Consumer products, such as foods, contain numerous polymeric and particulate additives that play critical roles in maintaining their stability, quality and function. The resulting materials exhibit complex bulk and interfacial rheological responses, and often display a distinctive power-law response under standard rheometric deformations. These power laws are not conveniently described using conventional rheological models, without the introduction of a large number of relaxation modes. We present a constitutive framework using fractional derivatives to model the power-law responses often observed experimentally. We first revisit the concept of quasiproperties and their connection to the fractional Maxwell model (FMM). Using Scott-Blair's original data, we demonstrate the ability of the FMM to capture the power-law response of 'highly anomalous' materials. We extend the FMM to describe the viscoelastic interfaces formed by bovine serum albumin and solutions of a common food stabilizer, Acacia gum. Fractional calculus allows us to model and compactly describe the measured frequency response of these interfaces in terms of their quasiproperties. Finally, we demonstrate the predictive ability of the FMM to quantitatively capture the behaviour of complex viscoelastic interfaces by combining the measured quasi-properties with the equation of motion for a complex fluid interface to describe the damped inertio-elastic oscillations that are observed experimentally.

Growing evidence supports a critical role of dynamic metal-coordination crosslinking in soft biological material properties such as self-healing and underwater adhesion1. Using bio-inspired metal-coordinating polymers, initial efforts to mimic these properties have shown promise2. Here we demonstrate how bio-inspired aqueous polymer network mechanics can be easily controlled via metal-coordination crosslink dynamics; metal ion-based crosslink stability control allows aqueous polymer network relaxation times to be finely tuned over several orders of magnitude. In addition to further biological material insights, our demonstration of this compositional scaling mechanism should provide inspiration for new polymer material property-control designs.

Globular proteins influence the flow, microstructure, phase behavior and transport of biofluids and biomolecules in the mammalian body. These proteins are essential constituents of food, drugs and cosmetics, and their dynamics determine the physical properties and application of these multicomponent materials. In conventional rheological studies conducted using typical geometries on torsional rheometers, solutions of globular proteins are commonly reported to have a solid-like response at concentrations as low as 0.03% by weight. Typical explanations invoke the presence of long-range repulsions that are stronger than electrostatic interactions. In this study, we probe the bulk and the interfacial viscoelasticity of surfactant-free bovine serum albumin (BSA) solutions using a stress-controlled torsional rheometer, augmented by microfluidic rheometry and interfacial rheometric measurements. We demonstrate that the origin of this yield-like behavior, which is manifested as a highly shear-thinning bulk rheological response, lies in the formation of a film of adsorbed protein, formed spontaneously at the solution/gas interface. We provide direct interfacial rheometric measurements to study the concentration-dependent viscoelasticity of the adsorbed protein and we describe a simple, but quantitative, additive model useful for extracting the interfacial viscosity contribution from bulk viscosity measurements over a wide range of shear rates.

The relaxation processes of a wide variety of soft materials frequently contain one or more broad regions of power-law-like or stretched exponential relaxation in time and frequency. Fractional constitutive equations have been shown to be excellent models for capturing the linear viscoelastic behavior of such materials, and their relaxation modulus can be quantitatively described very generally in terms of a Mittag-Leffler function. However, these fractional constitutive models cannot describe the nonlinear behavior of such power-law materials. We use the example of Xanthan gum to show how predictions of non-linear viscometric properties such as shear-thinning in the viscosity and in the first normal stress coefficient can be quantitatively described in terms a nonlinear fractional constitutive model. We adopt an integral K-BKZ framework and suitably modify it for power-law materials exhibiting MittagLeffler type relaxation dynamics at small strains. Only one additional parameter is needed to predict nonlinear rheology, which is introduced through an experimentally measured damping function. Empirical rules such as the Cox-Merz rule and Gleissle mirror relations are frequently used to estimate the nonlinear response of complex fluids from linear rheological data. We use the fractional model framework to assess the performance of such heuristic rules and quantify the systematic offsets, or shift factors, that can be observed between experimental data and the predicted nonlinear response. We also demonstrate how an appropriate choice of fractional constitutive model and damping function results in a nonlinear viscoelastic constitutive model that predicts a flow curve identical to the elastic Herschel-Bulkley model. This new constitutive equation satisfies the Rutgers-Delaware rule. that is appropriate for yielding materials. This K-BKZ framework can be used to generate canonical three-element mechanical models that provide nonlinear viscoelastic generalizations of other empirical inelastic models such as the Cross model. In addition to describing nonlinear viscometric responses, we are also able to provide accurate expressions for the linear viscoelastic behavior of complex materials that exhibit strongly shearthinning Cross-type or Carreau-type flow curve. The findings in this work provide a coherent and quantitative way of translating between the linear and nonlinear rheology of multiscale materials, using a constitutive modeling approach that involves only a few material parameters.

Improved friction performance is an important objective of equipment manufacturers for meeting improved energy efficiency demands. The addition of friction-reducing additives, or friction modifiers (FMs), to lubricants is a key part of the strategy. The performance of these additives is related to their surface activity and their ability to form adsorbed layers on the metal surface. However, the extent of surface coverage (mass per unit area) required for effective friction reduction is currently unknown. In this article, we show that full coverage is not necessary for significant friction reduction. We first highlight various features of surface adsorption that can influence the surface coverage, packing, and free energy of adsorption of organic FMs on iron oxide surfaces. Using stearic acid in heptane and hexadecane as model lubricant formulations, we employ a combination of experiments and molecular dynamics (MD) simulations to show how the dimerization of acid molecules in the bulk solvent and the crystallographic orientation of the surface modifies surface adsorption. In addition, we show that the solvent can strongly influence the adsorption kinetics, and MD simulations reveal that hexadecane tends to align on the surface, increasing the energy barrier for the adsorption of stearic acid to the surface. Furthermore, we present a combined approach using MD and molecular thermodynamic theory to calculate adsorption isotherms for stearic acid on iron oxide surfaces, which agrees well with experimental data obtained with a quartz crystal microbalance (QCM). Our results suggest that while the friction of systems lubricated with organic FMs decreases with increasing coverage, complete coverage of the surface is neither practically achievable nor necessary for effective friction reduction for the systems and conditions studied here.