Enhanced O/W emulsifying properties of pea proteins via deamidation: Insights into interfacial behavior

This study examines the effects of protein glutaminase modification on the interfacial properties and emulsion stability of pea protein isolates (PPI). Emulsions were prepared using native (NPPI) and deamidated PPI (DPPI) at concentrations from 0.5 wt% to 3.6 wt%. The stability of these emulsions was evaluated by examining droplet size distribution, flocculation index, ζ-potential, and CLSM. DPPI demonstrated superior emulsifying ability and stability, requiring only 2.0 wt% to prevent flocculation compared to NPPI's 3.6 wt%. Interfacial properties, such as protein coverage, composition, thickness, tension, and rheology, were characterized. Large Amplitude Oscillatory Dilatation analysis showed minimal differences between NPPI and DPPI-stabilized interfaces at 1 wt%. However, at 3.6 wt%, NPPI interfaces demonstrated abrupt intra-cycle yielding and viscous behavior, whereas DPPI interfaces exhibited gradual softening and a higher maximum linear strain. Additionally, DPPI showed higher interfacial protein coverage and lower interfacial tension. NPPI formed dense, brittle films prone to rupture under dynamic deformation, leading to poor stability. Deamidation of PPI unfolded the protein structure, exposing hydrophobic groups and increasing carboxyl groups, which reduced aggregation. This resulted in a uniform, extensible, and elastic interfacial film resistant to large deformations. Thus, DPPI-stabilized emulsions demonstrated superior stability, showcasing their potential for industrial applications.

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.

Toward Diverse Plant Proteins for Food Innovation

This review highlights the development of plant proteins from a wide variety of sources, as most of the research and development efforts to date have been limited to a few sources including soy, chickpea, wheat, and pea. The native structure of plant proteins during production and their impact on food colloids including emulsions, foams, and gels are considered in relation to their fundamental properties, while highlighting the recent developments in the production and processing technologies with regard to their impacts on the molecular properties and aggregation of the proteins. The ability to quantify structural, morphological, and rheological properties can provide a better understanding of the roles of plant proteins in food systems. The applications of plant proteins as dairy and meat alternatives are discussed from the perspective of food structure formation. Future directions on the processing of plant proteins and potential applications are outlined to encourage the generation of more diverse plant-based products.

Modified and generalized single-element Maxwell viscoelastic model

In this Letter, the single-element Maxwell model is generalized with respect to the wave vector and extended with a correction function that measures the reduced viscous response. This model has only two free parameters and avoids the attenuation-frequency locking present in the original model. Through molecular simulations it is shown that the model satisfactory predicts the transverse dynamics of the binary Lennard-Jones system at different temperatures, as well as water and toluene at ambient conditions. The correction function shows that the viscous response is significantly reduced compared to the predictions of the original Maxwell model and that there exists a characteristic length scale of minimum dissipation.

Sublinear drag regime at mesoscopic scales in viscoelastic materials

Stressed soft materials commonly present viscoelastic signatures in the form of power-law or exponential decay. Although exponential responses are the most common, power-law time dependencies arise peculiarly in complex soft materials such as living cells. Understanding the microscale mechanisms that drive rheologic behaviors at the macroscale shall be transformative in fields such as material design and bioengineering. Using an elastic network model of macromolecules immersed in a viscous fluid, we numerically reproduce those characteristic viscoelastic relaxations and show how the microscopic interactions determine the rheologic response. The macromolecules, represented by particles in the network, interact with neighbors through a spring constant k and with fluid through a non-linear drag regime. The dissipative force is given by γvα, where v is the particle's velocity, and γ and α are mesoscopic parameters. Physically, the sublinear regime of the drag forces is related to micro-deformations of the macromolecules, while α ≥ 1 represents rigid cases. We obtain exponential or power-law relaxations or a transitional behavior between them by changing k, γ, and α. We find that exponential decays are indeed the most common behavior. However, power laws may arise when forces between the macromolecules and the fluid are sublinear. Our findings show that in materials not too soft not too elastic, the rheological responses are entirely controlled by α in the sublinear regime. More specifically, power-law responses arise for 0.3 ⪅ α ⪅ 0.45, while exponential responses for small and large values of α, namely, 0.0 ⪅ α ⪅ 0.2 and 0.55 ⪅ α ⪅ 1.0.

