Dual yielding in capillary suspensions

Rheological measurements were performed to examine the yielding behavior of capillary suspensions prepared by mixing cocoa powder as dispersed phase, vegetable oil as the continuous primary fluid, and water as the secondary fluid. Here, we investigated the yielding behavior of solid-fluid-fluid systems with varying particle volume fraction, ?, spanning the regime from a low volume fraction (? = 0.25) to a highly filled regime (? = 0.65) using dynamic oscillatory measurements. While for ? ≤ 0.4 with a fixed water volume fraction (? _w ) of 0.06 as the secondary fluid, capillary suspensions exhibited a single yield point due to rupturing of aqueous capillary bridges between the particles, while capillary suspensions with ? ≥ 0.45 showed a two-step yielding behavior. On plotting elastic stress (G^′ γ) as a function of applied strain (γ), two distinct peaks, indicating two yield stresses, were observed. Both the yield stresses and storage modulus at low strains were found to increase with ? following a power law dependence. With increasing ? _w (0 – 0.08) at a fixed ? = 0.65, the system shifted to a frustrated, jammed state with particles strongly held together shown by rapidly increasing first and second yield stresses. In particular, the first yield stress was found to increase with ? _w following a power law dependence, while the second yield stress was found to increase exponentially with ? _w . Transient steady shear tests were also performed. The single stress overshoot for ? ≤ 0.4 with ? _w = 0.06 reflected one-step yielding behavior. In contrast, for high ? (≥ 0.45) values with ? _w = 0.06, two stress overshoots were observed in agreement with the two-step yielding behavior shown in the dynamic oscillatory measurements. Experiments on the effect of resting time on microstructure recovery demonstrated that aggregates could reform after resting under quiescent conditions.     

Stability of Traveling Waves of Nonlinear Schrödinger Equation with Nonzero Condition at Infinity

We study effective elastic behavior of the incompatibly prestrained thin plates, where the prestrain is independent of thickness and uniform through the plate’s thickness h. We model such plates as three-dimensional elastic bodies with a prescribed pointwise stress-free state characterized by a Riemannian metric G, and seek the limiting behavior as \({h \to 0}\). We first establish that when the energy per volume scales as the second power of h, the resulting \({\Gamma}\) -limit is a Kirchhoff-type bending theory. We then show the somewhat surprising result that there exist non-immersible metrics G for whom the infimum energy (per volume) scales smaller than h². This implies that the minimizing sequence of deformations carries nontrivial residual three-dimensional energy but it has zero bending energy as seen from the limit Kirchhoff theory perspective. Another implication is that other asymptotic scenarios are valid in appropriate smaller scaling regimes of energy. We characterize the metrics G with the above property, showing that the zero bending energy in the Kirchhoff limit occurs if and only if the Riemann curvatures R₁₂₁₃, R₁₂₂₃ and R₁₂₁₂ of G vanish identically. We illustrate our findings with examples; of particular interest is an example where \({G_{2 \times 2}}\), the two-dimensional restriction of G, is flat but the plate still exhibits the energy scaling of the Föppl–von Kármán type. Finally, we apply these results to a model of nematic glass, including a characterization of the condition when the metric is immersible, for \({G = Id_{3} + \gamma n \otimes n}\) given in terms of the inhomogeneous unit director field distribution \({ n \in \mathbb{R}^3}\).     

Power-law creep and residual stresses in a carbopol gel

We report on the interplay between creep and residual stresses in a carbopol microgel. When a constant shear stress σ is applied below the yield stress σ _y, the strain is shown to increase as a power law of time, γ(t) = γ ₀ + (t/τ) ^α , with an exponent α = 0.39 ± 0.04 that is strongly reminiscent of Andrade creep in hard solids. For applied shear stresses lower than some typical value σ _c ? 0.2σ _y, the microgel experiences a more complex, anomalous creep behavior, characterized by an initial decrease of the strain, that we attribute to the existence of residual stresses of the order of σ _c that persist after a rest time under a zero shear rate following preshear. The influence of gel concentration on creep and residual stresses are investigated as well as possible aging effects. We discuss our results in light of previous works on colloidal glasses and other soft glassy systems.     

