Quantifying the consistency and rheology of liquid foods using fractional calculus

Generalized vs. fractional: a comparative analysis of Maxwell models applied to entangled polymer solutions

Fractional viscoelastic models provide an excellent description of rheological data for polymer systems with power-law behaviour. However, the physical interpretation of their model parameters, which carry fractional units of time, often remains elusive. We show that for poly(ethylene oxide) (PEO) solutions, the fractional Maxwell model (FMM) requires much fewer model parameters than the classical generalized Maxwell model for a good description of the data and that it can be applied consistently to solutions with varying degrees of viscoelasticity. Despite their fractional units, the parameters exhibit scaling laws similar to classical parameters as a function of polymer concentration.

Scale-Dependent Rheology of Synovial Fluid Lubricating Macromolecules

Synovial fluid (SF) is the complex biofluid that facilitates the exceptional lubrication of articular cartilage in joints. Its primary lubricating macromolecules, the linear polysaccharide hyaluronic acid (HA) and the mucin-like glycoprotein proteoglycan 4 (PRG4 or lubricin), interact synergistically to reduce boundary friction. However, the precise manner in which these molecules influence the rheological properties of SF remains unclear. This study aimed to elucidate this by employing confocal microscopy and multiscale rheometry to examine the microstructure and rheology of solutions containing recombinant human PRG4 (rhPRG4) and HA. Contrary to previous assumptions of an extensive HA-rhPRG4 network, it is discovered that rhPRG4 primarily forms stiff, gel-like aggregates. The properties of these aggregates, including their size and stiffness, are found to be influenced by the viscoelastic characteristics of the surrounding HA matrix. Consequently, the rheology of this system is not governed by a single length scale, but instead responds as a disordered, hierarchical network with solid-like rhPRG4 aggregates distributed throughout the continuous HA phase. These findings provide new insights into the biomechanical function of PRG4 in cartilage lubrication and may have implications in the development of HA-based therapies for joint diseases like osteoarthritis.

Microrheological characterisation of Cyanoflan in human blood plasma

Naturally occurring polysaccharidic biopolymers released by marine cyanobacteria are of great interest for numerous biomedical applications, such as wound healing and drug delivery. Such polymers generally exhibit high molecular weight and an entangled structure that impact the rheology of biological fluids. However, biocompatibility tests focus not so much on rheological properties as on immune response. In the present study, the rheological behaviour of native blood plasma as a function of the concentration of a cyanobacterium biopolymer is investigated via multiple particle tracking microrheology, which measures the Brownian motion of probes embedded in a sample, and cryogenic scanning electron microscope microstructural characterisation. We use Cyanoflan as the biopolymer of choice, and profit from our knowledge of its chemical structure and its exciting potential for biotechnological applications. A sol-gel transition is identified using time-concentration superposition and the power-law behaviour of the incipient network's viscoelastic response is observed in a variety of microrheological data. Our results point to rheology-based principles for blood compatibility tests by facilitating the assignment of quantitative values to specific properties, as opposed to more heuristic approaches.

Consumer Assessment of 3D-Printed Food Shape, Taste, and Fidelity Using Chocolate and Marzipan Materials

Additive manufacturing enables the production of complex structures with emerging approaches showing great promise in the food industry for design customization. Three-dimensional food printing has benefits for providing personalized health and shape fabrication for consumers. Past studies have demonstrated positive consumer perceptions for 3D food printing, but there is still a need for consumer validation of the technology through consumption and rating of fabricated 3D-printed foods. This article measures consumer response on shape, taste, and fidelity for 3D-printed food designs. Participants (N = 28) were presented with a series of designs differing in shape complexity and ingredients (marzipan and chocolate) and provided ratings using a visual analog scale (100 mm line). The results show that fabricated shapes with higher complexity were preferred by participants with 8.8 ± 0.3 ratings over lower complexity shapes with 5.5 ± 0.4 ratings. Taste preference was primarily dependent on the material selection, with chocolate material preferred by participants with 8.2 ± 0.5 ratings over marzipan material with 6.0 ± 0.5. Results demonstrated that participants preferred 3D-printed shapes that achieved high fidelity in recreating their computer-aided design (CAD) with 7.3 ± 0.3 ratings that were greater than 5.5 ± 0.5 for low-fidelity prints. These findings demonstrate first measurements of 3D food printing from a consumer perspective and provide a foundation for future studies on personalized manufacturing and nutrition.