Acid-Induced Gelation of Carboxymethylcellulose Solutions

The present work offers a comprehensive description of the acid-induced gelation of carboxymethylcellulose (CMC), a water-soluble derivative of cellulose broadly used in numerous applications ranging from food packaging to biomedical engineering. Linear viscoelastic properties measured at various pH and CMC contents allow us to build a sol-gel phase diagram and show that CMC gels exhibit broad power-law viscoelastic spectra that can be rescaled onto a master curve following a time-composition superposition principle. These results demonstrate the microstructural self-similarity of CMC gels and inspire a mean-field model based on hydrophobic interchain association that accounts for the sol-gel boundary over the entire range of CMC content under study. Neutron scattering experiments further confirm this picture and suggest that CMC gels comprise a fibrous network cross-linked by aggregates. Finally, low-field NMR measurements offer an original signature of acid-induced gelation from a solvent perspective. Altogether, these results open avenues for the precise manipulation and control of CMC-based hydrogels.

Universal scaling of the diffusivity of dendrimers in a semidilute solution of linear polymers

The static and dynamic properties of dendrimers in semidilute solutions of linear chains of comparable size are investigated using Brownian dynamics simulations. The radius of gyration and diffusivity of a wide variety of low generation dendrimers and linear chains in solution follow universal scaling laws independent of their topology. Analysis of the shape functions and internal density of dendrimers shows that they are more spherical than linear chains and have a dense core. At intermediate times, dendrimers become subdiffusive, with an exponent higher than that previously reported for nanoparticles in semidilute polymer solutions. The long-time diffusivity of dendrimers does not follow theoretical predictions for nanoparticles. We propose a new scaling law for the long-time diffusion coefficients of dendrimers which accounts for the fact that, unlike nanoparticles, dendrimers shrink with an increase in background solution concentration. Analysis of the properties of a special case of a higher functionality dendrimer shows a transition from polymer-like to nanoparticle-like behaviour.

Critical-Like Gelation Dynamics in Cellulose Nanocrystal Suspensions

We use time-resolved mechanical spectroscopy to offer a detailed picture of the gelation dynamics of cellulose nanocrystal (CNC) suspensions following shear cessation in the presence of salt. CNCs are charged, rodlike colloids that self-assemble into various phases, including physical gels serving as soft precursors for biosourced composites. Here, a series of linear viscoelastic spectra acquired across the sol-gel transition of CNC suspensions are rescaled onto two master curves that correspond to a viscoelastic liquid state prior to gelation and to a soft solid state after gelation. These two states are separated by a critical gel point, where all rescaling parameters diverge in an asymmetric fashion yet with exponents that obey hyperscaling relations consistent with previous works on isotropic colloids and polymer gels. Upon varying the salt content, we further show that these critical-like dynamics result in both time-connectivity and time-concentration superposition principles.

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.

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.

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.

A GENERAL RETURN-MAPPING FRAMEWORK FOR FRACTIONAL VISCO-ELASTO-PLASTICITY

We develop a fractional return-mapping framework for power-law visco-elasto-plasticity. In our approach, the fractional viscoelasticity is accounted through canonical combinations of Scott-Blair elements to construct a series of well-known fractional linear viscoelastic models, such as Kelvin-Voigt, Maxwell, Kelvin-Zener and Poynting-Thomson. We also consider a fractional quasi-linear version of Fung's model to account for stress/strain nonlinearity. The fractional viscoelastic models are combined with a fractional visco-plastic device, coupled with fractional viscoelastic models involving serial combinations of Scott-Blair elements. We then develop a general return-mapping procedure, which is fully implicit for linear viscoelastic models, and semi-implicit for the quasi-linear case. We find that, in the correction phase, the discrete stress projection and plastic slip have the same form for all the considered models, although with different property and time-step dependent projection terms. A series of numerical experiments is carried out with analytical and reference solutions to demonstrate the convergence and computational cost of the proposed framework, which is shown to be at least first-order accurate for general loading conditions. Our numerical results demonstrate that the developed framework is more flexible, preserves the numerical accuracy of existing approaches while being more computationally tractable in the visco-plastic range due to a reduction of 50% in CPU time. Our formulation is especially suited for emerging applications of fractional calculus in bio-tissues that present the hallmark of multiple viscoelastic power-laws coupled with visco-plasticity.

Modelling viscoelastic relaxation mechanisms in thermorheologically complex Fe(III)-poly(acrylic acid) hydrogels

Mechanical properties of hydrogels with reversible transition metal-polymer crosslinks can be flexibly tuned depending on the dissociation kinetics of the metal bond. We use rheology to investigate the sol-gel transition of a Fe(III)-poly(acrylic acid) network with varying crosslinker content and model the corresponding mechanical relaxation at different stages of gelation. The system transitions from an unentangled chain regime to a crosslink dissociation dominated regime, where the relaxation is governed by two timescales with different activation energies. To account for the interplay of chain and crosslinker dynamics, a time-temperature-superposition procedure is introduced for both processes separately, thus separating the dynamic processes in these thermorheologically complex dynamic networks. The activation energy of chain relaxation remains unchanged whether or not the chain participates in the network. To model contributions to the dynamic modulus of each process, we combine concepts from fractional viscoelasticity with a generalized Maxwell model, which describes the dynamics of an unentangled chain solution with reversible crosslinks. This allows us to quantify the evolution of viscoelastic parameters in the course of gelation, where we find that the terminal relaxation time of the gels increases less than expected at high crosslinker contents. This result is attributed to a facilitated crosslink exchange mechanism and a lower pH of the gel matrix.