Mechanical Properties of Hard W-C Coating on Steel Substrate Deduced from Nanoindentation and Finite Element Modeling

Mechanical properties of a hard and stiff W-C coating on steel substrate have been investigated using nanoindentation combined with finite element modeling (FEM) and extended FEM (XFEM). The significant pile-up observed around the indents in steel substrate caused an overestimation of hardness and indentation modulus. A simple geometrical model, considering the additional contact surfaces due to pile-up, has been proposed to reduce this overestimation. The presence of W-C coating suppressed the pile-up in the steel substrate and a transition to sink-in behavior occurred. The FEM simulations adequately reproduced the surface topography of the indents in the substrate and coating/substrate systems as well. The maximum principal stresses of the indented W-C/steel coated system were tensile; they were always located in the coating and evolved in 3 stages. Cohesive cracking occurred during loading in the sink-in zone (stage III) when the ultimate tensile strength (σ _max ) of the coating was reached. The obtained hardness (H _c ), indentation modulus (E _c ), yield stress (Y) and strength (σ _max ) of the W-C coating were H _c ? =?20 GPa, E _c ? =?250 GPa, Y?=?9.0 GPa and σ _max ? =?9.35 GPa, respectively. XFEM resulted in fracture energy of the W-C coating of G?=?38.1 J?·?m^-2 and fracture toughness of K _IC ? =?3.5 MPa?·?m^0.5.     

Does Density Ratio Significantly Affect Turbulent Flame Speed?

In order to experimentally study whether or not the density ratio σ substantially affects flame displacement speed at low and moderate turbulent intensities, two stoichiometric methane/oxygen/nitrogen mixtures characterized by the same laminar flame speed S _L = 0.36 m/s, but substantially different σ were designed using (i) preheating from T _u = 298 to 423 K in order to increase S _L , but to decrease σ, and (ii) dilution with nitrogen in order to further decrease σ and to reduce S _L back to the initial value. As a result, the density ratio was reduced from 7.52 to 4.95. In both reference and preheated/diluted cases, direct images of statistically spherical laminar and turbulent flames that expanded after spark ignition in the center of a large 3D cruciform burner were recorded and processed in order to evaluate the mean flame radius \(\bar {R}_{f}\left (t \right )\) and flame displacement speed \(S_{t}=\sigma ^{-1}{d\bar {R}_{f}} \left / \right . {dt}\) with respect to unburned gas. The use of two counter-rotating fans and perforated plates for near-isotropic turbulence generation allowed us to vary the rms turbulent velocity \(u^{\prime }\) by changing the fan frequency. In this study, \(u^{\prime }\) was varied from 0.14 to 1.39 m/s. For each set of initial conditions (two different mixture compositions, two different temperatures T _u , and six different \(u^{\prime })\), five (respectively, three) statistically equivalent runs were performed in turbulent (respectively, laminar) environment. The obtained experimental data do not show any significant effect of the density ratio on S _t . Moreover, the flame displacement speeds measured at u′/S _L = 0.4 are close to the laminar flame speeds in all investigated cases. These results imply, in particular, a minor effect of the density ratio on flame displacement speed in spark ignition engines and support simulations of the engine combustion using models that (i) do not allow for effects of the density ratio on S _t and (ii) have been validated against experimental data obtained under the room conditions, i.e. at higher σ.     

