Describing the firmness, springiness and rubberiness of food gels using fractional calculus. Part I: Theoretical framework

Improvement of soybean protein isolate/konjac glucomannan-seaweed polysaccharide-based connective tissue simulants: effects of pH and water mobility on gel structure and gelling mechanism

Hydrogels are considered to have good potential to mimic connective tissue. In this study, the mechanical properties and thermal stability of protein-polysaccharide composite hydrogels were enhanced by moisture and acid-base modulation in an attempt to overcome the application limitations. The results of texture profile analysis (TPA) and compression experiments showed that the appropriate outward migration of moisture significantly improved the gel's mechanical properties. Rheological analysis showed that the gel exhibited optimal mechanical properties under an alkaline environment and, combined with the differential scanning calorimetry (DSC) results, excellent thermal stability was observed in the pH 10.5 sample group. Furthermore, magnetic resonance imaging (MRI) and scanning electron microscopy (SEM) results showed that the alkaline environment was also conducive to the formation of a denser gel network structure, and the outward migration of water led to a more orderly and uniform structure. Fourier transform infrared spectroscopy (FTIR) results showed that hydrogen bonding also played a major role in the formation of the cellular network structure of the gel. These findings demonstrate the positive contribution of moisture and pH modulation to the processing and edible property enhancement of animal connective tissue-mimicking structure and provide a theoretical basis for the regulation of hydrogel properties.

Modeling of Stress Relaxation Behavior in HDPE and PP Using Fractional Derivatives

In this work, the viscoelastic behavior of high-density polyethylene (HDPE) and polypropylene (PP) was studied through stress relaxation experiments conducted at different strain levels. The main objective was to evaluate classical, fractional, and conformable derivatives to analyze molecular mobility, using statistical methods to identify the most accurate representation of the viscoelastic response. Besides the coefficient of determination (R2), the average absolute deviation (AAD) and mean squared error (MSE) were used as evaluation metrics, along with a multivariate analysis of variance (MANOVA) and the response surface methodology (RSM) to optimize the correspondence between experimental data and model predictions. The findings demonstrate that the spring-pot, Fractional Maxwell (FMM), Fractional Voigt-Kelvin (FVKM), and Kohlrausch-Williams-Watts (KWW) models effectively describe stress relaxation under statistical criteria. However, a joint analysis using RSM revealed that the choice of mathematical model significantly influences the outcomes. The FVKM was identified as the most effective for HDPE, while the KWW model best characterized PP. These results highlight the importance of optimization tools in advancing the characterization of polymer viscoelasticity. The ability to select the most accurate models for HDPE and PP under varying conditions can directly improve the performance and durability of products in critical industrial sectors such as packaging, automotive, and medical devices, where long-term mechanical behavior is crucial. By offering a framework adaptable to other materials and modeling approaches, this work provides valuable insights for optimizing polymer processing, improving product design, and enhancing the reliability of polymer-based components in a range of industrial applications.

Both optical and rheological properties contribute to viscosity judgements when comparing real liquids using vision and touch

Does the opacity of a liquid, or the way it reflects light, affect how viscous it appears? Would the perceived viscosity change if we touch the liquid? Viscosity of a material, or how it flows, produces a rich stimulus that reflects the material's rheological properties, which can be independently inferred by touch or vision, or by combining modalities. In addition, the material's optical properties convey other cues not dependent on rheology, such as colour or transparency. How these multisensory cues form stable percepts of viscosity that drive behaviour remains unknown. To shed light on this mapping, we conducted a series of psychophysical experiments in which observers compared the thickness of real liquids. First, we show that perceptual discrimination tends to scale in proportion to stimulus viscosity. Next, we show that optical properties such as transparency and opacity, although not related to viscosity, influence visual judgments of thickness. This bias, driven by appearance, is reduced when observers combine visual and haptic information. Combining information across visual and haptic senses improves discrimination only over a limited viscosity range.