Magneto-Viscoelastic Materials: Memory Functionals and Rate Equations

The properties of viscoelastic solids subject to a magnetic field are modelled within two thermodynamically consistent approaches that are typical of models with a non-instantaneous response. One is based on memory functionals: the reversible changes are described by the instantaneous response, while the dissipativity is expressed by the dependence on histories. The other approach involves objective rate equations. While memory functionals lead to the difficulty of determining thermodynamically consistent free energy functionals, rate equations result in a simpler scheme. The greater simplicity allows the discovery of, in particular, models of magneto-hyperelastic materials, magneto-hypoelastic materials, and various forms of magneto-viscoelastic behaviour. The novelty of the procedure is based on two features: a representation formula, originating from the entropy inequality, and the use of the entropy production as a constitutive function. Relations with other approaches in the literature are examined in detail.

Structural and Dynamical Studies of a Lipid-Nanoclay Composite Layer at the Air-Water Interface

We modulate the adsorption affinities of nanoclay particles for the air-water interface by changing the cationic surface charge composition of the lipid monolayer and thereby tune the attractive electrostatic interaction between the positively charged lipid layer and the zwitterionic nanoclay particles in the water subphase. Our findings emphasize the significance of electrostatic interaction between lipids and the nanoclay, as well as its impact on the structural and viscoelastic features of the composite layer. We use surface pressure (Π)-mean molecular area (A) isotherms, atomic force microscope (AFM), Brewster angle microscopy (BAM), and energy dispersive X-ray spectrsocopy (EDXS) measurements to analyze the structure phases of lipid and lipid-nanoclay composite interfacial layer. The Π-A isotherm curve shows that the lipid-nanoclay composite layer has a larger lift-off area than the neat lipid layer, indicating that nanoparticles adsorb at the lipid layer via electrostatic interaction between lipid and nanoclay molecules. The surface density of the adsorbed nanoclay particles increases with an increase in the composition of the cationic lipid molecules. The stress relaxation response of the composite layer, measured using step compression measurements, exhibits exponential decay and ubiquitous dependence on the cationic dimyristoy-trimethylammonium propane (DMTAP) composition in the lipid layer with crossover to faster relaxation dynamics at DMTAP > 0.75. The power-law study of the frequency-dependent dynamic viscoelastic responses of the interfacial layer, measured using the barrier oscillation method, reveals a transition from glass-like response from neat lipid layer to gel-like dynamic response for the lipid-nanoclay composite layer. A solid-like behavior is evident for all the interface layers with dilation elastic modulus (E') > dilational viscous modulus (E″); however, the dynamic response of the neat layer is largely frequency-independent, whereas lipid-nanoclay composite layers with DMTAP > 0.75 reveal a frequency-dependent dynamic responses. The frequency-dependent power-law exponent of E', E″ increases on increasing the fractional composition of cationic DMTAP from 0.1 to 1.0, which forms a saturated interface of laponite particles and behaves as a viscoelastic gel in 2D.

Understanding the Dynamics of Cellulose Dissolved in an Ionic Liquid Solvent Under Shear and Extensional Flows