Experimental Study on Three-Dimensional Deformation Field of Portevin–Le Chatelier Effect Using Digital Image Correlation

In view of its high precision and high efficiency, three-dimensional digital image correlation (3D-DIC) is widely used to accurately measure full-field deformation. A spatiotemporal experimental study using 3D-DIC to explore the Portevin–Le Chatelier (PLC) deformational behavior, provides a new insight into the whole 3D deformation field, including the out-of-plane displacement, and in particular the relationship between the serrations and the strain field in the deformation bands corresponding to individual serrations. Specimens 1, 2 and 3 mm thick of 5456 Al-based alloy were tested in uniaxial tension at room temperature at strain rates from 1.8 × 10^?4 to 9.1 × 10^?3s^?1. The spatial and temporal characteristics of the strain localization were quantitatively analyzed. The out-of-plane displacement increment field (w) of the localized bands was observed by 3D-DIC, and found to be related to the specimen thickness and the in-plane strain increment. The largest displacement increments were respectively 15, 10 and 5 μm for 3, 2 and 1 mm specimens at maximum strain increment of about 12000 με. The elastic shrinkage outside the deformation bands was found to be an essential characteristic of the PLC effect. The width of the PLC band (w_band) increased with increasing thickness; the angle of the PLC band (??_band) was not affected by either specimen thickness or serration amplitude. Temporally, the serrations in the plots both of in-plane strain and out-of-plane displacement vs. time coincided throughout the entire loading procedure. When PLC banding occurred, the serration amplitude within the bands was found to be proportional to the maximum strain increment in the direction of the applied tensile force (??_max).     

On the orders of the best approximations of integrals of functions by integrals of rank <Emphasis Type="Italic">σ</Emphasis>

We study the values e _σ(f) of the best approximation of integrals of functions from the spaces L _p (A, dμ) by integrals of rank σ. We determine the orders of the least upper bounds of these values as σ → ∞ in the case where the function ? is the product of two nonnegative functions one of which is fixed and the other varies on the unit ball U _p (A) of the space L _p (A, dμ). We consider applications of the obtained results to approximation problems in the spaces S _p ^? .     

Evaluation of the Spectral Element Dynamic Model for Large-Eddy Simulation on Unstructured,Deformed Meshes

In this paper, the Spectral-Element Dynamic Model (SEDM), suited for Large-Eddy Simulation (LES) using Discontinuous Finite Element Methods (DFEM), is assessed using unstructured meshes. Five test cases of increasing complexity are considered, namely, the Taylor-Green vortex at Re =?5000, the turbulent channel flow at Re_τ =?587, the circular cylinder in cross-flow at Re_D =?3900, the square cylinder in cross-flow at Re_D =?22400 and the channel with periodic constrictions at Re_h =?10595. Various discretization parameters such as the grid spacing, polynomial degree and numerical flux are assessed and very accurate results are reported in all cases. This consistency in the results demonstrates the versatility of the SEDM approach and its ability to gage the actual resolution and quality of the mesh and, accordingly, to introduce an amount of sub-grid dissipation which is adapted to the spatial discretization considered.     

Spray-Flame Dynamics in a Rich Droplet Array

We numerically study spray-flame dynamics. The initial state of the spray is schematized by alkane droplets located at the nodes of a face-centered 2D-lattice. The droplets are surrounded by a gaseous mixture of alkane and air. The lattice spacing s reduced by the combustion length scale is large enough to consider that the chemical reaction occurs in a heterogeneous medium. The overall spray equivalence ratio is denoted by ?_T, with ?_T = ?_L + ?_G, where ?_G corresponds to the equivalence ratio of the gaseous surrounding mixture at the initial saturated partial pressure, while ?_L is the so-called liquid loading. To model such a heterogenous combustion, the retained chemical scheme is a global irreversible one-step reaction governed by an Arrhenius law, with a modified heat of reaction depending on the local equivalence ratio. ?_T is chosen in the range 0.9 ≤ ?_T ≤ 2. Three geometries (s = 3, s = 6, s = 12) and four liquid loadings, ?_L = 0.3, ?_L = 0.5, ?_L = 0.7, ?_L = 0.85 are studied. In the rich sprays, our model qualitatively retrieves the recent experimental measurements: the rich spray-flames can propagate faster than the single-phase flames with the same overall equivalence ratio. To analyse the conditions for this enhancement, we introduce the concept of “spray Peclet number”, which compares the droplet vaporization time with the combustion propagation time of the single-phase flame spreading in the fresh surrounding mixture.     

