Rheology of discrete failure regimes of anisotropic sea ice

A rheological model of sea ice is presented that incorporates the orientational distribution of ice thickness in leads embedded in isotropic floe ice. Sea ice internal stress is determined by coulombic, ridging and tensile failure at orientations where corresponding failure criteria are satisfied at minimum stresses. Because sea ice traction increases in thinner leads and cohesion is finite, such failure line angles are determined by the orientational distribution of sea ice thickness relative to the imposed stresses. In contrast to the isotropic case, sea ice thickness anisotropy results in these failure lines becoming dependent on the stress magnitude. Although generally a given failure criteria type can be satisfied at many directions, only two at most are considered. The strain rate is determined by shearing along slip lines accompanied by dilatancy and closing or opening across orientations affected by ridging or tensile failure. The rheology is illustrated by a yield curve determined by combining coulombic and ridging failure for the case of two pairs of isotropically formed leads of different thicknesses rotated with regard to each other, which models two events of coulombic failure followed by dilatancy and refreezing. The yield curve consists of linear segments describing coulombic and ridging yield as failure switches from one lead to another as the stress grows. Because sliding along slip lines is accompanied by dilatancy, at typical Arctic sea ice deformation rates a one-day-long deformation event produces enough open water that these freshly formed slip lines are preferential places of ridging failure.

Ice internal friction: Standard theoretical perspectives on friction codified, adapted for the unusual rheology of ice, and unified

Sea ice contains flaws including frictional contacts. We aim to describe quantitatively the mechanics of those contacts, providing local physics for geophysical models. With a focus on the internal friction of ice, we review standard micro-mechanical models of friction. The solid's deformation under normal load may be ductile or elastic. The shear failure of the contact may be by ductile flow, brittle fracture, or melting and hydrodynamic lubrication. Combinations of these give a total of six rheological models. When the material under study is ice, several of the rheological parameters in the standard models are not constant, but depend on the temperature of the bulk, on the normal stress under which samples are pressed together, or on the sliding velocity and acceleration. This has the effect of making the shear stress required for sliding dependent on sliding velocity, acceleration, and temperature. In some cases, it also perturbs the exponent in the normal-stress dependence of that shear stress away from the value that applies to most materials. We unify the models by a principle of maximum displacement for normal deformation, and of minimum stress for shear failure, reducing the controversy over the mechanism of internal friction in ice to the choice of values of four parameters in a single model. The four parameters represent, for a typical asperity contact, the sliding distance required to expel melt-water, the sliding distance required to break contact, the normal strain in the asperity, and the thickness of any ductile shear zone.

Continuum sea ice rheology determined from subcontinuum mechanics

[1] A method is presented to calculate the continuum-scale sea ice stress as an imposed, continuum-scale strain-rate is varied. The continuum-scale stress is calculated as the area-average of the stresses within the floes and leads in a region (the continuum element). The continuum-scale stress depends upon: the imposed strain rate; the subcontinuum scale, material rheology of sea ice; the chosen configuration of sea ice floes and leads; and a prescribed rule for determining the motion of the floes in response to the continuum-scale strain-rate. We calculated plastic yield curves and flow rules associated with subcontinuum scale, material sea ice rheologies with elliptic, linear and modified Coulombic elliptic plastic yield curves, and with square, diamond and irregular, convex polygon-shaped floes. For the case of a tiling of square floes, only for particular orientations of the leads have the principal axes of strain rate and calculated continuum-scale sea ice stress aligned, and these have been investigated analytically. The ensemble average of calculated sea ice stress for square floes with uniform orientation with respect to the principal axes of strain rate yielded alignment of average stress and strain-rate principal axes and an isotropic, continuum-scale sea ice rheology. We present a lemon-shaped yield curve with normal flow rule, derived from ensemble averages of sea ice stress, suitable for direct inclusion into the current generation of sea ice models. This continuum-scale sea ice rheology directly relates the size (strength) of the continuum-scale yield curve to the material compressive strength.

