A. E. Hosoi

Characterizing purely viscous or purely elastic rheological nonlinearities is straightforward using rheometric tests such as steady shear or step strains. However, a definitive framework does not exist to characterize materials which exhibit both viscous and elastic nonlinearities simultaneously. We define a robust and physically meaningful scheme to quantify such behavior, using an imposed large amplitude oscillatory shear (LAOS) strain. Our new framework includes new material measures and clearly defined terminology such as intra-/intercycle nonlinearities, strain-stiffening/softening, and shear-thinning/thickening. The method naturally lends a physical interpretation to the higher Fourier coefficients that are commonly reported to describe the nonlinear stress response. These nonlinear viscoelastic properties can be used to provide a “rheological fingerprint” in a Pipkin diagram that characterizes the material response as a function of both imposed frequency and strain amplitude. We illustrate our new framework by first examining prototypical nonlinear constitutive models (including purely elastic and purely viscous models, and the nonlinear viscoelastic constitutive equation proposed by Giesekus). In addition, we use this new framework to study experimentally two representative nonlinear soft materials, a biopolymer hydrogel and a wormlike micelle solution. These new material measures can be used to characterize the rheology of any complex fluid or soft solid and clearly reveal important nonlinear material properties which are typically obscured by conventional test protocols.

We introduce a comprehensive scheme to physically quantify both viscous and elastic rheological nonlinearities simultaneously, using an imposed large amplitude oscillatory shear (LAOS) strain. The new framework naturally lends a physical interpretation to commonly reported Fourier coefficients of the nonlinear stress response. Additionally, we address the ambiguities inherent in the standard definitions of viscoelastic moduli when extended into the nonlinear regime, and define new measures which reveal behavior that is obscured by conventional techniques.

Nonlinear rheological properties are often relevant in understanding the response of a material to its intended environment. For example, many gastropods crawl on a thin layer of pedal mucus using a technique called adhesive locomotion, in which the gel structure is periodically ruptured and reformed. We present a mechanical model that captures the key features of this process and suggests that the most important properties for optimal inclined locomotion are a large, reversible yield stress, followed by a small shear viscosity and a short thixotropic restructuring time. We present detailed rheological measurements of native pedal mucus in both the linear and nonlinear viscoelastic regimes and compare this "rheological fingerprint" with corresponding observations of two bioinspired slime simulants, a polymer gel and a clay-based colloidal gel, that are selected on the basis of their macroscopic rheological similarities to gastropod mucin gels. Adhesive locomotion (of snails or mechanical crawlers) imposes a large-amplitude pulsatile simple shear flow onto the supporting complex fluid, motivating the characterization of nonlinear rheological properties with large amplitude oscillatory shear (LAOS). We represent our results in the form of Lissajous curves of oscillatory stress against time-varying strain. The native pedal mucus gel is found to exhibit a pronounced strain-stiffening response, which is not imitated by either simulant.

A simple way to generate propulsion at low Reynolds number is to periodically oscillate a passive flexible filament. Here we present a macroscopic experimental investigation of such a propulsive mechanism. A robotic swimmer is constructed and both tail shape and propulsive force are measured. Filament characteristics and actuation are varied, and the resulting data are quantitatively compared with existing linear and nonlinear theories.

We consider a small droplet of water sitting on top of a heated superhydrophobic surface. A toroidal convection pattern develops in which fluid is observed to rise along the surface of the spherical droplet and to accelerate downwards in the interior towards the liquid/solid contact point. The internal dynamics arise due to the presence of a vertical temperature gradient; this leads to a gradient in surface tension which in turn drives fluid away from the contact point along the interface. We develop a solution to this thermocapillary-driven Marangoni flow analytically in terms of streamfunctions. Quantitative comparisons between analytical and experimental results, as well as effective heat transfer coefficients, are presented.