Ionic liquids (ILs) hold great potential as solvents to dissolve, recycle, and regenerate cellulosic fabrics, but the dissolved cellulose material system requires greater study in conditions relevant to fiber spinning processes, especially characterization of nonlinear shear and extensional flows. To address this gap, we aimed to disentangle the effects of the temperature, cellulose concentration, and degree of polymerization (DOP) on the shear and extensional flows of cellulose dissolved in an IL. We have studied the behavior of cellulose from two sources, fabric and filter paper, dissolved in 1-ethyl-3-methylimidazolium acetate ([C₂C₁Im][OAc]) over a range of temperatures (25 to 80 °C) and concentrations (up to 4%) that cover both semidilute and entangled regimes. The linear viscoelastic (LVE) response was measured using small-amplitude oscillatory shear techniques, and the results were unified by reducing the temperature, concentration, and DOP onto a single master curve using time superposition techniques. The shear rheological data were further fitted to a fractional Maxwell liquid (FML) model and were found to satisfy the Cox-Merz rule within the measurement range. Meanwhile, the material response in the non-LVE (NLVE) regime at large strains and strain rates has special relevance for spinning processes. We quantified the NLVE behavior using steady shear flow tests alongside uniaxial extension using a customized capillary breakup extensional rheometer. The results for both shear and extensional NLVE responses were described by the Rolie-Poly model to account for flow-dependent relaxation times and nonmonotonic viscosity evolution with strain rates in an extensional flow, which primarily arise from complex polymer interactions at high concentrations. The physically interpretable model fitting parameters were further compared to describe differences in material response to different flow types at varying temperatures, concentrations, and DOP. Finally, the fitting parameters from the FML and Rolie-Poly models were connected under the same superposition framework to provide a comprehensive description within the wide measured parameter window for the flow and handling of cellulose in [C₂C₁Im][OAc] in both linear and nonlinear regimes.

A Data-Driven Memory-Dependent Modeling Framework for Anomalous Rheology: Application to Urinary Bladder Tissue

We introduce a data-driven fractional modeling framework for complex materials, and particularly bio-tissues. From multi-step relaxation experiments of distinct anatomical locations of porcine urinary bladder, we identify an anomalous relaxation character, with two power-law-like behaviors for short/long long times, and nonlinearity for strains greater than 25%. The first component of our framework is an existence study, to determine admissible fractional viscoelastic models that qualitatively describe linear relaxation. After the linear viscoelastic model is selected, the second stage adds large-strain effects to the framework through a fractional quasi-linear viscoelastic approach for the nonlinear elastic response of the bio-tissue of interest. From single-step relaxation data of the urinary bladder, a fractional Maxwell model captures both short/long-term behaviors with two fractional orders, being the most suitable model for small strains at the first stage. For the second stage, multi-step relaxation data under large strains were employed to calibrate a four-parameter fractional quasi-linear viscoelastic model, that combines a Scott-Blair relaxation function and an exponential instantaneous stress response, to describe the elastin/collagen phases of bladder rheology. Our obtained results demonstrate that the employed fractional quasi-linear model, with a single fractional order in the range α = 0.25–0.30, is suitable for the porcine urinary bladder, producing errors below 2% without need for recalibration over subsequent applied strains. We conclude that fractional models are attractive tools to capture the bladder tissue behavior under small-to-large strains and multiple time scales, therefore being potential alternatives to describe multiple stages of bladder functionality.

A microfluidic approach to studying the injection flow of concentrated albumin solutions

Abstract

Subcutaneous injection by means of prefilled syringes allows patients to self-administrate high-concentration (100 g/L or more) protein-based drugs. Although the shear flow of concentrated globulins or monoclonal antibodies has been intensively studied and related to the injection force proper of SC processes, very small attention has been paid to the extensional behavior of this category of complex fluids. This work focuses on the flow of concentrated bovine serum albumin (BSA) solutions through a microfluidic “syringe-on-chip” contraction device which shares some similarities with the geometry of syringes used in SC self-injection. By comparing the velocity and pressure measurements in complex flow with rheometric shear measurements obtained by means of the “Rheo-chip” device, it is shown that the extensional viscosity plays an important role in the injection process of protinaceous drugs.

Article Highlights

A microfluidic “syringe on chip” device mimicking the injection flow of protinaceous drugs has been developed.

The velocity field of concentrated BSA solutions through the “syringe on chip” is Newtonian-like.

The extensional viscosity of concentrated protein solutions should also be considered when computing injection forces through needles.

Anomalous Nonlinear Dynamics Behavior of Fractional Viscoelastic Beams

Fractional models and their parameters are sensitive to intrinsic microstructural changes in anomalous materials. We investigate how such physics-informed models propagate the evolving anomalous rheology to the nonlinear dynamics of mechanical systems. In particular, we study the vibration of a fractional, geometrically nonlinear viscoelastic cantilever beam, under base excitation and free vibration, where the viscoelasticity is described by a distributed-order fractional model. We employ Hamilton's principle to obtain the equation of motion with the choice of specific material distribution functions that recover a fractional Kelvin-Voigt viscoelastic model of order α. Through spectral decomposition in space, the resulting time-fractional partial differential equation reduces to a nonlinear time-fractional ordinary differential equation, where the linear counterpart is numerically integrated through a direct L1-difference scheme. We further develop a semi-analytical scheme to solve the nonlinear system through a method of multiple scales, yielding a cubic algebraic equation in terms of the frequency. Our numerical results suggest a set of α-dependent anomalous dynamic qualities, such as far-from-equilibrium power-law decay rates, amplitude super-sensitivity at free vibration, and bifurcation in steady-state amplitude at primary resonance.