Large-Scale Production of Wholly Cellular Bioinks via the Optimization of Human Induced Pluripotent Stem Cell Aggregate Culture in Automated Bioreactors

Combining the sustainable culture of billions of human cells and the bioprinting of wholly cellular bioinks offers a pathway toward organ-scale tissue engineering. Traditional 2D culture methods are not inherently scalable due to cost, space, and handling constraints. Here, the suspension culture of human induced pluripotent stem cell-derived aggregates (hAs) is optimized using an automated 250 mL stirred tank bioreactor system. Cell yield, aggregate morphology, and pluripotency marker expression are maintained over three serial passages in two distinct cell lines. Furthermore, it is demonstrated that the same optimized parameters can be scaled to an automated 1 L stirred tank bioreactor system. This 4-day culture results in a 16.6- to 20.4-fold expansion of cells, generating approximately 4 billion cells per vessel, while maintaining >94% expression of pluripotency markers. The pluripotent aggregates can be subsequently differentiated into derivatives of the three germ layers, including cardiac aggregates, and vascular, cortical and intestinal organoids. Finally, the aggregates are compacted into a wholly cellular bioink for rheological characterization and 3D bioprinting. The printed hAs are subsequently differentiated into neuronal and vascular tissue. This work demonstrates an optimized suspension culture-to-3D bioprinting pipeline that enables a sustainable approach to billion cell-scale organ engineering.

Origin of the effects of optical spectrum and flow behaviour in determining the quality of dry fig, jujube, pomegranate, date palm and concentrated grape vinegars

In this study, we focused on physical characterization and quality control of dry fig, jujube, pomegranate, date palm and concentrated grape vinegars using UV spectroscopy method and rheology technique. The optical spectra and flow behaviour of the vinegars were analysed in detail in the selected specific wavelength, shear rate and frequency ranges, respectively. It was determined that the peak values seen in the UV spectra of the vinegars were caused by the organic acid and phenolic compound concentration. The peak values in the UV spectra of the vinegars wavelength range of 190 nm to 240 nm and 250 nm to 300 nm were caused by the organic acid and phenolic compound concentration, respectively. In this context, it was predicted that concentrated grape vinegar, which has the highest absorbance value, has higher organic acid content and more antibacterial/antioxidant properties compared to the others. It is thought that the optical energy gaps of vinegars are related to the organic acid concentration and the release time. Flow properties of the vinegars were non-Newtonian thickening fluids (dilatant fluids) and compatible with the Power law model. The stable flow of the vinegars in the high shear rate region was interpreted as having a successful production process and being of good quality.

A method for evaluating time-resolved rheological functionalities of fluid foods

We have developed an effective method for evaluating time-resolved rheological functionalities of swallowed foods using ultrasonic spinning rheometry (USR). USR can obtain variations over time in the rheological properties of fluids despite the fluids being in heterogeneous and non-equilibrium conditions. In addition, USR can evaluate time variations of shear-thinning property changing in a few seconds. Demonstrations were conducted with typical thickener solutions: starch, guar gum, and xanthan gum-based solutions, with alpha-amylase as a digestive enzyme. The flow curve of the starch-based solutions lowered with time, and a few minutes after addition of the amylase, the viscosity dropped to one-hundredth of the original value. In contrast, the guar gum and xanthan gum-based solutions maintained the original viscosities as generally known. Applying the power law fitting to series of these flow curves, the time variation of the shear thinning property is quantitatively characterized by the plots on typical K-n space, where K and n are parameters in the model, consistency index and power law exponent. The qualitative characteristics of the thickeners are successfully quantified in the K-n space, and this will be a practical tool for evaluating the time-resolved rheological properties of swallowed foods.

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.

Oscillations of a soft viscoelastic drop

A soft viscoelastic drop has dynamics governed by the balance between surface tension, viscosity, and elasticity, with the material rheology often being frequency dependent, which are utilized in bioprinting technologies for tissue engineering and drop-deposition processes for splash suppression. We study the free and forced oscillations of a soft viscoelastic drop deriving (1) the dispersion relationship for free oscillations, and (2) the frequency response for forced oscillations, of a soft material with arbitrary rheology. We then restrict our analysis to the classical cases of a Kelvin-Voigt and Maxwell model, which are relevant to soft gels and polymer fluids, respectively. We compute the complex frequencies, which are characterized by an oscillation frequency and decay rate, as they depend upon the dimensionless elastocapillary and Deborah numbers and map the boundary between regions of underdamped and overdamped motions. We conclude by illustrating how our theoretical predictions for the frequency-response diagram could be used in conjunction with drop-oscillation experiments as a "drop vibration rheometer", suggesting future experiments using either ultrasonic levitation or a microgravity environment.

