ALBERT

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Description: An efficient algorithm for hydrodynamical interaction of many deformable drops subject to shear flow at small Reynolds numbers with triply periodic boundaries is developed. The algorithm, at each time step, is a hybrid of boundary-integral and economical multipole techniques, and scales practically linearly with the number of drops N in the range N 〈 1000, for N Δ ~ 103 boundary elements per drop. A new near-singularity subtraction in the double layer overcomes the divergence of velocity iterations at high drop volume fractions c and substantial viscosity ratio λ. Extensive long-time simulations for N = 100-200 and NΔ = 1000-2000 are performed up to c = 0.55 and drop-to-medium viscosity ratios up to λ = 5, to calculate the non-dimensional emulsion viscosity μ* = Σ12⊤ (μe·γ), and the first N1 = (Σ11 - Σ22) ⊤ (μe·γ) and second N2 = (Σ22 - Σ33) ⊤ (μe·γ) normal stress differences, where ·γ is the shear rate, μe is the matrix viscosity, and Σij is the average stress tensor. For c = 0.45 and 0.5, μ* is a strong function of the capillary number Ca = μe·γaσ (where α is the non-deformed drop radius, and σ is the interfacial tension) for Ca ≪ 1, so that most of the shear thinning occurs for nearly non-deformed drops. For c = 0.55 and λ =1, however, the results suggest phase transition to a partially ordered state at Ca ≤ 0.05, and μ* becomes a weaker function of c and Ca; using λ = 3 delays phase transition to smaller Ca. A positive first normal stress difference, N1, is a strong function of Ca; the second normal stress difference, N2, is always negative and is a relatively weak function of Ca. It is found at c = 0.5 that small systems (N ~ 10) fail to predict the correct behaviour of the viscosity and can give particularly large errors for N1, while larger systems N ≥. O(102) show very good convergence. For N ~ 102 and N Δ ~ 103, the present algorithm is two orders of magnitude faster than a standard boundary-integral code, which has made the calculations feasible.

Description: Experiments were performed to measure the rebound velocities of small plastic and metal spheres dropped from various heights onto a smooth quartz surface coated with a thin layer of viscous fluid. The spheres stick without rebounding for low impact velocities, due to viscous dissipation in the thin fluid layer. Above a critical impact velocity, however, the lubrication forces in the thin layer cause elastic deformation and rebound of the spheres. The apparent coefficient of restitution increases with the ratio of the Stokes number to its critical value for rebound, where the Stokes number is a dimensionless ratio of the inertia of the sphere to viscous forces in the fluid. The critical Stokes number required for rebound decreases weakly with increasing values of a dimensionless elasticity parameter which is a ratio of the viscous forces which cause deformation to the elastic forces which resist deformation. The experimental results show good agreement with an approximate model based on lubrication theory for undeformed spheres and scaling relations for elastic deformation.

Description: We consider viscous shear flow of a monolayer of solid spheres and discuss the effect that microscopic particle surface roughness has on the stress in the suspension. We consider effects both within and outside the dilute régime. Away from jamming concentrations, the viscosity is lowered by surface roughness, and for dilute suspensions it is insensitive to friction between the particles. Outside the dilute region, the viscosity increases with increasing friction coefficient. For a dilute system, roughness causes a negative first normal stress difference (N1) at order c2 in particle area concentration. The magnitude of N1 increases with increasing roughness height in the dilute limit but the trend reverses for more concentrated systems. N1 is largely insensitive to interparticle friction. The dilute results are in accord with the three-dimensional results of our earlier work (Wilson and Davis 2000), but with a correction to the sign of the tangential friction force.

Description: Capillarity is an important feature in controlling the spreading of liquid drops and in the coating of substrates by liquid films. For thin films and small contact angles, lubrication theory enables the analysis of the motion to be reduced to single evolution equations for the heights of the drops or films, provided the inertia of the liquid can be neglected. In general, the presence of inertia destroys the major simplification provided by lubrication theory, but two special cases that can be treated are identified here. In the first example, the approach of a drop to its equilibrium position is studied. For sufficiently low Reynolds numbers, the rate of approach to the terminal state and the contact angle are slightly reduced by inertia, but, above a critical Reynolds number, the approach becomes oscillatory. In the latter case there is no simple relation connecting the dynamic contact angle and contact-line speed. In the second example, the spreading drop is supported by a plate that is forced to oscillate in its own plane. For the parameter range considered, the mean spreading is unaffected by inertia, but the oscillatory motion of the contact line is reduced in magnitude as inertia increases, and the drop lags behind the plate motion. The oscillatory contact angle increases with inertia, but is not in phase with the plate oscillation.

