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New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear
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Synopsis Characterizing purely viscous or purely elastic rheological nonlinearities is straightforward using rheometric tests such as steady shear or step strains. However, a definitive framework does not exist to characterize materials which exhibit both viscous and elastic nonlinearities simultaneously. We define a robust and physically meaningful scheme to quantify such behavior, using an imposed large amplitude oscillatory shear LAOS strain. Our new framework includes new material measures and clearly defined terminology such as intra-/intercycle nonlinearities, strain-stiffening/ softening, and shear-thinning/thickening. The method naturally lends a physical interpretation to the higher Fourier coefficients that are commonly reported to describe the nonlinear stress response. These nonlinear viscoelastic properties can be used to provide a "rheological fingerprint" in a Pipkin diagram that characterizes the material response as a function of both imposed frequency and strain amplitude. We illustrate our new framework by first examining prototypical nonlinear constitutive models including purely elastic and purely viscous models, and the nonlinear viscoelastic constitutive equation proposed by Giesekus. In addition, we use this new framework to study experimentally two representative nonlinear soft materials, a biopolymer hydrogel and a wormlike micelle solution. These new material measures can be used to characterize the rheology of any complex fluid or soft solid and clearly reveal important nonlinear material properties which are typically obscured by conventional test protocols.
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... The resulting material functions, namely the elastic storage modulus G ′ and the viscous loss modulus G ′′ are observed to be mostly unaffected by the polymer additives across the examined strain amplitudes and angular frequencies ( deformations. Additionally, we apply Fourier and Chebyshev decomposition to investigate the nonlinear behavior in the large amplitude oscillatory shear (LAOS) configuration, as detailed in Ref. [39,40] and SI Appendix . This approach has been used extensively to reveal key rheological and structural properties critical for the functionality of food and DIW systems [41,42]. ...
... Although FT rheology is sensitive in detecting the nonlinear response, it lacks a physical interpretation of these higher harmonics. Ewoldt et al. [39,40] developed a framework combining FT and Chebyshev polynomials to analyze nonlinear viscoelasticity. Utilizing Chebyshev decomposition, this approach allows for a physical interpretation of the higher-order coefficients. ...
In this study, we delve into the intricacies of elastoviscoplastic (EVP) fluids, particularly focusing on how polymer additives influence their extensional behavior. Our findings reveal that polymer additives significantly alter the extensional properties of the EVP fluids, such as relaxation time and extensional stresses, while having negligible impact on the shear rheology. Interestingly, the modified fluids exhibit a transition from yield stress-like behavior to viscoelastic-like behavior under high extensional rates, ultimately leading to destabilization under extreme deformation. This research enhances the fundamental understanding of EVP fluids and highlights potential advancements in applications, especially in precision-demanding fields like 3D printing.
... The responses of the starch gels in LAOS tests were evaluated by Lissajous plots created using Matlab R2022b software with a home-built Matlab script. The dissipation ratio and strain stiffening ratio (S) were calculated using [35] Dissipation ratio = (π γ0 G″1)/(4 σmax) (4) ...
The objective of this study was to investigate granule size and distribution and deformability of granules and their effect on the rheological properties of waxy starch gels. Native (granular) waxy rice gels (10%) were prepared, and their response in oscillatory shear was investigated in the linear and non-linear viscoelastic regime. The results show the gels were mainly composed of aggregated and deformed swollen granules. Significance of granule size and its distribution, deformability of granules, and the molecular characteristics of amylopectin (AP) on storage modulus of those gels was demonstrated. A low degree of deformability of granules, typical for small granules with a broad size distribution and small molecular size of AP with short external chains, resulted in rigid and brittle gels. Highly deformed granules and high AP leachates, however, yielded soft gels. It was found that the transition of elastic to plastic behavior in the non-linear regime (LAOS) was gradual when AP had long external chains, but an abrupt transition was observed with the gel with short exterior chains of AP. Differences in rheological properties of cohesive waxy starch gels appear to be mainly impacted by the varying degrees of granule deformability and rigidity, which is further attributed to a combination of factors, including granule size, particle size distribution, molecular size, the external chain length of amylopectin (AP), and lipid content. The significance of this study is that it will assist the food industry in selecting suitable waxy rice starches to gain desired textural properties of end products.