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.

Influence of thickening agents on rheological properties and sensory attributes of dysphagic diet

Dysphagia is the difficulty during the progression of the bolus from the mouth to the stomach. Modifying the texture of the food is a fundamental factor for safe swallowing in patients with dysphagia since inadequate consistency can result in complications. To personalize and develop diets for dysphagia, understanding, and controlling the rheological and sensory properties of thickeners is useful. This review examines the different types of thickeners used to modify the texture of foods, as well as their influence on rheological properties and sensory attributes to efficiently manage the diet in dysphagia. The study discusses characteristics such as: hardness, viscosity, viscoelasticity, as well as sensory attributes related to rheology. The thickeners xanthan gum, methylcellulose, carboxymethylcellulose, guar gum, linseed, and chia, carboxymethylated curdlan, and konjac glucomannan were reviewed in this work. Sensory evaluations of different foods have already been carried out on some products such as: meats, carrots, soups, pates, and timbales with their modified textures. The sensory attributes measured among hydrocolloids are strongly correlated with rheological parameters. Dysphagic diets should have less hardness and adherence, but with adequate cohesiveness to facilitate chewing, swallowing to protect from aspiration and reduction of residues in the oropharynx. The use of a single type of thickener may not be ideal, their mixtures and synergistic effect can improve the viscous and elastic characteristics of foods, to obtain safe food to swallow and to improve the sensory interest of dysphagic patients. Personalized recommendations with follow-up on swallowing approaches, respecting patient's individuality, explaining thickening agents' differences would be pertinent.

Investigation of the traditional organic vinegars by UV-VIS spectroscopy and rheology techniques

Optical, rheological and metabolic properties of the apple, hawthorn, artichoke, grape, rosehip and blackberry organic vinegar produced by deep culture method (handmade traditional method) were analysed using UV-Vis spectroscopy and rheology techniques. Flow behaviours for all samples were analysed in the shear rate range of 10^-3 to 10³ 1/s and in frequency range of 10^-3 to 10³rad/s, respectively. Absorption spectra for six organic vinegars was observed two peaks around 215 and 285nm due to the presence of phenolic compounds and organic acids such as acetic. The effects of optical transitions of organic molecules on the absorption coefficient values for vinegars were determined. Optical energy band gaps of all samples were found to be consistent with Planck's radiation approach known as Rayleigh-Jeans law and Tauc law. The rheological/flow properties of the all vinegars were found to be relevant with non-Newtonian flow behaviour and Ostwald-de Waele model. From the results of optical and rheological analysis, which determines the quantity and quality characteristics of all organic vinegars, it was concluded that these vinegars are in a level that people can drink easily.

Effect of a moderate electric field on the salting of Atlantic Salmon (Salmo salar): An experimental study and phenomenological understanding

Salting is one of the oldest methods of preserving food. The main limitation of salting is its extended processing time due to slow salt diffusion. A moderate electric field (MEF) can improve the mass transfer rate through electroporation. Regularly, mass transfer processes are modeled with Fick's second law. However, due to the anisotropic nature of food microstructures, it might be more appropriate to use an anomalous model. The main objective of this study was to search for a phenomenological explanation for salt and water diffusion in the salmon brining process coupled with MEF. Salmon fillets were cut into finite cylinders (0.025 × 0.025 m) and brined in two salt concentrations (6 and 24% w/w NaCl) at 6 °C for 20 h. MEFs were applied in the range of 0 to 2 V/cm. The salt and water contents of the salmon were measured during the process. Fick's second law and anomalous model based on fractional calculus were used to describe the diffusion phenomena. The results showed that an MEF tended to reduce the brining processing time and increase the salt content of salmon. This effect is predominantly due to an increase in the equilibrium salt concentration in the salmon tissue. Mathematical analysis shows that the anomalous diffusion model is more suitable for representing the brining process, exhibiting superdiffusion behavior (α > 1). An MEF accelerates the salt mass transfer into salmon tissue even at lower temperatures, significantly reducing the processing time. In addition, the diffusion process can be characterized with an anomalous model.