Entire Solutions to Equivariant Elliptic Systems with Variational Structure

We consider the system Δu ? W _u (u) = 0, where \({u : \mathbb{R}^n \to \mathbb{R}^n}\) , for a class of potentials \({W : \mathbb{R}^n \to \mathbb{R}}\) that possess several global minima and are invariant under a general finite reflection group G. We establish existence of nontrivial G-equivariant entire solutions connecting the global minima of W along certain directions at infinity.     

Filling the gap between transient and steady shear rheology of aqueous graphene oxide dispersions

Even though the rheological behavior of aqueous graphene oxide (G-O) dispersions has been shown to be strongly time-dependent, only few transient measurements have been reported in the literature. In this work, we attempt to fill the gap between transient and steady shear rheological characterizations of aqueous G-O dispersions in the concentration range of 0.004 < ? <?3.5 wt%, by conducting comprehensive rheological measurements, including oscillatory shear flow, transient shear flow, and steady shear flow. Steady shear measurements have been performed after the evaluation of transient properties of the G-O dispersions, to assure steady-state conditions. We identify the critical concentration ? _c =?0.08 wt% (where G-O sheets start to interact) from oscillatory shear experiments. We find that the rheology of G-O dispersions strongly depends on the G-O concentration ?. Transient measurements of shear viscosity and first normal stress difference suggest that G-O dispersions behave like nematic polymeric liquid crystals at ?/? _c =?25, in agreement with other work reported in the literature. G-O dispersions also display a transition from negative to positive values of the first normal stress difference with increasing shear rates. Experimental findings of aqueous graphene oxide dispersions are compared and discussed with models and experiments reported for nematic polymeric liquid crystals, laponite, and organoclay dispersions.     

Effect of vibration on the creep of tensile-test specimens of the aluminum alloy Al−Mg−Si (PA-4)

In this work are presented the results of research on vibrational creep at normal temperature of an aluminum alloy containing magnesium and silicon (designated PA-4). A uni-directional positive load is applied to a tensile-test specimen, such that the stress intensity in the specimen is of the type\(\sigma (t) = \sigma _m (1 + Asin\omega t)\) whereσ _m is the mean (static) stress intensity andA =σ _a /σ _m is the ratio of the vibratory-stress intensity to the mean intensity. The results are given in the form of families of curves of plastic (i.e., permanent) deformation for various values ofA, namely,A=0.0000, 0.0065, 0.05500, 0.1000 and 0.2000. Taking the creep limit for plastic strain as ε _p = 1.8 percent, equations for this creep limit were deduced from experimental data. The following conclusions are drawn from these investigations:

1. 1.
   Vibrations of small-stress-amplitude ratioA encourage creep, particularly with more lengthy tests.     
   
   

Turbulent Drag Reduction by a Near Wall Surface Tension Active Interface

In this work we study the turbulence modulation in a viscosity-stratified two-phase flow using Direct Numerical Simulation (DNS) of turbulence and the Phase Field Method (PFM) to simulate the interfacial phenomena. Specifically we consider the case of two immiscible fluid layers driven in a closed rectangular channel by an imposed mean pressure gradient. The present problem, which may mimic the behaviour of an oil flowing under a thin layer of different oil, thickness ratio h₂/h₁ =?9, is described by three main flow parameters: the shear Reynolds number Re _τ (which quantifies the importance of inertia compared to viscous effects), the Weber number We (which quantifies surface tension effects) and the viscosity ratio λ = ν₁/ν₂ between the two fluids. For this first study, the density ratio of the two fluid layers is the same (ρ₂ = ρ₁), we keep Re _τ and We constant, but we consider three different values for the viscosity ratio: λ =?1, λ =?0.875 and λ =?0.75. Compared to a single phase flow at the same shear Reynolds number (Re _τ =?100), in the two phase flow case we observe a decrease of the wall-shear stress and a strong turbulence modulation in particular in the proximity of the interface. Interestingly, we observe that the modulation of turbulence by the liquid-liquid interface extends up to the top wall (i.e. the closest to the interface) and produces local shear stress inversions and flow recirculation regions. The observed results depend primarily on the interface deformability and on the viscosity ratio between the two fluids (λ).     