... For increasing strain amplitude, this representation illustrates very well the growth of harmonics in the stress signal and the transition from the linear regime, i.e., σ(γ) close to a straight line and σ(γ) close to a circle, to the non-linear regime where σ(γ) and σ(γ) display more complex shapes. In order to quantify the intra-cyle evolution of the sample response, we use two additional elastic moduli introduced in ref. [57], which are the elastic modulus computed at the minimum strain within the cycle, i.e, G ′ M = (∂σ/∂γ) | γ=0 , and the elastic modulus computed at the largest strain applied to the sample, i.e., G ′ L = (σ/γ) | γ=γ0 [see Fig. 8(b)]. The gel response within an oscillation is well captured by the strain-stiffening ratio S, a dimensionless quantity defined as S = (G ′ L − G ′ M )/G ′ L , where S > 0 indicates intra-cycle strain-stiffening, whereas S < 0 corresponds to an intra-cycle strain-softening behavior. ...
Cellulose ethers represent a class of water-soluble polymers widely utilized across diverse sectors, spanning from healthcare to the construction industry. This experimental study specifically delves into aqueous suspensions of carboxymethylcellulose (CMC), a polymer that undergoes gel formation in acidic environments due to attractive interactions between hydrophobic patches along its molecular chain. We use rheometry to determine the linear viscoelastic properties of both CMC suspensions and acid-induced gels at various temperatures. Then, applying the time-temperature superposition principle, we construct master curves for the viscoelastic spectra, effectively described by fractional models. The horizontal shift factors exhibit an Arrhenius-like temperature dependence, allowing us to extract activation energies compatible with hydrophobic interactions. Furthermore, we show that acid-induced CMC gels are physical gels that display a reversible yielding transition under external shear. In particular, we discuss the influence of pH on the non-linear viscoelastic response under large-amplitude oscillatory shear. Overall, our results offer a comprehensive description of the linear and non-linear rheological properties of a compelling case of physical hydrogel involving hydrophobic interactions.
The concentrated noncolloidal suspensions show complex rheological behavior, which is related to the existence of contact stress. However, determining the contact stress in time-varying flow like oscillatory shear is challenging. Herein, we propose a contact stress decomposition method to decompose the total stress directly into contact stress and hydrodynamic stress in large amplitude oscillatory shear (LAOS). The results of hydrodynamic stress and contact stress are consistent with those determined by the shear reversal experiment. The contact stress decomposition also explains the failure of the Cox–Merz rule in noncolloidal suspensions because the particle contacts exist in steady shear but are absent in small amplitude oscillatory shear. The intracycle and intercycle of contact stress are further analyzed through the general geometric average method. The intracycle behaviors exhibit strain hardening, strain softening, and shear thickening. The intercycle behaviors show bifurcations in stress-strain and stress-strain rate relations, where the transition strains at different concentrations define the state boundaries between the discrete particle contacts, the growing of particle contacts, and the saturated contacts. We also established a phenomenological constitutive model using a structural parameter to describe the shear effect on the buildup and breakdown of particle contacts. The contact stress of noncolloidal suspensions with wide ranges of particle concentrations and strain amplitudes under LAOS can be well described by the model.
In this study, we delve into the intricacies of elastoviscoplastic (EVP) fluids, particularly focusing on how polymer additives influence their extensional behavior. Our findings reveal that polymer additives significantly alter the extensional properties of the EVP fluids, such as relaxation time and extensional stresses while having negligible impact on the shear rheology. Interestingly, the modified fluids exhibit a transition from yield stress-like behavior to viscoelastic-like behavior under high extensional rates, ultimately leading to destabilization under extreme deformation. This research enhances the fundamental understanding of EVP fluids and highlights potential advancements in applications, especially in precision-demanding fields like 3D printing.
Lupins are rich in proteins (∼40%) and fibers (∼40%), and have been widely used for animal feed, but limitedly for human consumption due to the presence of alkaloids. Due to their high protein content, lupins have a high potential to be used as protein sources in diverse food manufacturing processes, including emulsion and foam stabilization. However, the interfacial properties of lupin protein isolates (LPI), especially their performance at different pH values, are not well understood so far. Here, we systematically investigated the air-water interfacial and foaming properties of the soluble fraction of LPI at pH 7.0, pH 6.0, pH 4.0, and pH 3.5. We observed that LPI at pH 4.0 (LPI-4) and pH 3.5 (LPI-3.5) adsorbed faster at the air-water interface than at pH 7.0 (LPI-7) and pH 6.0 (LPI-6) due to a smaller particle size and higher surface hydrophobicity of LPI-4 and LPI-3.5. This resulted in a higher foam overrun of LPI-4 and LPI-3.5 (300% and 331%, respectively). The air-water interfaces formed by LPI at different pH values were dramatically different in terms of interfacial structure and mechanical properties. LPI-4 and LPI-3.5 formed stiff and solid-like interfaces, leading to higher foam stability. In contrast, for LPI-7 there were clearly more protein aggregates at the interface, and this structure was weaker and less stretchable in response to shear and dilatational deformation, causing lower foam stability. LPI-6 also showed weaker air-water interfaces and thus formed less stable foams. Overall, LPI at acid pH (3.5 and 4) has a better performance in foam stabilization than at a pH close to neutral (6 and 7). Our results suggest that LPI can be potentially used as a plant-based clean-label additive in the production of foam-based food products in acidic environments.