Description: We examine the fracture of a quasi-two-dimensional surfactant-laden aqueous foam under an applied driving pressure, using a network modelling approach developed for metallic foams by Stewart & Davis (J. Rheol., vol. 56, 2012, p. 543). In agreement with experiments, we observe two distinct mechanisms of failure analogous to those observed in a crystalline solid: a slow ductile mode when the driving pressure is applied slowly, where the void propagates as bubbles interchange neighbours through the T1 process; and a rapid brittle mode for faster application of pressures, where the void advances by successive rupture of liquid films driven by Rayleigh-Taylor instability. The simulations allow detailed insight into the mechanics of the fracturing medium and the role of its microstructure. In particular, we examine the stress distribution around the crack tip and investigate how brittle fracture localizes into a single line of breakages. We also confirm that pre-existing microstructural defects can alter the course of fracture. © 2015 Cambridge University Press.

Description: The rheology of highly concentrated monodisperse emulsions is studied by rigorous multidrop numerical simulations for three types of steady macroscopic flow, (i) simple shear (γx〈inf〉2〈/inf〉, 0 0), (ii) planar extension (PE) (Γ x〈inf〉1〈/inf〉, - Γ x〈inf〉2〈/inf〉, 0) and (iii) mixed (γx〈inf〉2〈/inf〉, γ χx〈inf〉1〈/inf〉, 0), where γ and Γ are the deformation rates, and χ ∈ (-1, 1) is the flow parameter, in order to construct and validate a general constitutive model for emulsion flows with arbitrary kinematics. The algorithm is a development of the multipole-accelerated boundary-integral (BI) code of Zinchenko & Davis (J. Fluid Mech., vol. 455, 2002, pp. 21-62). It additionally incorporates periodic boundary conditions for (ii) and (iii) (based on the reproducible lattice dynamics of Kraynik-Reinelt for PE), control of surface overlapping, much more robust controllable surface triangulations for long-time simulations, and more efficient acceleration. The emulsion steady-state viscometric functions (shear viscosity and normal stress differences) for (i) and extensiometric functions (extensional viscosity and stress cross-difference) for (ii) are studied in the range of drop volume fractions c = 0.45-0.55, drop-to-medium viscosity ratios λ = 0.25-10 and various capillary numbers Ca, with 100-400 drops in a periodic cell and 2000-4000 boundary elements per drop. High surface resolution is important for all three flows at small Ca. Large system size and strains γt of up to several thousand are imperative in some shear-flow simulations to identify the onset of phase transition to a partially ordered state, and evaluate (although still not precisely) the viscometric functions in this state. Below the phase transition point, the shear viscosity versus Ca shows a kinked behaviour, with the local minimum most pronounced at λ = 1 and c = 0.55. The λ = 0.25 emulsions flow in a partially ordered manner in a wide range of Ca even when c = 0.45. Increase of λ to 3-10 shifts the onset of ordering to much smaller Ca, often outside the simulation range. In contrast to simple shear, phase transition is never observed in PE or mixed flow. A generalized five-parameter Oldroyd model with variable coefficients is fitted to our extensiometric and viscometric functions at arbitrary flow intensities (but outside the phase transition range). The model predictions compare very well with precise simulation results for strong mixed flows, χ = 0.25. Time-dependent PE flow is also considered. Ways to overcome the phase transition and drop breakup limitations on constitutive modelling are discussed. © 2015 Cambridge University Press.

Description: Since the mid-19th century, western Oregon's Willamette Valley has been a source of remains from a wide variety of extinct megafauna. Few of these have been previously described or dated, but new chronologic and isotopic analyses in conjunction with updated evaluations of stratigraphic context provide substantial new information on the species present, timing of losses, and paleoenvironmental conditions. Using subfossil material from the northern valley, we use AMS radiocarbon dating, stable isotope (δ13C and δ15N) analyses, and taxonomic dietary specialization and habitat preferences to reconstruct environments and to develop a local chronology of events that we then compare with continental and regional archaeological and paleoenvironmental data. Analysis of twelve bone specimens demonstrates the presence of bison, mammoth, horse, sloth, and mastodon from ~ 15,000–13,000 cal yr BP. The latest ages coincide with changing regional climate corresponding to the onset of the Younger Dryas. It is suggested that cooling conditions led to increased forest cover, and along with river aggradation, reduced the area of preferred habitat for the larger bodied herbivores, which contributed to the demise of local megafauna. Archaeological evidence for megafauna–human interactions in the Pacific Northwest is scarce, limiting our ability to address the human role in causing extinction.