A thin rivulet or ridge subject to a uniform transverse shear stress at its free surface due to an external airflow

We use the lubrication approximation to analyse three closely related problems involving a thin rivulet or ridge (i.e. a two-dimensional droplet) of fluid subject to a prescribed uniform transverse shear stress at its free surface due to an external airflow, namely a rivulet draining under gravity down a vertical substrate, a rivulet driven by a longitudinal shear stress at its free surface, and a ridge on a horizontal substrate, and find qualitatively similar behaviour for all three problems. We show that, in agreement with previous numerical studies, the free surface profile of an equilibrium rivulet/ridge with pinned contact lines is skewed as the shear stress is increased from zero, and that there is a maximum value of the shear stress beyond which no solution with prescribed semi-width is possible. In practice, one or both of the contact lines will de-pin before this maximum value of the shear stress is reached, and so we consider situations in which the rivulet/ridge de-pins at one or both contact lines. In the case of de-pinning only at the advancing contact line, the rivulet/ridge is flattened and widened as the shear stress is increased from its critical value, and there is a second maximum value of the shear stress beyond which no solution with a prescribed advancing contact angle is possible. In contrast, in the case of de-pinning only at the receding contact line, the rivulet/ridge is thickened and narrowed as the shear stress is increased from its critical value, and there is a solution with a prescribed receding contact angle for all values of the shear stress. In general, in the case of de-pinning at both contact lines there is a critical “yield” value of the shear stress beyond which no equilibrium solution is possible and the rivulet/ridge will evolve unsteadily. In an Appendix we show that an equilibrium rivulet/ridge with prescribed flux/area is quasi-statically stable to two-dimensional perturbations

Stress overshoot in a simple yield stress fluid: an extensive study combining rheology and velocimetry

We report a large amount of experimental data on the stress overshoot phenomenon which takes place during start-up shear flows in a simple yield stress fluid, namely a carbopol microgel. A combination of classical rheological measurements and ultrasonic velocimetry makes it possible to get physical insights on the transient dynamics of both the stress $\sigma(t)$ and the velocity field across the gap of a rough cylindrical Couette cell during the start-up of shear under an applied shear rate $\dot\gamma$. (i) At small strains ($\gamma <1$), $\sigma(t)$ increases linearly and the microgel undergoes homogeneous deformation. (ii) At a time $t_m$, the stress reaches a maximum value $\sigma_m$ which corresponds to the failure of the microgel and to the nucleation of a thin lubrication layer at the moving wall. (iii) The microgel then experiences a strong elastic recoil and enters a regime of total wall slip while the stress slowly decreases. (iv) Total wall slip gives way to a transient shear-banding phenomenon, which occurs on timescales much longer than that of the stress overshoot and has been described elsewhere [Divoux \textit{et al., Phys. Rev. Lett.}, 2010, \textbf{104}, 208301]. This whole sequence is very robust to concentration changes in the explored range ($0.5 \le C \le 3$ w/w). We further demonstrate that the maximum stress $\sigma_m$ and the corresponding strain $\gamma_m=\dot\gamma t_m$ both depend on the applied shear rate $\dot \gamma$ and on the waiting time $t_w$ between preshear and shear start-up: they remain roughly constant as long as $\dot\gamma$ is smaller than some critical shear rate $\dot\gamma_w\sim 1/t_w$ and they increase as weak power laws of $\dot \gamma$ for $\dot\gamma> \dot\gamma_w$ [...].Comment: 18 pages, 14 figures, accepted for publication in Soft Matte

Absence of `fragility' and mechanical response of jammed granular materials

We perform molecular dynamic (MD) simulations of frictional non-thermal particles driven by an externally applied shear stress. After the system jams following a transient flow, we probe its mechanical response in order to clarify whether the resulting solid is 'fragile'. We find the system to respond elastically and isotropically to small perturbations of the shear stress, suggesting absence of fragility. These results are interpreted in terms of the energy landscape of dissipative systems. For the same values of the control parameters, we check the behaviour of the system during a stress cycle. Increasing the maximum stress value, a crossover from a visco-elastic to a plastic regime is observed.Comment: 6 pages, 9 figures, accepted in Granular Matter on 01-02-201

Overshoots in stress strain curves: Colloid experiments and schematic mode coupling theory

The stress versus strain curves in dense colloidal dispersions under start-up shear flow are investigated combining experiments on model core-shell microgels, computer simulations of hard disk mixtures, and mode coupling theory. In dense fluid and glassy states, the transient stresses exhibit first a linear increase with the accumulated strain, then a maximum ('stress overshoot') for strain values around 5%, before finally approaching the stationary value, which makes up the flow curve. These phenomena arise in well-equilibrated systems and for homogeneous flows, indicating that they are generic phenomena of the shear-driven transient structural relaxation. Microscopic mode coupling theory (generalized to flowing states by integration through the transients) derives them from the transient stress correlations, which first exhibit a plateau (corresponding to the solid-like elastic shear modulus) at intermediate times, and then negative stress correlations during the final decay. We introduce and validate a schematic model within mode coupling theory which captures all of these phenomena and handily can be used to jointly analyse linear and large-amplitude moduli, flow curves, and stress-strain curves. This is done by introducing a new strain- and time-dependent vertex into the relation between the the generalized shear modulus and the transient density correlator.Comment: 21 pages, 13 figure

Dynamic analysis of offshore wind turbine blades under the action of wind shear and fluctuating wind

Aiming at large-scale offshore wind turbine blades, governing equations in fluid domain and motion equations in structural domain with geometric nonlinearity were built by the aid of ALE method. A three dimensional model under fluid-structure interaction (FSI) was established by using UG software and Geometry module, and numerical calculation for FSI vibration characteristics of wind turbine blades under the effects of wind shear and fluctuating wind was carried out based on ANSYS Workbench. The results indicate that the contribution of the combined action to displacement and Mises stress chiefly derives from the wind shear effect, which not only causes a comparatively larger increase for the maximum displacement and Mises stress, but also becomes bigger and bigger with the increase of average wind speed, and the fluctuating wind effect is insignificant. The maximum value of Mises stress in the blade section appears at the relative wingspan of 0.55, the maximum Mises stress varying with relative span length decreases progressively from the middle to both sides of the blade, and the contribution of wind shear effect alone, the combined action or wind speed increment to stress also shows the same change rule. Furthermore, in the maximum stress section along wingspan, Mises stress along the direction of blade thickness or chord length respectively presents two distribution laws, and reaches the maximum on the blade surface

Particle dynamics of a cartoon dune

The spatio-temporal evolution of a downsized model for a desert dune is observed experimentally in a narrow water flow channel. A particle tracking method reveals that the migration speed of the model dune is one order of magnitude smaller than that of individual grains. In particular, the erosion rate consists of comparable contributions from creeping (low energy) and saltating (high energy) particles. The saltation flow rate is slightly larger, whereas the number of saltating particles is one order of magnitude lower than that of the creeping ones. The velocity field of the saltating particles is comparable to the velocity field of the driving fluid. It can be observed that the spatial profile of the shear stress reaches its maximum value upstream of the crest, while its minimum lies at the downstream foot of the dune. The particle tracking method reveals that the deposition of entrained particles occurs primarily in the region between these two extrema of the shear stress. Moreover, it is demonstrated that the initial triangular heap evolves to a steady state with constant mass, shape, velocity, and packing fraction after one turnover time has elapsed. Within that time the mean distance between particles initially in contact reaches a value of approximately one quarter of the dune basis length