Comprehensive Characterization of the Viscoelastic Properties of Bovine Submaxillary Mucin (BSM) Hydrogels and the Effect of Additives

This study presents a comprehensive characterization of the viscoelastic and structural properties of bovine submaxillary mucin (BSM), which is widely used as a commercial source to conduct mucus-related research. We conducted concentration studies of BSM and examined the effects of various additives, NaCl, CaCl2, MgCl2, lysozyme, and DNA, on its rheological behavior. A notable connection between BSM concentration and viscoelastic properties was observed, particularly under varying ionic conditions. The rheological spectra could be well described by a fractional Kelvin-Voigt model with a minimum of model parameters. A detailed proteomics analysis provided insight into the protein, especially mucin composition within BSM, showing MUC19 as the main component. Cryo-scanning electron microscopy enabled the visualization of the porous BSM network structure. These investigations give us a more profound comprehension of the BSM properties, especially those pertaining to viscoelasticity, and how they are influenced by concentration and environmental conditions, aspects relevant to the field of mucus research.

Non-Maxwellian viscoelastic stress relaxations in soft matter

Viscoelastic stress relaxation is a basic characteristic of soft matter systems such as colloids, gels, and biological networks. Although the Maxwell model of linear viscoelasticity provides a classical description of stress relaxation, it is often not sufficient for capturing the complex relaxation dynamics of soft matter. In this Tutorial, we introduce and discuss the physics of non-Maxwellian linear stress relaxation as observed in soft materials, the ascribed origins of this effect in different systems, and appropriate models that can be used to capture this relaxation behavior. We provide a basic toolkit that can assist the understanding and modeling of the mechanical relaxation of soft materials for diverse applications.

Effects of Annona muricata Extract on Trypsin, Cathepsin B and Collagenase Activities and Textural Changes in Chilled Macrobrachium rosenbergii

Texture is an important sensory attribute for overall quality and consumer acceptance of prawns. However, texture is affected during cold storage due to the proteolytic activity of endogenous proteases, resulting in poor quality and a short shelf life. The objective of this study is to determine the inhibitory effects of Annona muricata leaves extract (AMLE) (0, 3, 10 and 20%) on the trypsin, cathepsin B and collagenase activities extracted from the cephalothorax of Macrobrachium rosenbergii. In addition, the textural changes in M. rosenbergii during 20 days of cold storage (4 °C) were also determined. M. rosenbergii were soaked in four different treatments: 0, 3, 10 and 20% AMLE and 1.25% sodium metabisulphate for 10 min at 4 °C. Protease activity was significantly (p < 0.05) reduced at 10 and 20% AMLE. Similarly, cathepsin B showed a significant (p < 0.05) low after treatment at 20% AMLE. The maximum inhibitory activity of trypsin was achieved at 20% AMLE and the standard inhibitor (Tosyl-L-lysyl-chloromethane hydrochloride (TLCK)) compared to the control. Whereas, the lowest collagenase activity was obtained at 20% AMLE compared to the control. These inhibitory effects further maintain the firmness of M. rosenbergii coated with 20% AMLE up to the eighth day of storage when compared to the control. Meanwhile, the highest penetration work was found in the M. rosenbergii coated with 20% AMLE at the twentieth day of storage. In conclusion, treatment at 20% AMLE could be used as a natural preservative to inhibit protease, trypsin and collagenase activity of M. rosenbergii and thus can maintain firmness for up to 8 days of storage.

Diversity of viscoelastic properties of an engineered muscle-inspired protein hydrogel

Folded protein hydrogels are prime candidates as tuneable biomaterials but it is unclear to what extent their mechanical properties have mesoscopic, as opposed to molecular origins. To address this, we probe hydrogels inspired by the muscle protein titin and engineered to the polyprotein I27₅, using a multimodal rheology approach. Across multiple protocols, the hydrogels consistently exhibit power-law viscoelasticity in the linear viscoelastic regime with an exponent β = 0.03, suggesting a dense fractal meso-structure, with predicted fractal dimension d_f = 2.48. In the nonlinear viscoelastic regime, the hydrogel undergoes stiffening and energy dissipation, indicating simultaneous alignment and unfolding of the folded proteins on the nanoscale. Remarkably, this behaviour is highly reversible, as the value of β, d_f and the viscoelastic moduli return to their equilibrium value, even after multiple cycles of deformation. This highlights a previously unrevealed diversity of viscoelastic properties that originate on both at the nanoscale and the mesoscopic scale, providing powerful opportunities for engineering novel biomaterials.