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.

Fractional-order model representations of apparent vascular compliance as an alternative in the analysis of arterial stiffness: anin-silicostudy

Objective. Recent studies have demonstrated the advantages of fractional-order calculus tools for probing the viscoelastic properties of collagenous tissue, characterizing the arterial blood flow and red cell membrane mechanics, and modeling the aortic valve cusp. In this article, we present novel lumped-parameter equivalent circuit models for apparent arterial compliance using a fractional-order capacitor (FOC). FOCs, which generalize capacitors and resistors, display a fractional-order behavior that can capture both elastic and viscous properties through a power-law formulation.Approach. The proposed framework describes the dynamic relationship between the blood-pressure input and the blood volume, using linear fractional-order differential equations.Main results. The results show that the proposed models present a reasonable fit with thein-silicodata of more than 4000 subjects. Additionally, strong correlations have been identified between the fractional-order parameter estimates and the central hemodynamic determinants as well as the pulse-wave velocity indexes.Significance. Therefore, the fractional-order-based paradigm for arterial compliance shows notable potential as an alternative tool in the analysis of arterial stiffness.

Two modes of cluster dynamics govern the viscoelasticity of colloidal gels

Colloidal gels formed by strongly attractive particles at low particle volume fractions are composed of space-spanning networks of uniformly sized clusters. We study the thermal fluctuations of the clusters using differential dynamic microscopy by decomposing them into two modes of dynamics, and link them to the macroscopic viscoelasticity via rheometry. The first mode, dominant at early times, represents the localized, elastic fluctuations of individual clusters. The second mode, pronounced at late times, reflects the collective, viscoelastic dynamics facilitated by the connectivity of the clusters. By mixing two types of particles of distinct attraction strengths in different proportions, we control the transition time at which the collective mode starts to dominate, and hence tune the frequency dependence of the linear viscoelastic moduli of the binary gels.

Complex coacervation and metal-ligand bonding as synergistic design elements for aqueous viscoelastic materials

The application of complex coacervates in promising areas such as coatings and surgical glues requires a tight control of their viscous and elastic behaviour, and a keen understanding of the corresponding microscopic mechanisms. While the viscous, or dissipative, aspect is crucial at pre-setting times and in preventing detachment, elasticity at long waiting times and low strain rates is crucial to sustain a load-bearing joints. The independent tailoring of dissipative and elastic properties proves to be a major challenge that can not be addressed adequately by the complex coacervate motif by itself. We propose a versatile model of complex coacervates with customizable rheological fates by functionalization of polyelectrolytes with terpyridines, which provide transient crosslinks through complexation with metals. We show that the rheology of the hybrid complexes shows distinct footprints of both metal-ligand and coacervate dynamics, the former as a contribution very close to pure Maxwell viscoelasticity, the latter approaching a sticky Rouse fluid. Strikingly, when the contribution of metal-ligand bonds is dominant at long times, the relaxation of the overall complex is much slower than either the "native" coacervate relaxation time or the dissociation time of a comparable non-coacervate polyelectrolyte-metal-ligand complex. We recognize this slowing-down of transient bonds as a synergistic effect that has important implications for the use of complementary transient bonding in coacervate complexes.

Acoustic bubble dynamics in a yield-stress fluid

Yield-stress fluids naturally trap small bubbles when their buoyancy applies an insufficient stress to induce local yielding of the material. Under acoustic excitation, trapped bubbles can be driven into volumetric oscillations and apply an additional local strain and stress that can trigger yielding and assist their release. In this paper we explore different regimes of microbubble oscillation and translation driven by an ultrasound field in a model yield-stress fluid, a Carbopol microgel. We first analyse the linear bubble oscillation dynamics to measure the local, high-frequency viscosity of the material. We then use acoustic pressure gradients to induce bubble translation and examine the elastic part of the response of the material below yielding. We find that, at moderate pressure amplitude, the additional stresses applied by volumetric oscillations and acoustic radiation forces do not lead to any detectable irreversible bubble motion. At high pressure amplitude, we observe non-spherical shape oscillations that result in erratic bubble motion. The critical pressures we observe differ from the predictions of a recent model of shape oscillations in soft solids. Based on our findings, we discuss possible reasons for the lack of bubble release in Carbopol and suggest other systems in which ultrasound-assisted bubble rise may be observed.