Modelling the rheology of sea ice as a collection of diamond-shaped floes

In polar oceans, seawater freezes to form a layer of sea ice of several metres thickness that can cover up to 8% of the Earth’s surface. The modelled sea ice cover state is described by thickness and orientational distribution of interlocking, anisotropic diamond-shaped ice floes delineated by slip lines, as supported by observation. The purpose of this study is to develop a set of equations describing the mean-field sea ice stresses that result from interactions between the ice floes and the evolution of the ice floe orientation, which are simple enough to be incorporated into a climate model. The sea ice stress caused by a deformation of the ice cover is determined by employing an existing kinematic model of ice floe motion, which enables us to calculate the forces acting on the ice floes due to crushing into and sliding past each other, and then by averaging over all possible floe orientations. We describe the orientational floe distribution with a structure tensor and propose an evolution equation for this tensor that accounts for rigid body rotation of the floes, their apparent re-orientation due to new slip line formation, and change of shape of the floes due to freezing and melting. The form of the evolution equation proposed is motivated by laboratory observations of sea ice failure under controlled conditions. Finally, we present simulations of the evolution of sea ice stress and floe orientation for several imposed flow types. Although evidence to test the simulations against is lacking, the simulations seem physically reasonable.

Method of determining a geophysical-scale sea ice rheology from laboratory measurements

We present a methodology that allows a sea ice rheology, suitable for use in a General Circulation Model (GCM), to be determined from laboratory and tank experiments on sea ice when combined with a kinematic model of deformation. The laboratory experiments determine a material rheology for sea ice, and would investigate a nonlinear friction law of the form τ ∝ σ n⅔, instead of the more familiar Amonton's law, τ = μσn (τ is the shear stress, μ is the coefficient of friction and σ n is the normal stress). The modelling approach considers a representative region R containing ice floes (or floe aggregates), separated by flaws. The deformation of R is imposed and the motion of the floes determined using a kinematic model, which will be motivated from SAR observations. Deformation of the flaws is inferred from the floe motion and stress determined from the material rheology. The stress over R is then determined from the area-weighted contribution from flaws and floes

Modelling the rheology of anisotropic particles adsorbed on a two-dimensional fluid interface

We present a general approach based on nonequilibrium thermodynamics for bridging the gap between a well-defined microscopic model and the macroscopic rheology of particle-stabilised interfaces. Our approach is illustrated by starting with a microscopic model of hard ellipsoids confined to a planar surface, which is intended to simply represent a particle-stabilised fluid–fluid interface. More complex microscopic models can be readily handled using the methods outlined in this paper. From the aforementioned microscopic starting point, we obtain the macroscopic, constitutive equations using a combination of systematic coarse-graining, computer experiments and Hamiltonian dynamics. Exemplary numerical solutions of the constitutive equations are given for a variety of experimentally relevant flow situations to explore the rheological behaviour of our model. In particular, we calculate the shear and dilatational moduli of the interface over a wide range of surface coverages, ranging from the dilute isotropic regime, to the concentrated nematic regime.

Effect of fat replacement by inulin on textural and structural properties of short dough biscuits

The aim of this study was to evaluate the effects of inulin as fat replacer on short dough biscuits and their corresponding doughs. A control formulation, with no replacement, and four formulations in which 10, 20, 30, and 40 % of shortening was replaced by inulin were studied. In the dough, shortening was observed surrounding flour components. At higher fat replacement levels, flour was more available for hydration leading to significant (P<0.05) harder doughs: from 2.76 (0.12)N in 10 % fat-replaced biscuits to 5.81 (1.56)N in 30 % fat-replaced ones. Biscuit structure was more continuous than dough structure. A continuous fat layer coated the matrix surface, where starch granules were embedded. In general, weight loss during baking and water activity decreased significantly (P<0.05) as fat replacement increased. Biscuit dimensions and aeration decreased when fat replacement increased, e.g., width gain was +1.20 mm in 10 fat-replaced biscuits and only +0.32 mm in 40 % fat-replaced ones. Panelist found biscuits with 20 % of fat replacement slightly harder than control biscuits. It can be concluded that shortening may be partially replaced, up to 20 %, with inulin. These low fat biscuits are similar than the control biscuits, and they can have additional health benefits derived from inulin presence.