Instrumental and sensory techniques to characterize the texture of foods suitable for dysphagic people: A systematic review

The interest to characterize texture-modified foods (TMFs) intended for people with oropharyngeal dysphagia (OD) has grown significantly since 2011. Several instrumental and sensory techniques have been applied in the analysis of these foods. The objective of the present systematic review was to identify the most appropriate techniques, especially for the food industry and clinical setting. The search was carried out in three online databases according to the "Preferred Reporting Items for Systematic Reviews and Meta-Analyses" (PRISMA). Across the multiple trials reviewed, Texture Profile Analysis and the Uniaxial Compression Test were most used as the instrumental technique for solid foods, and the Back Extrusion Test for fluid and semisolid foods. All trials used descriptive analysis as the sensory technique. However, the experimental conditions of the trials lacked standardization. Consequently, the results of the trials were not comparable. To properly characterize the texture of TMFs intended for OD by each technique, an international consensus is needed to establish standardized experimental conditions. Methods based on these techniques should also be validated by collaborative studies to verify repeatability, replicability, and reproducibility.

Predicting thickness perception of liquid food products from their non-Newtonian rheology

The "mouthfeel" of food products is a key factor in our perception of food quality and in our appreciation of food products. Extensive research has been performed on what determines mouthfeel, and how it can be linked to laboratory measurements and eventually predicted. This was mainly done on the basis of simple models that do not accurately take the rheology of the food products into account. Here, we show that the subjectively perceived "thickness" of liquid foods, or the force needed to make the sample flow or deform in the mouth, can be directly related to their non-Newtonian rheology. Measuring the shear-thinning rheology and modeling the squeeze flow between the tongue and the palate in the oral cavity allows to predict how a panel perceives soup "thickness". This is done for various liquid bouillons with viscosities ranging from that of water to low-viscous soups and for high-viscous xanthan gum solutions. Our findings show that our tongues, just like our eyes and ears, are logarithmic measuring instruments in agreement with the Weber-Fechner law that predicts a logarithmic relation between stimulus amplitude and perceived strength. Our results pave the way for more accurate prediction of mouthfeel characteristics of liquid food products.

Incorporating Rheological Nonlinearity into Fractional Calculus Descriptions of Fractal Matter and Multi-Scale Complex Fluids

In this paper, we use ideas from fractional calculus to study the rheological response of soft materials under steady-shearing flow conditions. The linear viscoelastic properties of many multi-scale complex fluids exhibit a power-law behavior that spans over many orders of magnitude in time or frequency, and we can accurately describe this linear viscoelastic rheology using fractional constitutive models. By measuring the non-linear response during large step strain deformations, we also demonstrate that this class of soft materials often follows a time-strain separability principle, which enables us to characterize their nonlinear response through an experimentally determined damping function. To model the nonlinear response of these materials, we incorporate the damping function with the integral formulation of a fractional viscoelastic constitutive model and develop an analytical framework that enables the calculation of material properties such as the rate-dependent shear viscosity measured in steady-state shearing flows. We focus on a general subclass of fractional constitutive equations, known as the Fractional Maxwell Model, and consider several different analytical forms for the damping function. Through analytical and computational evaluations of the shear viscosity, we show that for sufficiently strong damping functions, for example, an exponential decay of fluid memory with strain, the observed shear-thinning behavior follows a power-law response with exponents that are set by the power-law indices of the linear fractional model. For weak damping functions, however, the power-law index of the high shear rate viscosity is set by the terminal behavior of the damping function itself at large strains. In the limit of a very weak damping function, the theoretical formulation predicts an unbounded growth of the shear stress with time and a continuously growing transient viscosity function that does not converge to a meaningful steady-state value. By determining the leading terms in our analytical solution for the viscosity at both low and high shear rates, we construct an approximate analytic expression for the rate-dependent viscosity. An error analysis shows that, for each of the damping functions considered, this closed-form expression is accurate over a wide range of shear rates.