The relationship between viscoelasticity and elasticity

Soft materials that are subjected to large deformations exhibit an extremely rich phenomenology, with properties lying in between those of simple fluids and those of elastic solids. In the continuum description of these systems, one typically follows either the route of solid mechanics (Lagrangian description) or the route of fluid mechanics (Eulerian description). The purpose of this review is to highlight the relationship between the theories of viscoelasticity and of elasticity, and to leverage this connection in contemporary soft matter problems. We review the principles governing models for viscoelastic liquids, for example solutions of flexible polymers. Such materials are characterized by a relaxation time λ, over which stresses relax. We recall the kinematics and elastic response of large deformations, and show which polymer models do (and which do not) correspond to a nonlinear elastic solid in the limit λ → ∞. With this insight, we split the work done by elastic stresses into reversible and dissipative parts, and establish the general form of the conservation law for the total energy. The elastic correspondence can offer an insightful tool for a broad class of problems; as an illustration, we show how the presence or absence of an elastic limit determines the fate of an elastic thread during capillary instability.

High-Fidelity Hydrogel Thin Films Processed from Deep Eutectic Solvents

Polyampholyte (PA) hydrogels are a fascinating class of soft materials that can exhibit high toughness while retaining self-healing characteristics. This behavior results from the random distribution of oppositely charged monomers along the polymer chains that form transient bonds with a range of bond strengths. PAs can be dissolved in aqueous salt solutions and then recast via immersion precipitation, making them particularly useful as surface coatings in biomedical applications. Moreover, this immersion precipitation technique allows these PA hydrogels to be fabricated into films less than 100 nm. One critical challenge to this aqueous processing method is the recrystallization of the salt upon water evaporation. Such recrystallization can disrupt the hydrogel morphology especially in thin films. In this study, a deep eutectic solvent (DES) formed from urea and choline chloride was used to dissolve PAs made from p-styrenesulfonic acid sodium salt and 3-(methacryloylamino)propyl trimethylammonium chloride. This DES has a freezing point of 12 °C, allowing it to remain stable and liquid-like at room temperatures. Thus, these PAs can be processed in DES solutions, without this issue of recrystallization and with simple methods such as spin coating and dip coating. These methods allow these hydrogels to be used in thin (<100 nm)-film coating applications. Finally, the complete miscibility of DES in water allows a wider range of one-phase compositions and expands the processing window of these polyampholyte materials.

Fractional viscoelastic models for power-law materials

Soft materials often exhibit a distinctive power-law viscoelastic response arising from broad distribution of time-scales present in their complex internal structure. A promising tool to accurately describe the rheological behaviour of soft materials is fractional calculus. However, its use in the scientific community remains limited due to the unusual notation and non-trivial properties of fractional operators. This review aims to provide a clear and accessible description of fractional viscoelastic models for a broad audience and to demonstrate the ability of these models to deliver a unified approach for the characterisation of power-law materials. The use of a consistent framework for the analysis of rheological data would help classify the empirical behaviours of soft and biological materials, and better understand their response.

Advanced materials modelling via fractional calculus: challenges and perspectives

Fractional calculus is now a well-established tool in engineering science, with very promising applications in materials modelling. Indeed, several studies have shown that fractional operators can successfully describe complex long-memory and multiscale phenomena in materials, which can hardly be captured by standard mathematical approaches as, for instance, classical differential calculus. Furthermore, fractional calculus has recently proved to be an excellent framework for modelling non-conventional fractal and non-local media, opening valuable prospects on future engineered materials. The theme issue gathers cutting-edge theoretical, computational and experimental studies on advanced materials modelling via fractional calculus, with a focus on complex phenomena and non-conventional media. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.

Assessment of Fractional-Order Arterial Windkessel as a Model of Aortic Input Impedance

Goal: Fractional-order Windkessel model is proposed to describe the aortic input impedance. Compared with the conventional arterial Windkessel, the main advantage of the proposed model is the consideration of the viscoelastic nature of the arterial wall using the fractional-order capacitor (FOC). Methods: The proposed model, along with the standard two-element Windkessel, three-element Windkessel, and the viscoelastic Windkessel models, are assessed and compared using in-silico data. Results: The results show that the fractional-order model fits better the moduli of the aortic input impedance and fairly approximates the phase angle. In addition, by its very nature, the pseudo-capacitance of FOC makes the proposed model's dynamic compliance complex and frequency-dependent. Conclusions: The analysis of the proposed fractional-order model indicates that fractional-order impedance yields a powerful tool for a flexible characterization of the arterial hemodynamics.

