The evolution of granular shear flow is investigated as a function of height in a split-bottom Couette cell. Using particle tracking, magnetic-resonance imaging, and large-scale simulations we find a transition in the nature of the shear as a characteristic height H * is exceeded. Below H * there is a central stationary core; above H * we observe the onset of additional axial shear associated with torsional failure. Radial and axial shear profiles are qualitatively different: the radial extent is wide and increases with height while the axial width remains narrow and fixed.PACS numbers: 45.70. Mg, 83.50.Ax Shear bands in dense granular materials are localized regions of large velocity gradients; they are the antithesis of the broad uniform flows seen in slowly-sheared Newtonian fluids [1,2,3,4,5,6]. Until recently it was generally assumed that all granular shear bands were narrow. However, in 2003 Fenistein et al. [7] discovered that in modified Couette cells granular shear bands can be made arbitrarily broad. In this geometry, the bottom of a cylindrical container is split at radius r = R s and shear is produced by rotating both the outer ring and the cylindrical boundary of the container while keeping the central disk (r < R s ) stationary. For very shallow packs, the shear band measured at the top surface is narrow and located at r = R s so that the inner region directly above the central disk is stationary while the remaining part rotates as a solid. As the filling height of the material, H, increases, the shear band increases in radial width and moves toward the cylinder axis. For sufficiently large H, the shear band overlaps the axis at r = 0 and one might expect qualitatively new behavior. Indeed, Unger et al. [8] predicted that the shape of the boundary between moving and stationary material would undergo a first-order transition as H is increased past a threshold value H * : the shearing region which for H < H * is open at the top and intersects the free surface abruptly collapses to a closed cupola completely buried inside the bulk.Previous experiments focused primarily on the surface flows in shallow containers and left unexplored many questions about the shape and evolution of the shear profiles for large H. Here, we combine magnetic resonance imaging (MRI) and high-speed video observations with large-scale simulations to explore shear flow both for shallow and tall packs. In addition to monitoring the evolution of the flow profiles in the radial direction, we also examine shear in the vertical direction. Instead of a first order collapse of the shear zone as proposed by Unger et al.[8], we find that above H * ≃ 0.6R s , the inner core of immobile material disappears gradually as shear along the central axis of the cylinder sets in. Our setup is similar to that of Fenistein et al. [7] except that we rotate the inner disk instead of the outer ring and cylinder (Fig.1b inset). In the absence of inertial effects, this makes no difference to the results. For surface observations with high-speed video ...
Evaporation and condensation at a liquid/vapor interface are ubiquitous interphase mass and energy transfer phenomena that are still not well understood. We have carried out large scale molecular dynamics simulations of Lennard-Jones (LJ) fluids composed of monomers, dimers, or trimers to investigate these processes with molecular detail. For LJ monomers in contact with a vacuum, the evaporation rate is found to be very high with significant evaporative cooling and an accompanying density gradient in the liquid domain near the liquid/vapor interface. Increasing the chain length to just dimers significantly reduces the evaporation rate. We confirm that mechanical equilibrium plays a key role in determining the evaporation rate and the density and temperature profiles across the liquid/vapor interface. The velocity distributions of evaporated molecules and the evaporation and condensation coefficients are measured and compared to the predictions of an existing model based on kinetic theory of gases. Our results indicate that for both monatomic and polyatomic molecules, the evaporation and condensation coefficients are equal when systems are not far from equilibrium and smaller than one, and decrease with increasing temperature. For the same reduced temperature T /T c , where T c is the critical temperature, these two coefficients are higher for LJ dimers and trimers than for monomers, in contrast to the traditional viewpoint that they are close to unity for monatomic molecules and decrease for polyatomic molecules. Furthermore, data for the two coefficients collapse onto a master curve when plotted against a translational length ratio between the liquid and vapor phase.
We present a review and critique of several methods for the simulation of the dynamics of colloidal suspensions at the mesoscale. We focus particularly on simulation techniques for hydrodynamic interactions, including implicit solvents (Fast Lubrication Dynamics, an approximation to Stokesian Dynamics) and explicit/particle-based solvents (Multi-Particle Collision Dynamics and Dissipative Particle Dynamics). Several variants of each method are compared quantitatively for the canonical system of monodisperse hard spheres, with a particular focus on diffusion characteristics, as well as shear rheology and microstructure. In all cases, we attempt to match the relevant properties of a well-characterized solvent, which turns out to be challenging for the explicit solvent models. Reasonable quantitative agreement is observed among all methods, but overall the Fast Lubrication Dynamics technique shows the best accuracy and performance. We also devote significant discussion to the extension of these methods to more complex situations of interest in industrial applications, including models for non-Newtonian solvent rheology, non-spherical particles, drying and curing of solvent and flows in complex geometries. This work identifies research challenges and motivates future efforts to develop techniques for quantitative, predictive simulations of industrially relevant colloidal suspension processes.
The form of the stress tensor is investigated in smooth, dense granular flows which are generated in split-bottom shear geometries. We find that, within a fluctuation fluidized spatial region, the form of the stress tensor is directly dictated by the flow field: The stress and strain-rate tensors are co-linear. The effective friction, defined as the ratio between shear and normal stresses acting on a shearing plane, is found not to be constant but to vary throughout the flowing zone. This variation can not be explained by inertial effects, but appears to be set by the local geometry of the flow field. This is in agreement with a recent prediction, but in contrast with most models for slow grain flows, and points to there being a subtle mechanism that selects the flow profiles.
SUMMARYA method is developed for modeling fluid transport in domains that do not conform to the finite element mesh. One or more level set functions are used to describe the fluid domain. A background, non-conformal mesh is decomposed into elements that conform to the level set interfaces. Enrichment takes place by adding nodes that lie on the interfaces. Unlike other enriched finite element methods, the proposed technique requires no changes to the underlying element assembly, element interpolation, or element quadrature. The complexity is entirely contained within the element decomposition routines. It is argued that the accuracy of the method is no less than that for eXtended Finite Element Methods (XFEM) with Heaviside enrichment. The accuracy is demonstrated using multiple numerical tests. In all cases, optimal rates of convergence are obtained for both volume and surface quantities. Jacobi preconditioning is shown to remove the ill-conditioning that may result from the nearly degenerate conformal elements.
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