The Effects of Hydrocolloids-Protein Mixture as a Fat Replacer on Physicochemical Characteristics of Sugar-Free Muffin Cake: Modeling and Optimization

The purpose of this study was to evaluate the hydrocolloids-protein mixture as a fat replacer in sugar-free low-fat muffin cakes. In this study, a hydrocolloids mixture including konjac and guar gums and soy protein isolate (SPI) was applied to the cake. The combination of gums and SPI was named as mixture of stabilizers (MOS), and the treatments were designed using Design-Expert software and the response surface methodology (RSM) in order to optimize and reduce the oil content of muffin cakes by replacing it with MOS. Evaluation of treatments characteristics were investigated on days 1 and 15 of their production. The dependent variables were moisture content, water activity, specific volume, porosity, hardness, cohesiveness, springiness, chewiness and crumb color of cakes. The results show that increasing the percentage of MOS has positive effects on the final products in comparison to oil. In other words, an increase in the MOS content resulted in an increase in the moisture content, water activity, specific volume, height, springiness, cohesiveness, chewiness and L* (lightness) values, but negative effect on hardness, a* (redness) and b* (yellowness) values. As a result of optimizing using RSM, the usage of 4.08% oil and 0.31% MOS resulted in a 62.9% reduction in oil content in comparison with the control sample. The panelists assigned the lowest score to hardness and crumb color and the highest score to overall acceptability and cohesiveness to the optimized muffin.

Biofilm mechanics in an extremely acidic environment: microbiological significance

A variety of natural biofilms were collected from an extremely acidic environment at Río Tinto (Spain). In order to provide insights into the structure-function relationship, the microstructure of the biofilms was explored using low temperature scanning electron microscopy (LTSEM) in combination with rheological analysis. The creep-recovery experiment results have demonstrated the typical behaviour of viscoelastic materials that combine both elastic and viscous characters. The LTSEM visualization and rheological characterization of biofilms revealed that the network density increased in bacterial biofilms and was the lowest in protist Euglena biofilms. This means that, in the latter biofilms, a lower density of interactions exist, suggesting that the whole system experiences enhanced mobility under external mechanical stress. The samples with the highest dynamic moduli (Leptospirillum-Acidiphilium, Zygnemopsis, Chlorella and Cyanidium) have shown the typical strain thinning behaviour, whereas the Pinnularia and Euglena biofilms exhibited a viscous thickening reaction. The Zygnemopsis filamentous floating structure has the highest cohesive energy and has shown distinctive enhanced resilience and connectivity. This suggests that biofilms should be viewed as soft viscoelastic systems the properties of which are determined by the main organisms and their extracellular polymeric substances. The fractional Maxwell model has been found to explain the rheological behaviour of the observed complex quite well, particularly the power-law behaviour and the characteristic broad relaxation response of these systems.

Probing gels and emulsions using large-amplitude oscillatory shear and frictional studies with soft substrate skin surrogates

Water swellable crosslinked polymers are widely used in oil-in-water emulsions for the healthcare and cosmetic industries due to their thickening properties. In this study, we investigate the rheological and lubrication behavior of a microgel-forming polymer, a lightly-crosslinked hydrophobically modified polyacrylic acid (HMPAA), in an aqueous medium and in an emulsion. Hydrogenated phosphatidylcholine, a class of phospholipids, is used as a surfactant in the emulsions composed of different oil content. Rheological behavior is probed both in the linear and non-linear regimes using small strain amplitude and large amplitude oscillatory shear (LAOS) experiments, respectively. We observe all systems to exhibit gel-like behavior with the elastic modulus (G') dominating and being frequency independent. Lissajous-Bowditch plots and nonlinear parameters obtained under large deformation show that the emulsions can resist greater deformations with smaller increase in the viscous dissipation when compared to a HMPAA gel. For tribology experiments, friction curves in a range of entrainment speeds are examined using substrates to mimic the skin surface (PDMS and Bioskin®). The role of polymer hydrophobicity on the different substrates are also explored by comparing the behavior of HMPAA to that of its hydrophilic analog, a polyacrylic acid highly crosslinked. We find the friction coefficient to be dependent on the hydrophobicity of the substrate and the polymer as well as the substrate roughness. These results taken together provide insights in the formulation of skincare products with efficient lubrication properties for different skin characteristics.