Double power-law viscoelastic relaxation of living cells encodes motility trends

Living cells are constantly exchanging momentum with their surroundings. So far, there is no consensus regarding how cells respond to such external stimuli, although it reveals much about their internal structures, motility as well as the emergence of disorders. Here, we report that twelve cell lines, ranging from healthy fibroblasts to cancer cells, hold a ubiquitous double power-law viscoelastic relaxation compatible with the fractional Kelvin-Voigt viscoelastic model. Atomic Force Microscopy measurements in time domain were employed to determine the mechanical parameters, namely, the fast and slow relaxation exponents, the crossover timescale between power law regimes, and the cell stiffness. These cell-dependent quantities show strong correlation with their collective migration and invasiveness properties. Beyond that, the crossover timescale sets the fastest timescale for cells to perform their biological functions.

Single-molecule lamellar hydrogels from bolaform microbial glucolipids

Lipid lamellar hydrogels are rare soft fluids composed of a phospholipid lamellar phase instead of fibrillar networks. The mechanical properties of these materials are controlled by defects, induced by local accumulation of a polymer or surfactant in a classical lipid bilayer. Herein we report a new class of lipid lamellar hydrogels composed of one single bolaform glycosylated lipid obtained by fermentation. The lipid is self-organized into flat interdigitated membranes, stabilized by electrostatic repulsive forces and stacked in micrometer-sized lamellar domains. The defects in the membranes and the interconnection of the lamellar domains are responsible, from the nano- to the micrometer scales, for the elastic properties of the hydrogels. The lamellar structure is probed by combining small angle X-ray and neutron scattering (SAXS, SANS), the defect-rich lamellar domains are visualized by polarized light microscopy while the elastic properties are studied by oscillatory rheology. The latter show that both storage G' and loss G'' moduli scale as a weak power-law of the frequency, that can be fitted with fractional rheology models. The hydrogels possess rheo-thinning properties with second-scale recovery. We also show that ionic strength is not only necessary, as one could expect, to control the interactions in the lamellar phase but, most importantly, it directly controls the elastic properties of the lamellar gels.

Nanofabrication of Au nanoparticles over conductive metallohydrogel nanofibers for nanocatalysis application

A conductive and fluorescent metallohydrogel (1% w/v, CPH) has been synthesized and utilized for nanofabrication of AuNps and nanocatalysis applications.

Interfacial Dilational Viscoelasticity of Adsorption Layers at the Hydrocarbon/Water Interface: The Fractional Maxwell Model

In this communication, the single element version of the fractional Maxwell model (single-FMM or Scott–Blair model) is adopted to quantify the observed behavior of the linear interfacial dilational viscoelasticity. This mathematical tool is applied to the results obtained by capillary pressure experiments under low-gravity conditions aboard the International Space Station, for adsorption layers at the hydrocarbon/water interface. Two specific experimental sets of steady-state harmonic oscillations of interfacial area are reported, respectively: a drop of pure water into a Span-80 surfactant/paraffin-oil matrix and a pure n-hexane drop into a C13DMPO/TTAB mixed surfactants/aqueous-solution matrix. The fractional constitutive single-FMM is demonstrated to embrace the standard Maxwell model (MM) and the Lucassen–van-den-Tempel model (L–vdT), as particular cases. The single-FMM adequately fits the Span-80/paraffin-oil observed results, correctly predicting the frequency dependence of the complex viscoelastic modulus and the inherent phase-shift angle. In contrast, the single-FMM appears as a scarcely adequate tool to fit the observed behavior of the mixed-adsorption surfactants for the C13DMPO/TTAB/aqueous solution matrix (despite the single-FMM satisfactorily comparing to the phenomenology of the sole complex viscoelastic modulus). Further speculations are envisaged in order to devise combined FMM as rational guidance to interpret the properties and the interfacial structure of complex mixed surfactant adsorption systems.

Rate-dependent constitutive modeling of brain tissue

In this paper, the dynamic behavior of bovine brain tissue, measured from a set of in vitro experiments, is investigated and represented through a nonlinear viscoelastic constitutive model. The brain samples were tested by employing unconfined compression tests at three different deformation rates of 10, 100, and 1000 mm/s. The tissue exhibited a significant rate-dependent behavior with different compression speeds. Based on the parallel rheological framework approach, a nonlinear viscoelastic model that captures the key aspects of the rate dependency in large-strain behavior was introduced. The proposed model was numerically calibrated to the tissue test data from three different deformation rates. The determined material parameters provided an excellent constitutive representation of tissue response in comparison with the test results. The obtained material parameters were employed in finite element simulations of tissue under compression loadings and successfully verified by the experimental results, thus demonstrating the computational compatibility of the proposed material model. The results of this paper provide groundwork in developing a characterization framework for large-strain and rate-dependent behavior of brain tissue at moderate to high strain rates which is of the highest importance in biomechanical analysis of the traumatic brain injury.