Significance of cross correlations in the stress relaxation of polymer melts

According to linear response theory, all relaxation functions in the linear regime can be obtained using time correlation functions calculated under equilibrium. In this paper, we demonstrate that the cross correlations make a significant contribution to the partial stress relaxation functions in polymer melts. We present two illustrations in the context of polymer rheology using (1) Brownian dynamics simulations of a single chain model for entangled polymers, the slip-spring model, and (2) molecular dynamics simulations of a multichain model. Using the single chain model, we analyze the contribution of the confining potential to the stress relaxation and the plateau modulus. Although the idea is illustrated with a particular model, it applies to any single chain model that uses a potential to confine the motion of the chains. This leads us to question some of the assumptions behind the tube theory, especially the meaning of the entanglement molecular weight obtained from the plateau modulus. To shed some light on this issue, we study the contribution of the nonbonded excluded-volume interactions to the stress relaxation using the multichain model. The proportionality of the bonded/nonbonded contributions to the total stress relaxation (after a density dependent "colloidal" relaxation time) provides some insight into the success of the tube theory in spite of using questionable assumptions. The proportionality indicates that the shape of the relaxation spectrum can indeed be reproduced using the tube theory and the problem is reduced to that of finding the correct prefactor. (c) 2007 American Institute of Physics

Characterisation of an s-type low molecular weight glutenin subunit of wheat and its proline and glutamine-rich repetitive domain

The low molecular weight glutenin subunits (LMW-GS) are major components of the glutenin polymers which determine the elastomeric properties of wheat (Triticum aestivum L.) gluten and dough. They comprise a complex mixture of components and have proved to be difficult to purify for detailed characterisation. The mature LMW subunit proteins comprise two structural domains, with one domain consisting of repeated sequences based on short peptide motifs. DNA sequences encoding this domain and a whole subunit were expressed in Escherichia coli and the recombinant proteins purified. Detailed comparisons by spectroscopy (CD, FT-IR) and dynamic light scattering indicated that the repetitive and non-repetitive domains of the proteins formed different structures with the former having an extended conformation with an equilibrium between poly-L-proline II-like structure and type II’ b-turns, and the latter a more compact globular structure rich in a-helix. Although the structures of these two domains appear to form independently, dynamic light scattering of the whole subunit dissolved in trifluoroethanol(TFE) suggested that they interact, leading to a more compact conformation. These observations may have relevance to the role of the LMW-GS in gluten structure and functionality.

Effects of triazole and strobilurin fungicide programmes, with and without late-season nitrogen fertiliser, on the baking quality of Malacca winter wheat

Field experiments were conducted over 3 years to study the effect of applying triazole and strobilurin fungicides on the bread-making quality of Malacca winter wheat. Averaged over all years the application of a fungicide programme increased yields, particularly when strobilurin fungicides were applied. Reductions in protein concentration, sulphur concentration, Hageberg failing number and loaf volumes also occurred as the amount of fungicide applied increased. However, there were no deleterious effects of fungicide application on sodium dodecyl sulphate (SDS) sedimentation volumes, N:S ratios or dough theology. Effects of fungicide application on bread-making quality were not product specific. Therefore, it appears that new mechanisms to explain strobilurin effects on bread-making quality do not need to be invoked. Where reductions in protein concentration did occur they could be compensated for by a late-season application of nitrogen either as granular ammonium nitrate at flag leaf emergence or foliar urea at anthesis. These applications, however, sometimes increased the N:S ratio of the extracted flour and failed to improve loaf volume. Multiple regression analysis revealed that main effects of year, flour protein concentration and N:S ratio could explain 93% of the variance in loaf volume caused by season, fungicide and nitrogen treatments. However, an equally good fit was achieved by just including sulphur concentration with year. (C) 2004 Elsevier Ltd. All rights reserved.

Wormlike micelle formation and flow alignment of a pluronic block copolymer in aqueous solution

The self-assembly into wormlike micelles of a poly(ethylene oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide) triblock copolymer Pluronic P84 in aqueous salt solution (2 M NaCl) has been studied by rheology, small-angle X-ray and neutron scattering (SAXS/SANS), and light scattering. Measurements of the flow curves by controlled stress rheometry indicated phase separation under flow. SAXS on solutions subjected to capillary flow showed alignment of micelles at intermediate shear rates, although loss of alignment was observed for high shear rates. For dilute solutions, SAXS and static light scattering data on unaligned samples could be superposed over three decades in scattering vector, providing unique information on the wormlike micelle structure over several length scales. SANS data provided information on even shorter length scales, in particular, concerning "blob" scattering from the micelle corona. The data could be modeled based on a system of semiflexible self-avoiding cylinders with a circular cross-section, as described by the wormlike chain model with excluded volume interactions. The micelle structure was compared at two temperatures close to the cloud point (47 degrees C). The micellar radius was found not to vary with temperature in this region, although the contour length increased with increasing temperature, whereas the Kuhn length decreased. These variations result in an increase of the low-concentration radius of gyration with increasing temperature. This was consistent with dynamic light scattering results, and, applying theoretical results from the literature, this is in agreement with an increase in endcap energy due to changes in hydration of the poly(ethylene oxide) blocks as the temperature is increased.