Bottlebrush Bridge between Soft Gels and Firm Tissues

Softness and firmness are seemingly incompatible traits that synergize to create the unique soft-yet-firm tactility of living tissues pursued in soft robotics, wearable electronics, and plastic surgery. This dichotomy is particularly pronounced in tissues such as fat that are known to be both ultrasoft and ultrafirm. However, synthetically replicating this mechanical response remains elusive since ubiquitously employed soft gels are unable to concurrently reproduce tissue firmness. We have addressed the tissue challenge through the self-assembly of linear-bottlebrush-linear (LBL) block copolymers into thermoplastic elastomers. This hybrid molecular architecture delivers a hierarchical network organization with a cascade of deformation mechanisms responsible for initially low moduli followed by intense strain-stiffening. By bridging the firmness gap between gels and tissues, we have replicated the mechanics of fat, fetal membrane, spinal cord, and brain tissues. These solvent-free, nonleachable, and tissue-mimetic elastomers also show enhanced biocompatibility as demonstrated by cell proliferation studies, all of which are vital for the safety and longevity of future biomedical devices.

Comparison of different bread types: Chemical and physical parameters

In this work, the chemical and physical profile of 5 different bread types (Multicereal bread, Bavaria wheat bread, Wholemeal bread, Rye and Oat bread) were analysed in depth, namely the nutritional profile, individual fatty acids and soluble sugars through GC-FID and HPLC-RI, respectively, as well as the mineral profile, including micro and macroelements. Furthermore, a texture profile analysis was carried out in addition to the measurement of the crust colour. Each bread type showed a distinct profile, with Wholemeal and Bavaria having the lowest calories, and Oat the highest. Multicereal showed the highest amount of unsaturated fatty acids, while Wholemeal and Rye scored the least sodium amounts. The hardest bread was Rye and the easiest to chew were Oat and Bavaria breads. The latter was also the one with the darkest crumb of all the analysed breads. This work shows that bread can be baked to meet the needs and particularities of various kinds of diets.

Visuo-Haptic Discrimination of Viscoelastic Materials

In our daily lives, we interact with different types of deformable materials. Regarding their mechanical behavior, some of those materials lie in a range that is between purely elastic and purely viscous. This range of mechanical behavior is described as viscoelasticity. In certain types of haptic interactions, such as assessment of ripeness of fruit, firmness of cheese, and consistency of organ tissue, we rely heavily on our haptic perception of viscoelastic materials. The relationship between the mechanical behavior of viscoelastic materials and our perception of them has been investigated in the field of psychorheology. However, our knowledge on how we perceive viscoelastic materials is still quite limited though some research work has already been done on purely elastic and purely viscous materials. History- and frequency-dependent behavior of viscoelastic materials result in a complex time-dependent response, which requires relatively more sophisticated models to investigate their behavior than those of purely elastic and viscous materials. In this study, we model viscoelasticity using a "springpot" (i.e., fractional-order derivative element) and express its behavior in the frequency domain using two physical parameters-"magnitude" and "phase" of complex stiffness. In the frequency domain, we are able to devise signal detection experiments where we can investigate the perception of viscoelastic materials using the perceptual terms of "firmness" and "bounciness," corresponding to the physical parameters of "magnitude" and "phase." The results of our experiments show that the just-noticeable difference (JND) for bounciness increases linearly with increasing "phase," following Weber's law, while the JND for firmness is surprisingly independent of the level of "phase."

Concentration-independent mechanics and structure of hagfish slime

The defense mechanism of hagfish slime is remarkable considering that hagfish cannot control the concentration of the resulting gel directly; they simply exude a concentrated material into a comparably "infinite" sea of water to form a dilute, sticky, cohesive elastic gel. This raises questions about the robustness of gel formation and rheological properties across a range of concentrations, which we study here for the first time. Across a nearly 100-fold change in concentration, we discover that the gel has similar viscoelastic time-dependent properties with constant power-law exponent (α=0.18±0.01), constant relative damping tanδ=G^''/G^'≈0.2-0.3, and varying overall stiffness that scales linearly with the concentration (∼c^0.99±0.05). The power-law viscoelasticity (fit by a fractional Kelvin-Voigt model) is persistent at all concentrations with nearly constant fractal dimension. This is unlike other materials and suggests that the underlying material structure of slime remains self-similar irrespective of concentration. This interpretation is consistent with our microscopy studies of the fiber network. We derive a structure-rheology model to test the hypothesis that the origins of ultra-soft elasticity are based on bending of the fibers. The model predictions show an excellent agreement with the experiments. Our findings illustrate the unusual and robust properties of slime which may be vital in its physiological use and provide inspiration for the design of new engineered materials.

