with silica. This situation significantly reduced the thinning behavior in the first region of the rheology curves and provided a stable and continuous thickening behavior after the critical shear rate. In addition, with the increase in the silica ratio, the thickening situation changed from continuous to discontinuous. Increment of silica also decreased the critical shear rate while increasing the initial and maximum viscosity. Increasing the silica content from 22 to 26% resulted in the thickening ratio increasing by 686% from 6.6 to 45 in the samples synthesized with polyethylene glycol while decreasing the thickening period from 559 to 41.2. Similar situations are observed in the samples synthesized with glycerin and diethylene glycol. All of the samples obtained exhibited a reversible behavior rheologically. When the applied shear rate was removed, the sample returned to its former fluid state. Moreover, suspensions synthesized by mixing dispersion liquids showed superior performance compared to single-liquid samples. It is thought that the dispersion liquids interact to form a branched network by making more bonds both with each other and with the silica particles, and it provides an increase in the resistance of the fluid against deformation under high shear stress.

A protocol based on Bayesian optimization is demonstrated for determining model parameters in a coarse-grained polymer simulation. This process takes as input the microscopic distribution functions and temperature-dependent density for a targeted polymer system. The process then iteratively considers coarse-grained simulations to sample the space of model parameters, aiming to minimize the discrepancy between the new simulations and the target. Successive samples are chosen using Bayesian optimization. Such a protocol can be employed to systematically coarse-grained expensive high-resolution simulations to extend accessible length and time scales to make contact with rheological experiments. The Bayesian coarsening protocol is compared to a previous machine-learned parameterization technique which required a high volume of training data. The Bayesian coarsening process is found to precisely and efficiently discover appropriate model parameters, in spite of rough and noisy fitness landscapes, due to the natural balance of exploration and exploitation in Bayesian optimization.

Materials with viscoplastic characteristics have been widely studied due to their applicability in various industries, but also because they are common in nature. The flow curve of viscoplastic fluids is generally well-captured by the Herschel-Bulkley (HB) model, which can account for yield stress and has a power-law behavior after flow occurs. Carbopol solutions are the most common kind of fluids used in experimental studies involving viscoplastic behavior. Carbopol solutions generally need a neutralizing agent, which acts as a pH regulator and prevents the formation of fungus. However, this agent can also affect the rheological properties of the original solution. In this work, yield stress measurements from different techniques (flow curve, oscillatory, and creep tests) were conducted for a combination of Carbopol and triethanolamine (neutralizing agent) concentrations of aqueous solutions. In addition, pH measurements for all samples were performed. For the analyzed cases, it was found that triethanolamine concentrations must be higher than 500 ppm to avoid the formation of fungi but below 700 ppm to obtain a homogeneous solution. The yield stress was shown to increase with the increment in the concentration of both components. In a more fundamental analysis, we employed the Suspension of Fractal Aggregates (SoFA) model, conceived to represent waxy crude oils, to evaluate the system considered and found an accurate agreement with respect to the data. This result shows that there can be similarities between the dynamics of both aggregate structures, to be verified in future studies.