Revisiting History Effects in Adverse-Pressure-Gradient Turbulent Boundary Layers

The goal of this study is to present a first step towards establishing criteria aimed at assessing whether a particular adverse-pressure-gradient (APG) turbulent boundary layer (TBL) can be considered well-behaved, i.e., whether it is independent of the inflow conditions and is exempt of numerical or experimental artifacts. To this end, we analyzed several high-quality datasets, including in-house numerical databases of APG TBLs developing over flat-plates and the suction side of a wing section, and five studies available in the literature. Due to the impact of the flow history on the particular state of the boundary layer, we developed three criteria of convergence to well-behaved conditions, to be used depending on the particular case under study. (i) In the first criterion, we develop empirical correlations defining the R e _?? -evolution of the skin-friction coefficient and the shape factor in APG TBLs with constant values of the Clauser pressure-gradient parameter β = 1 and 2 (note that β = δ ^?/τ _w dP _e /dx, where δ ^? is the displacement thickness, τ _w the wall-shear stress and dP _e /dx the streamwise pressure gradient). (ii) In the second one, we propose a predictive method to obtain the skin-friction curve corresponding to an APG TBL subjected to any streamwise evolution of β, based only on data from zero-pressure-gradient TBLs. (iii) The third method relies on the diagnostic-plot concept modified with the shape factor, which scales APG TBLs subjected to a wide range of pressure-gradient conditions. These three criteria allow to ensure the correct flow development of a particular TBL, and thus to separate history and pressure-gradient effects in the analysis.     

Exact solution of 3D Timoshenko beam problem using linked interpolation of arbitrary order

For arbitrary polynomial loading and a sufficient finite number of nodal points N, the solution for the 3D Timoshenko beam differential equations is polynomial and given as \({{\varvec \theta} = \sum_{i=1}^N I_i {\varvec \theta}_i}\) for the rotation field and \({{\bf u} = \sum_{i=1}^{N+1} J_i {\bf u}_i}\) for the displacement field, where I _i and J _i are the Lagrangian polynomials of order N?1 and N, respectively. It has been demonstrated in this work that the exact solution for the displacement field may be also written in a number of alternative ways involving contributions of the nodal rotations including \({{\bf u} = \sum_{i=1}^N I_i \left[ {\bf u}_i + \frac 1 N ( {\varvec \theta} - {\varvec \theta}_i ) \times {\bf R}_i \right]}\), where R _i are the beam nodal positions.     

Effects of Fuel Lewis Number on Localised Forced Ignition of Globally Stoichiometric Stratified Mixtures: a Numerical Investigation

The influences of fuel Lewis number Le_F on localised forced ignition of globally stoichiometric stratified mixtures have been analysed using three-dimensional compressible Direct Numerical Simulations (DNS) for cases with Le_F ranging from 0.8 to 1.2. The globally stoichiometric stratified mixtures with different values of root-mean-square (rms) equivalence ratio fluctuation (i.e. ?^′= 0.2, 0.4 and 0.6) and the Taylor micro-scale l_? of equivalence ratio ? variation (i.e. l_?/l_f= 2.1, 5.5 and 8.3 with l_f being the Zel’dovich flame thickness of the stoichiometric laminar premixed flame) have been considered for different initial rms values of turbulent velocity u^′. A pseudo-spectral method is used to initialise the equivalence ratio variation following a presumed bi-modal distribution for prescribed values of ?^′ and l_?/l_f for global mean equivalence ratio 〈?〉=1.0. The localised ignition is accounted for by a source term in the energy transport equation that deposits energy for a stipulated time interval. It has been observed that the maximum values of temperature and the fuel reaction rate magnitude increase with decreasing Le_F during the period of external energy deposition. The initial values of Le_F, u^′/S_b(?=1), ?^′ and l_?/l_f have been found to have significant effects on the extent of burning of the stratified mixtures following localised ignition. For a given value of u^′/S_b(?=1), the extent of burning decreases with increasing Le_F. An increase in u^′ leads to a monotonic reduction in the burned gas mass for all values of Le_F in all stratified mixture cases but an opposite trend is observed for the Le_F=0.8 homogeneous mixture. It has been found that an increase in ?^′ has adverse effects on the burned gas mass, whereas the effects of l_?/l_f on the extent of burning are non-monotonic and dependent on ?^′ and Le_F. Detailed physical explanations have been provided for the observed Le_F, u^′/S_b(?=1), ?^′ and l_?/l_f dependences.     