STATEMENT OF SIGNIFICANCE

Hagfish produce a unique gel-like material to defend themselves against predator attacks. The successful use of the defense gel is remarkable considering that hagfish cannot control the concentration of the resulting gel directly; they simply exude a small quantity of biomaterial which then expands by a factor of 10,000 (by volume) into an "infinite" sea of water. This raises questions about the robustness of gel formation and properties across a range of concentrations. This study provides the first ever understanding of the mechanics of hagfish slime over a very wide range of concentration. We discover that some viscoelastic properties of slime are remarkably constant regardless of its concentration. Such a characteristic is uncommon in most known materials.

Perception and measurement of food texture: Solid foods

There is still a gap between instrumental measurement and sensory evaluation because of the complexity of food texture in spite of many efforts. In sensory evaluation, the terms describing the texture should be well understood by panelists, which poses a problem of establishing lexicons and training panelists. In the instrumental measurement, more efforts are required to understand the large deformation and fracture behavior of foods. The texture profile analysis (TPA) proposed by Alina Szczesniak, Malcolm Bourne, and Sherman has been applied to many foods, and was useful to develop the understanding of textures. But sometimes confusion of the interpretation of TPA parameters appeared. Many new techniques have been introduced to quantify TPA parameters. Recent efforts to fill the gap between sensory evaluation and instrumental measurements, human measurements, or physiological measurements have been introduced. This endeavor is an effort of synthesizing the dentistry and biomedical approach, sensory and psychological approach, and material science approach, and therefore, the collaboration among these disciplines is necessary. This manuscript mainly discusses texture studies for solid foods.

PRACTICAL APPLICATIONS

To fill the gap between the sensory evaluation and the instrumental measurement of texture, it is necessary to examine the physical change of foods during the oral processing. This will give us the designing principle of palatable and safe foods.

Weak and Strong Gels and the Emergence of the Amorphous Solid State

Gels are amorphous solids whose macroscopic viscoelastic response derives from constraints in the material that serve to localize the constituent molecules or particles about their average positions in space. These constraints may either be local in nature, as in chemical cross-linking and direct physical associations, or non-local, as in case of topological "entanglement" interactions between highly extended fiber or sheet structures in the fluid. Either of these interactions, or both combined, can lead to "gelation" or "amorphous solidification". While gels are often considered to be inherently non-equilibrium materials, and correspondingly termed "soft glassy matter", this is not generally the case. For example, the formation of vulcanized rubbers by cross-linking macromolecules can be exactly described as a second order phase transition from an equilibrium fluid to an equilibrium solid state, and amorphous solidification also arises in diverse physical gels in which molecular and particle localization occurs predominantly through transient molecuar associations, or even topological interactions. As equilibrium, or near equilibrium systems, such gels can be expected to exhibit universal linear and non-linear viscoelastic properties, especially near the "critical" conditions at which the gel state first emerges. In particular, a power-law viscoelastic response is frequently observed in gel materials near their "gelation" or "amorphous solidification" transition. Another basic property of physical gels of both theoretical and practical interest is their response to large stresses at constant shear rate or under a fixed macrocopic strain. In particular, these materials are often quite sensitive to applied stresses that can cause the self-assembled structure to progressively break down under flow or deformation. This disintegration of gel structure can lead to "yield" of the gel material, i.e., a fluidization transition, followed by shear thinning of the resulting heterogeneous "jelly-like" fluid. When the stress is removed, however, the material can relax back to its former equilibrium gel state, i.e., gel rejuvenation. In constrast, a non-equilibrium material will simply change its form and properties in a way that depends on processing history. Physical gels are thus unique self-healing materials in which the existence of equilibrium ensures their eventual recovery. The existence of equilibrium also has implications for the nature of both the linear and non-linear rheological response of gel materials, and the present paper explores this phenomenon based on simple scaling arguments of the kind frequently used in describing phase transitions and the properties of polymer solutions.