On Dynamic Systems in the Frame of Singular Function Dependent Kernel Fractional Derivatives

In this article, we discuss the existence and uniqueness theorem for differential equations in the frame of Caputo fractional derivatives with a singular function dependent kernel. We discuss the Mittag-Leffler bounds of these solutions. Using successive approximation, we find a formula for the solution of a special case. Then, using a modified Laplace transform and the Lyapunov direct method, we prove the Mittag-Leffler stability of the considered system.

A mesoscale study of creep in a microgel using the acoustic radiation force

We study the motion of a sphere of diameter 330 μm embedded in a Carbopol microgel under the effect of the acoustic radiation pressure exerted by a focused ultrasonic field. The sphere motion within the microgel is tracked using videomicroscopy and compared to conventional creep and recovery measurements performed with a rheometer. We find that under moderate ultrasonic intensities, the sphere creeps as a power law of time with an exponent α ≃ 0.2 that is significantly smaller than the one inferred from global creep measurements below the yield stress of the microgel (α ≃ 0.4). Moreover, the sphere relaxation motion after creep and the global recovery are respectively consistent with these two different exponents. By allowing a rheological characterization at the scale of the sphere with forces of the order of micronewtons, the present experiments pave the way for acoustic "mesorheology" which probes volumes and forces an intermediate between standard macroscopic rheology and classical microrheology. They also open new questions about the effects of the geometry of the deformation field and of the sphere size and surface properties on the creep behaviour of soft materials.

Dynamic heterogeneity in complex interfaces of soft interface-dominated materials

Complex interfaces stabilized by proteins, polymers or nanoparticles, have a much richer dynamics than those stabilized by simple surfactants. By subjecting fluid-fluid interfaces to step extension-compression deformations, we show that in general these complex interfaces have dynamic heterogeneity in their relaxation response that is well described by a Kohlrausch-Williams-Watts function, with stretch exponent β between 0.4-0.6 for extension, and 0.6-1.0 for compression. The difference in β between expansion and compression points to an asymmetry in the dynamics. Using atomic force microscopy and simulations we prove that the dynamic heterogeneity is intimately related to interfacial structural heterogeneity and show that the dominant mode for stretched exponential relaxation is momentum transfer between bulk and interface, a mechanism which has so far largely been ignored in experimental surface rheology. We describe how its rate constant can be determined using molecular dynamics simulations. These interfaces clearly behave like disordered viscoelastic solids and need to be described substantially different from the 2d homogeneous viscoelastic fluids typically formed by simple surfactants.

Colloidal Gels with Tunable Mechanomorphology Regulate Endothelial Morphogenesis

Endothelial morphogenesis into capillary networks is dependent on the matrix morphology and mechanical properties. In current 3D gels, these two matrix features are interdependent and their distinct roles in endothelial organization are not known. Thus, it is important to decouple these parameters in the matrix design. Colloidal gels can be engineered to regulate the microstructural morphology and mechanics in an independent manner because colloidal gels are formed by the aggregation of particles into a self-similar 3D network. In this work, gelatin based colloidal gels with distinct mechanomorphology were developed by engineering the electrostatic interaction mediated aggregation of particles. By altering the mode of aggregation, colloidal gels showed either compact dense microstructure or tenuous strand-like networks, and the matrix stiffness was controlled independently by varying the particle fraction. Endothelial Cell (EC) networks were favored in tenuous strand-like microstructure through increased cell-matrix and cell-cell interactions, while compact dense microstructure inhibited the networks. For a given microstructure, as the gel stiffness was increased, the extent of EC network was reduced. This result demonstrates that 3D matrix morphology and mechanics provide distinct signals in a bidirectional manner during EC network formation. Colloidal gels can be used to interrogate the angiogenic responses of ECs and can be developed as a biomaterial for vascularization.

Precursors of fluidisation in the creep response of a soft glass

Via extensive numerical simulations, we study the fluidisation process of dense amorphous materials subjected to an external shear stress, using a three-dimensional colloidal glass model. In order to disentangle possible boundary effects from finite size effects in the process of fluidisation, we implement a novel geometry-constrained protocol with periodic boundary conditions. We show that this protocol is well controlled and that the longtime fluidisation dynamics is, to a great extent, independent of the details of the protocol parameters. Our protocol, therefore, provides an ideal tool to investigate the bulk dynamics prior to yielding and to study finite size effects regarding the fluidisation process. Our study reveals the existence of precursors to fluidisation observed as a peak in the strain-rate fluctuations, that allows for a robust definition of a fluidisation time. Although the exponents in the power-law creep dynamics seem not to depend significantly on the system size, we reveal strong finite size effects for the onset of fluidisation.