Non-linear rheological behaviours of high fluorine content fluoroelastomer (HF-FKM) mixtures with varied carbon black (CB) filling amounts were investigated. Non-linear viscoelastic characteristics of HF-FKM mixture are characterised by large amplitude oscillatory shear (LAOS) tests, correlations between rheological behaviour and CB content were then discussed. Each non-linear viscoelastic parameter of HF-FKM mixture presents a three-stage characteristic with increasing CB content, corresponding to ranges of 0–20 phr, 25–30 phr, and 35–45 phr. Three stages of viscoelasticity characteristics for HF-FKM mixtures were considered to depend on the alteration of CB-elastomer network structure with increasing CB content, corresponding to the states where continuous phase of gum, CB-elastomer mesophase and excessive CB agglomerates predominate in mixture compound, respectively. After vulcanisation, samples with 30 phr CB content show the best resilience performance against thermal ageing, contributing to the existence of CB-elastomer mesophase. Samples with 25 phr CB content possess the second lowest compression sets at 225 and 250 °C ageing conditions but perform no better than those with 35 phr at 275 °C. The reason is presumed to be that the presence of excessive CB agglomerates in HF-FKM vulcanisate reduced irreversible deformation of the CB-elastomer network under compression at elevated temperatures.
This book is designed to fulfill a dual role. On the one hand it provides a description of the rheological behavior of molten poly mers. On the other, it presents the role of rheology in melt processing operations. The account of rheology emphasises the underlying principles and presents results, but not detailed deriva tions of equations. The processing operations are described qualita tively, and wherever possible the role of rheology is discussed quantitatively. Little emphasis is given to non-rheological aspects of processes, for example, the design of machinery. The audience for which the book is intended is also dual in nature. It includes scientists and engineers whose work in the plastics industry requires some knowledge of aspects of rheology. Examples are the polymer synthetic chemist who is concerned with how a change in molecular weight will affect the melt viscosity and the extrusion engineer who needs to know the effects of a change in molecular weight distribution that might result from thermal degra dation. The audience also includes post-graduate students in polymer science and engineering who wish to acquire a more extensive background in rheology and perhaps become specialists in this area. Especially for the latter audience, references are given to more detailed accounts of specialized topics, such as constitutive relations and process simulations. Thus, the book could serve as a textbook for a graduate level course in polymer rheology, and it has been used for this purpose.
We compare FT (Fourier Transform) and SD (Stress Decomposition), the interpretation methods for LAOS (Large Amplitude Oscillatory Shear). Although the two methods are equivalent in mathematics, they are significantly different in numerical procedures. Precision of FT greatly depends on sampling rate and length of data because FT of experimental data is the discrete version of Fourier integral theorem. FT inevitably involves unnecessary frequencies which must not appear in LAOS. On the other hand, SD is free from the problems from which FT suffers, because SD involves only odd harmonics of primary frequency. SD is based on two axioms on shear stress: [1] shear stress is a sufficiently smooth function of strain and its time derivatives; [2] shear stress satisfies macroscopic time-reversal symmetry. In this paper, we compared numerical aspects of the two interpretation methods for LAOS.
Although linear viscoelastic properties can be measured in many ways, the small-amplitude oscillatory shear test is the most widely used method. Non-linear viscoelastic properties can also be measured in many ways, but no predominant test method has emerged among experimentalists. Whereas there is a unifying theory that describes linear behaviour, there is no unifying constitutive theory for non-linear viscoelasticity. For this reason, each non-linear test reveals a different aspect of a material’s behaviour. Hence, experimentalists have designed various transient experiments to capture different features of non-linear viscoelasticity.