A SAXS study of flow alignment of thermotropic liquid crystal mixtures

We report on the capillary flow behaviour of thermotropic liquid crystal mixtures containing 4-n-octyl-4'-cyanobiphenyl (8CB) and 4-n-pentyl-4'-cyanobiphenyl (5CB). The liquid crystal mixtures are studied in the Nematic (N) and Smectic (SA) phases at room temperature. Polarised optical microscopy (POM), rheology and simultaneous X-ray diffraction (XRD)/capillary flow experiments are performed to characterise the system. Polarised optical microscopy reveals a dramatic change in optical texture when the 5CB content is increased from 20 to 30% in the mixtures. X-ray diffraction results show that the system goes through a SA-N phase transition, such that the mixtures are smectic for 10-20% 5CB and nematic for 30-90% 5CB. Smectic mixtures flow with the layers aligned along the flow direction (mesogens perpendicular to flow) while nematic mixtures flow with the mesogens aligned in the flow direction. Simultaneous XRD/shear flow experiments show that the SA-N transition is independent of the flow rate in the range 1-6 ml min-1. The correlation length of the liquid crystal order decreases with increasing 5CB content. Rheology is used to prove that the correlation length behaviour is related to a reduction in the viscosity of the mixture.

Nematic and columnar ordering of a PEG-peptide conjugate in aqueous solution

The self-assembly in aqueous solution of a PEG-peptide conjugate is studied by spectroscopy, electron microscopy, rheology and small-angle Xray and neutron scattering (SAXS and SANS). The peptide fragment, FFKLVFF is based on fragment KLVFF of the amyloid beta-peptide, A beta(16-20), extended by two hydrophobic phenylalanine units. This is conjugated to PEG which confers water solubility and leads to distinct self-assembled structures. Small-angle scattering reveals the formation of cylindrical fibrils comprising a peptide core and PEG corona. This constrained structure leads to a model parallel beta-sheet self-assembled structure with a radial arrangement of beta sheets. Oil increasing concentration, successively nematic and hexagonal columnar phases are formed. The flow-induced alignment of both structures was studied in situ by SANS using a Couette cell. Shear-induced alignment is responsible for the shear thinning behaviour observed by dynamic shear rheometry. Incomplete recovery of moduli after cessation of shear is consistent with the observation from SANS of retained orientation in the sample.

Interactions of bovine serum albumin with ethylene oxide/butylene oxide copolymers in aqueous solution

The interactions of bovine serum albumin (BSA) with three ethylene oxide/butylene oxide (E/B) copolymers having different block lengths and varying molecular architectures is examined in this study in aqueous solutions. Dynamic light scattering (DLS) indicates the absence of BSA-polymer binding in micellar systems of copolymers with lengthy hydrophilic blocks. On the contrary, stable protein-polyrner aggregates were observed in the case of E18B10 block copolymer. Results from DLS and SAXS suggest the dissociation of E/B copolymer micelles in the presence of protein and the absorption of polymer chains to BSA surface. At high protein loadings, bound BSA adopts a more compact conformation in solution. The secondary structure of the protein remains essentially unaffected even at high polymer concentrations. Raman spectroscopy was used to give insight to the configurations of the bound molecules in concentrated solutions. In the vicinity of the critical gel concentration of E18B10 introduction of BSA can dramatically modify the phase diagram, inducing a gel-sol-gel transition. The overall picture of the interaction diagram of the E18B10-BSA reflects the shrinkage of the suspended particles due to destabilization of micelles induced by BSA and the gelator nature of the globular protein. SAXS and rheology were used to further characterize the structure and flow behavior of the polymer-protein hybrid gels and sols.