The compression specificity of plant tissue

The aim of this study was to determine the compression characteristics of nonhomogeneous plant materials with a complex morphological structure (beetroots, celery roots, and potato tubers), to compare the analyzed samples with the compression characteristics of reference materials (homogeneous isotropic structural materials: steel coil spring and vulcanized rubber), and to determine the influence of the compression rate on stress in compressed samples. Structural materials and plant materials clearly differed in compression characteristics. Excluding the short initial compression phase, the compression curves for the steel coil spring and vulcanized rubber were straight parallel lines, and the higher the crosshead speed, the higher the lines' location in the diagram. In tests conducted on plant materials, the rate of changes in compression force increased throughout the experiment with an increase in crosshead speed. The greatest variations in compression force resulting from differences in crosshead speed were observed in potato samples. The apparent retardation times determined in the developed rheological model ranged from 0.079 s for the steel coil spring to 6.863 s for potatoes.

Epidermal biopolysaccharides from plant seeds enable biodegradable turbulent drag reduction

The high cost of synthetic polymers has been a key impediment limiting the widespread adoption of polymer drag reduction techniques in large-scale engineering applications, such as marine drag reduction. To address consumable cost constraints, we investigate the use of high molar mass biopolysaccharides, present in the mucilaginous epidermis of plant seeds, as inexpensive drag reducers in large Reynolds number turbulent flows. Specifically, we study the aqueous mucilage extracted from flax seeds (Linum usitatissimum) and compare its drag reduction efficacy to that of poly(ethylene oxide) or PEO, a common synthetic polymer widely used as a drag reducing agent in aqueous flows. Macromolecular and rheological characterisation confirm the presence of high molar mass (≥2 MDa) polysaccharides in the extracted mucilage, with an acidic fraction comprising negatively charged chains. Frictional drag measurements, performed inside a bespoke Taylor-Couette apparatus, show that the as-extracted mucilage has comparable drag reduction performance under turbulent flow conditions as aqueous PEO solutions, while concurrently offering advantages in terms of raw material cost, availability, and bio-compatibility. Our results indicate that plant-sourced mucilage can potentially serve as a cost-effective and eco-friendly substitute for synthetic drag reducing polymers in large scale turbulent flow applications.

Experimental and Computational Investigation of the IDDSI Flow Test of Liquids Used in Dysphagia Management

The International Dysphagia Diet Standardisation Initiative (IDDSI) flow test, using a standard 10-mL syringe, is being adopted in many countries for clinical measurement of the consistency of drinks. The working hypothesis is that thickening drinks to retard flow can be advantageous for individuals who struggle to cope with thin drinks. This study assesses how the IDDSI test relates to rheology and clinical knowledge of physiological flows during swallowing. With no pre-existing analytical solution for internal flow through the syringe, a computational model was designed, incorporating rheometry data from a variety of Newtonian and non-Newtonian liquids. The computational model was validated experimentally across the range of liquids but the technique showed limitations in simulating dripping and cohesiveness. Gum-based liquids which were strongly shear-thinning (0.12 < n < 0.25) showed plug-flow characteristics with 90% of the shear occurring in only 22% of the radial dimension. Shear rates were maximal at the nozzle outlet (> 60 times higher than the barrel) and reached 7400/s for the thinnest gum-based liquid. Shear rheology data alone was unable to describe the flow of these drinks. The flow conditions in the test varied according to the type and consistency of liquid, relating to the desired clinical effect.

Comparison of two methods to categorize thickened liquids for dysphagia management in a clinical care setting context: The Bostwick consistometer and the IDDSI Flow Test. Are we talking about the same concept?