Although the stress of oscillatory shear flow can be decomposed into elastic and viscous parts in the linear regime, it is not yet known how to decompose the stress of a large amplitude oscillatory shear (LAOS) flow. We developed a method of analyzing LAOS data, which decomposes the stress into elastic and viscous components on the basis of a sound mathematical and physical foundation. This method is based on the symmetry of the stress and is a generalization of linear viscoelasticity from the viewpoint of geometry. The proposed method is more powerful than previous methods such as Fourier transform analysis and the Lissajous plot, in that it is more sensitive to the presence of nonlinearities and it is easier to determine nonlinear parameters.
The application of large amplitude oscillatory shear (LAOS) leads, in the non-linear regime, to a torque response that contains higher mechanical harmonic contributions. These harmonic contributions can be analyzed as spectra in Fourier space with respect to their frequencies, amplitudes and phase angle. In this Feature Article, we present first the experimental technique to measure these Fourier rheology spectra. A main emphasize of this feature article is given to a broad variety of applications of this technique to explore the potential use of this mechanical characterization method. The article is organized in the following way: In the first paragraphs the basic ideas and the motivation regarding the ideas of this work are explained. This is important for this technique since these details are often not treated in already published work. This information should facilitate the spread of the technique itself by describing ways to overcome practical problems that may have hindered similar development elsewhere. After this first section several applications of the FT-rheology method are described. Due to the fact that our set up achieves an increased sensitivity by a factor 100–1 000 compared to former work, many applications in polymer science are anticipated, e. g. the characterization of polymers with different molecular weights, the different responses of polymer dispersions and the identification of the alignment kinetics in block copolymers under shear, just to give some examples. Moreover, FT-rheology will provide valuable information regarding the comparison of the experiment and theoretical models, e.g. constitutive equations, analytical or numerical simulations. At the end an outlook is given towards further development of this technique where for example a new extension of the FT-rheology method into two dimensions is presented. In this experiment a step experiment and oscillatory shear are combined to reach a separation between linear and non-linear response in materials. The outlook section emphasizes that FT-rheology opens up a field with a variety of new possibilities for theoreticians, scientists who develop mechanical characterization methods and personnel responsible for quality control or companies that manufacture rheological devices.
Linear and Fourier-transform rheology were used to study the influence
of the oscillatory shear amplitude, gamma0, on the isothermal
crystallization at 140° C of three commercial isotactic
polypropylenes. The development of the crystallization was monitored
through the time dependence of the dynamic storage modulus, G'(t), and
the normalized intensity of the third harmonic of the stress waveform,
I3 (t), a quantification of the degree of nonlinearity under
oscillatory shear conditions. A change in the exponent, n, of the power
law describing growth, according to Gnorm '(t) ~
tn, was observed at t ~ 4 h. For t < 4 h, n was between 3
and 4. This change in growth kinetics was also accompanied by a maximum
in I3 (t). Below gamma0 = 0.05, these results were
independent of the applied strain amplitude. Above gamma0 =
0.05, failure of the polypropylene in the parallel plate geometry due to
stress build-up was often observed in the late stages of
crystallization. This was accompanied by a sharp decrease of G'(t), and
a simultaneous sharp increase of I3 (t). Additionally, the
presence of even harmonics in the spectrum was observed after failure.
Notably, a plateau of I3 (t) at least 1 h before actual
failure indicating a greater sensitivity to its onset than that of
G'(t).
Nonlinear rheological properties are often relevant in understanding the response of a material to its intended environment. For example, many gastropods crawl on a thin layer of pedal mucus using a technique called adhesive locomotion, in which the gel structure is periodically ruptured and reformed. We present a mechanical model that captures the key features of this process and suggests that the most important properties for optimal inclined locomotion are a large, reversible yield stress, followed by a small shear viscosity and a short thixotropic restructuring time. We present detailed rheological measurements of native pedal mucus in both the linear and nonlinear viscoelastic regimes and compare this ''rheological fingerprint'' with corresponding observations of two bioinspired slime simulants, a polymer gel and a clay-based colloidal gel, that are selected on the basis of their macroscopic rheological similarities to gastropod mucin gels. Adhesive locomotion (of snails or mechanical crawlers) imposes a large-amplitude pulsatile simple shear flow onto the supporting complex fluid, motivating the characterization of nonlinear rheological properties with large amplitude oscillatory shear (LAOS). We represent our results in the form of Lissajous curves of oscillatory stress against time-varying strain. The native pedal mucus gel is found to exhibit a pronounced strain-stiffening response, which is not imitated by either simulant.