A. E. Hosoi

New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear

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. PACS numbers: 83.60.Df, 83.85.Ns, 83.80.Qr, 83.80.Lz ∗Electronic address: peko@mit.edu 1 ar X iv :0 71 0. 55 09 v1 [ co nd -m at .s of t] 2 9 O ct 2 00 7 Biopolymer networks [1, 2, 3], wormlike micelles [4], colloidal gels [5], and metastable soft solids in general [6], can be classified as nonlinear viscoelastic materials and as such have been of interest to experimentalists for many decades (e.g. [7]). The biological and industrial processes associated with these materials often involve large deformations, yet standard methods of characterizing their nonlinear rheological properties rely on techniques designed for small strains. In this Letter, we develop a new and systematic framework for quantifying the nonlinear viscoelastic response of soft materials which enables us to describe a unique “rheological fingerprint” of an a priori unknown substance. Both the elastic and viscous characteristics of a material can be examined simultaneously by imposing an oscillatory shear strain, γ(t) = γ0 sin(ωt), which consequently imposes a phase-shifted strain-rate γ̇(t). Here ω is the imposed oscillation frequency, γ0 is the maximum strain amplitude and t is time. At small strain amplitudes when the response is linear, the material is commonly characterized by the viscoelastic moduli G′(ω), G′′(ω), as determined from the components of the stress in phase with γ(t) and γ̇(t), respectively. For a purely elastic linear solid, the elastic modulus G′ is equivalent to the shear modulus G. Similarly, for a purely viscous Newtonian fluid with viscosity μ, the loss modulus G′′ = μω. However, these viscoelastic moduli are not uniquely defined once the material response becomes nonlinear, since higher order harmonics emerge. For convenience the moduli are often determined by the coefficients of the first harmonic, G1 and G ′′ 1 (see Eqn. 1). These measures of the viscoelastic moduli are arbitrary and often fail to capture the rich nonlinearities that appear in the raw data signal [8]. An example of such rich behavior is shown in the large amplitude oscillatory shear (LAOS) results from a wormlike micelle solution in Fig. 1. The periodic stress response σ(t;ω, γ0) at steady state is plotted against either γ(t) or γ̇(t), the simultaneous phase-shifted inputs. These parametric plots are commonly called Lissajous curves (or more accurately, BowditchLissajous curves [21]). In this parameter space, a linear viscoelastic response appears as an ellipse which is progressively distorted by material nonlinearity. We refer to the σ(t) vs. γ(t) curves (Fig. 1a) as elastic Lissajous curves to distinguish them from the viscous Lissajous curves (Fig. 1b) which plot σ(t) as a function of the shear-rate γ̇(t). The most common method of quantifying LAOS tests is Fourier transform (FT) rheology [9]. For a sinusoidal strain input γ(t) = γ0 sinωt, the stress response can be represented asCharacterizing 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 ...

Design and Analysis of a Robust, Low-cost, Highly Articulated manipulator enabled by jamming of granular media

Hyper-redundant manipulators can be fragile, expensive, and limited in their flexibility due to the distributed and bulky actuators that are typically used to achieve the precision and degrees of freedom (DOFs) required. Here, a manipulator is proposed that is robust, high-force, low-cost, and highly articulated without employing traditional actuators mounted at the manipulator joints. Rather, local tunable stiffness is coupled with off-board spooler motors and tension cables to achieve complex manipulator configurations. Tunable stiffness is achieved by reversible jamming of granular media, which-by applying a vacuum to enclosed grains-causes the grains to transition between solid-like states and liquid-like ones. Experimental studies were conducted to identify grains with high strength-to-weight performance. A prototype of the manipulator is presented with performance analysis, with emphasis on speed, strength, and articulation. This novel design for a manipulator-and use of jamming for robotic applications in general-could greatly benefit applications such as human-safe robotics and systems in which robots need to exhibit high flexibility to conform to their environments.

Experimental investigations of elastic tail propulsion at low Reynolds number

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.

Building a better snail: Lubrication and adhesive locomotion

Many gastropods, such as slugs and snails, crawl via an unusual mechanism known as adhesive locomotion. We investigate this method of propulsion using two mathematical models: one for direct waves and one for retrograde waves. We then test the effectiveness of both proposed mechanisms by constructing two mechanical crawlers. Each crawler uses a different mechanical strategy to move on a thin layer of viscous fluid. The first uses a flexible flapping sheet to generate lubrication pressures in a Newtonian fluid, which in turn propel the mechanical snail. The second generates a wave of compression on a layer of Laponite, a non-Newtonian, finite-yield stress fluid with characteristics similar to those of snail mucus. This second design can climb smooth vertical walls and perform an inverted traverse.

Axial instability of a free-surface front in a partially filled horizontal rotating cylinder

We investigate the axial instability of the free-surface front of a viscous fluid in a horizontal cylinder rotating about its longitudinal axis. A simplified model equation for the evolution of the free surface is derived and includes the effects of gravity, capillarity, inertia, and viscosity. This equation is solved numerically to determine the base state with no axial variation, and a numerical linear stability analysis is carried out to examine the onset of unstable axial modes. Various computational results are presented for the wavelength of the axial instability. Inertia is found to play an important role in the onset of the instability and the wavelength of the instability λ satisfies the power law λ∼γ1/3, where γ is surface tension. Finally some numerical simulations of the simplified evolution equation are presented to show that they can capture the steady shark-teeth patterns observed in recent experiments [R. E. Johnson, in Engineering Science, Fluid Dynamics: A Symposium to Honor T. Y. Wu (Wo...

Marangoni convection in droplets on superhydrophobic surfaces

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.

The effect of surface tension on rimming flows in a partially filled rotating cylinder

We study the shape of the interface in a partially filled horizontal cylinder which is rotating about its axis. Two-dimensional steady solutions for the interface height are examined under the assumptions that the filling fraction is small, inertia may be neglected, and the fluid forms a continuous film covering the surface. Three different regimes of steady solutions have been reported in the literature, corresponding to limits in which the ratio of gravitational to viscous forces (as defined in the text) is small, moderate or large. In each case, solutions have only been described analytically in the limit that surface tension effects are negligible everywhere. We use analytical and numerical methods, include surface tension and study steady solutions in a regime when the ratio of gravitational to viscous forces is large. This solution comprises a fluid pool that sits near the bottom of the cylinder and a film that coats the sides and top of the cylinder, the thickness of which can be determined by Landau–Levich–Derjaguin type arguments. We also examine the effect of surface tension on the solutions in the limits of the ratio of gravity to viscous forces being moderate and small.

An experimental investigation of the stability of the circular hydraulic jump

We present the results of an experimental investigation of the striking flow structures that may arise when a vertical jet of fluid impinges on a thin fluid layer overlying a horizontal boundary. Ellegaard et al . ( Nature , vol. 392, 1998, p. 767; Nonlinearity , vol. 12, 1999, p. 1) demonstrated that the axial symmetry of the circular hydraulic jump may be broken, resulting in steady polygonal jumps. In addition to these polygonal forms, our experiments reveal a new class of steady asymmetric jump forms that include structures resembling cats eyes, three- and four-leaf clovers, bowties and butterflies. An extensive parameter study reveals the dependence of the jump structure on the governing dimensionless groups. The symmetry-breaking responsible for the asymmetric jumps is interpreted as resulting from a capillary instability of the circular jump. For all steady non-axisymmetric forms observed, the wavelength of instability of the jump is related to the surface tension,

Evaporative instabilities in climbing films

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Optimal feeding and swimming gaits of biflagellated organisms

, fluid density