On relations for general two-dimensional ideal plasticity problems under the full plasticity condition

Relations for two-dimensional ideal plasticity problems under the full plasticity condition are determined with material anisotropy, inhomogeneity, and compressibility properties taken into account. These properties are determined by the direction cosines of the principal stress, the coordinates of points in space, and the mean stress.For the yield strength we take a function of the form k = k(σ, n ₁, n ₂, n ₃, x, y, z). The desired relations are determined for the general plane ideal plasticity problem. The relations thus obtained are generalized to the cases of axisymmetric and spherical plasticity problems.     

Rheology and structural changes of plasticized zeins in the molten state

Zeins, storage proteins from maize, are suitable for making biobased thermoplastic materials. The rheological behavior of a commercial zein plasticized with 20 w% glycerol was studied in the molten state by steady-state flow experiments in extrusion conditions and oscillatory rheometry. For low residence times, a shear-thinning viscoelastic behavior was observed, with G″ exceeding G′. After 300 s at 130 °C, the complex viscosity |η ^?|?=?7?×?10³ ω ^?0.46 was found to be similar to that of thermoplastic polymer melts used in fused deposition modeling. However, the ratio between the exponents of the power laws describing G′(ω) and G″(ω) did not meet the typical value of 2 for entangled polymer melts. Moreover, for longer residence times, the viscosity increased and a gelation phenomenon was observed with a crossing over of G′(ω) and G″(ω). Gel times ranged from 6000 s at 120 °C to 1700 s at 150 °C. The evolution of the macromolecular structure assessed by sodium dodecyl sulfate-polyacrylamide gel electrophoresis and high-performance size exclusion chromatography suggested that this gelation phenomenon involves various types of covalent and non-covalent cross-links. Disulfide bonds played a significant role in gelation kinetics despite a very low cysteine residue content in the protein primary structure (about 1 mol%). These results suggested that plasticized zeins initially behave like a low-viscosity non-entangled polymer melt, before cross-linking progressively led to a continuous network.     

New Periodic Solutions for Newtonian n-Body Problems with Dihedral Group Symmetry and Topological Constraints

In this paper, we prove the existence of a family of new non-collision periodic solutions for the classical Newtonian n-body problems. In our assumption, the \({n=2l \geqq 4}\) particles are invariant under the dihedral rotation group D_l in \({\mathbb{R}^3}\) such that, at each instant, the n particles form two twisted l-regular polygons. Our approach is the variational minimizing method and we show that the minimizers are collision-free by level estimates and local deformations.     

Multipulse Phases in k-Mixtures of Bose–Einstein Condensates

For the system

$-\Delta U_i+ U_i=U_i^3-\beta U_i\sum_{j\neq i}U_j^2,\quad i=1,\dots,k,$

(with k ≧ 3), we prove the existence for β large of positive radial solutions on \({\mathbb R^N}\) . We show that as β →  + ∞, the profile of each component U _i separates, in many pulses, from the others. Moreover, we can prescribe the location of such pulses in terms of the oscillations of the changing-sign solutions of the scalar equation  ? ΔW  +  W  =  W³. Within an Hartree–Fock approximation, this provides a theoretical indication of phase separation into many nodal domains for the k-mixtures of Bose–Einstein condensates.