The Bostwick consistometer and the International Dysphagia Diet Standardization Initiative (IDDSI) Flow Test are both proposed methods to measure and categorize thickened liquids for dysphagia management. The objectives were to: (a) compare the Bostwick consistometer reference values used in clinical settings and the IDDSI reference values of thickened liquids suggested for nutrition care plans in the management of dysphagia when measuring commercially available preprepared thickened liquids; (b) explore the relationship between the two methods; (c) assess the interchangeability; (d) document the intra-rater reliability. Preprepared thickened liquids (n = 32) were measured twice with the Bostwick consistometer and 3 times with the IDDSI Flow Test, using a rigorous methodology. A registered dietitian nutritionist and a registered nutrition and dietetic technician performed the measurements. The Pearson's correlation coefficient was calculated to explore the relationship between the two methods. Using a linear regression equation, back-calculations of the IDDSI Flow Test values were done, based on the experimental Bostwick results. Interchangeability was assessed by documenting the level of agreement between the results with a Bland and Altman graphical analysis. Intraclass correlation coefficients calculation and a Bland and Altman graphical analysis were performed to assess reliability. The strong correlation (r = -.93, p < .001) between the IDDSI Flow Test and the Bostwick consistometer measurements suggests that they measure flow rate in a similar manner, but not exactly the same, as confirmed with the Bland and Altman graphical analysis. Thus, they produced results that are not interchangeable. However, both tests show excellent intra-rater reliability (ICC ≥ 0.99) when using a rigorous methodology. PRACTICAL APPLICATIONS: Thickened liquids are used to manage oropharyngeal dysphagia. Clinicians need to provide quality assurance/quality control (QA/QC) support in the selection or production of thickened liquids as well as staff training or patient education regarding these products. Methods and classification have been proposed to measure and categorize thickened liquids for dysphagia management, such as the line spread test, the Bostwick consistometer method, and the IDDSI Flow Test. Although empirical, these methods are more accessible to clinicians than viscometer or rheometer assessments. Clinicians need to understand the limitations of these techniques as neither appear to capture the full extent of consistency for potential beverages available on the market or produced in-house. In this article, we compare the Bostwick consistometer and the IDDSI Flow Test methods and classifications and propose a standard operating procedure in order to maximize the quality of results. We point out the large variations in consistency levels of commercial preprepared thickened liquids in light of the absence of evidence of clinical outcomes associated with either proposed methods or consistency classifications.

Viscosity of liquid and semisolid materials: Establishing correlations between instrumental analyses and sensory characteristics

Considering the importance of texture for food products, we aimed to evaluate viscosity of different liquid and semisolid materials through instrumental analyses (rheometer and texture analyzer), as well sensory descriptive analysis, and establishing correlations between all these analyses. Eight materials were used: water, strawberry yogurt, condensed milk, honey, UHT cream, creamy dairy dessert, petit suisse strawberry flavor (a traditional French cheese from Normandy region, and sold as an infant product), and dulce de leche (obtained through cooking of a can of condensed milk, during 15 min under pressure, resulting in a brownish color product and more consistent than condensed milk). All materials were submitted to rheological analysis, analysis on texture analyzer, and descriptive sensory analysis. All techniques of measurement discriminated the texture of samples. The visual viscosity, defined as a sensory attribute evaluated by visual observation, was negatively correlated to apparent viscosity measured through rheological analysis with shear rate at 10 s^-1 . Oral viscosity and body (both defined as sensory attributes evaluated by oral perception) were positively correlated with areas from graphs obtained in the texture analyzer, and with apparent viscosity measured through rheological analysis at shear rate of 10 s^-1 , although positive strong correlation was also found between body and apparent viscosity at higher shear rates (50 and 100 s^-1 ). The strong correlations enable application of these instrumental tests as indicators of the sensory texture of liquid and semisolid materials. PRACTICAL APPLICATIONS: Texture has a minor importance to liquid and semisolid materials in comparison to meat and crunchy products. However, the relevance of texture to these kinds of products has growing up recently. Therefore, measuring and understanding viscosity of liquid and semisolid materials, using different ways of evaluation, brings relevant information to the area. Moreover, establishing correlations between instrumental and sensory analyses may indicate which instrumental analysis and which analysis condition would be more adequate to correlate with sensory perception of texture, allowing a convergence for future studies and for discussion of results.

Fractional Maxwell model of viscoelastic biological materials

This article focuses on fractional Maxwell model of viscoelastic materials, which are a generalization of classic Maxwell model to non-integer order derivatives. To build a fractional Maxwell model when only the noise-corrupted discrete-time measurements of the relaxation modulus are accessible for identification is a basic concern. For fitting the original measurement data an approach is suggested, which is based on approximate Scott Blair fundamental fractional non-integer models, and which means that the data are fitted by solving two dependent but simple linear least-squares problems in two separable time intervals. A complete identification algorithm is presented. The usability of the method to find the fractional Maxwell model of real biological material is shown. The parameters of the fractional Maxwell model of carrot root that approximate the experimental stress relaxation data closely are given.