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Register a new userGranular-like behavior of molecular flow in constricted nanopores
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The fluid flow through porous media is described by Darcys law, while the fluid/wall interactions can be neglected. In nanopores, where adsorption dominates, Darcys extension has been made, but approaches able to describe flows in mesopores are still lacking. We show here that molecular flows through nano-constrictions is well described by Berverloos law, predicting the mass flow rate of granular material through macro-apertures. This molecular and granular analogy, allows to derive a relationship providing a theoretical framework for the molecular flow in disordered mesoporous systems.
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Large-scale three dimensional molecular dynamics simulations of hopper flow are presented. The flow rate of the system is controlled by the width of the aperture at the bottom. As the steady-state flow rate is reduced, the force distribution $P(f)$ changes only slightly, while there is a large change in the impulse distribution $P(i)$. In both cases, the distributions show an increase in small forces or impulses as the systems approach jamming, the opposite of that seen in previous Lennard-Jones simulations. This occurs dynamically as well for a hopper that transitions from a flowing to a jammed state over time. The final jammed $P(f)$ is quite distinct from a poured packing $P(f)$ in the same geometry. The change in $P(i)$ is a much stronger indicator of the approach to jamming. The formation of a peak or plateau in $P(f)$ at the average force is not a general feature of the approach to jamming.
We present a multiscale simulation algorithm for amorphous materials, which we illustrate and validate in a canonical case of dense granular flow. Our algorithm is based on the recently proposed Spot Model, where particles in a dense random packing undergo chain-like collective displacements in response to diffusing spots of influence, carrying a slight excess of interstitial free volume. We reconstruct the microscopic dynamics of particles from the coarse grained dynamics of spots by introducing a localized particle relaxation step after each spot-induced block displacement, simply to enforce packing constraints with a (fairly arbitrary) soft-core repulsion. To test the model, we study to what extent it can describe the dynamics of up to 135,000 frictional, viscoelastic spheres in granular drainage simulated by the discrete-element method (DEM). With only five fitting parameters (the radius, volume, diffusivity, drift velocity, and injection rate of spots), we find that the spot simulations are able to largely reproduce not only the mean flow and diffusion, but also some subtle statistics of the flowing packings, such as spatial velocity correlations and many-body structural correlations. The spot simulations run over 100 times faster than DEM and demonstrate the possibility of multiscale modeling for amorphous materials, whenever a suitable model can be devised for the coarse-grained spot dynamics.
We study the localization of vibrational modes of frictionless granular media. We introduce a new method, motivated by earlier work on non-Hermitian quantum problems, which works well both in the localized regime where the localization length $xi$ is much less than the linear size $L$ and in the regime $xi$ grater or of order $L$ when modes are extended throughout our finite system. Our very lowest frequency modes show quasi-localized resonances away from the jamming point; the spatial extent of these regions increases as the jamming point is approached, as expected theoretically. Throughout the remaining frequency range, our data show no signature of the nearness of the jamming point and collapse well when properly rescaled with the system size. Using Random Matrix Theory we derive the scaling relation $xi$ ~ $L^{d/2}$ for the regime $xi$ >> $L$ in $d$ dimensions.
We test the elasticity of granular aggregates using increments of shear and volume strain in a numerical simulation. We find that the increment in volume strain is almost reversible, but the increment in shear strain is not. The strength of this irreversibility increases as the average number of contacts per particle (the coordination number) decreases. For increments of volume strain, an elastic model that includes both average and fluctuating motions between contacting particles reproduces well the numerical results over the entire range of coordination numbers. For increments of shear strain, the theory and simulations agree quite well for high values of the coordination number.
The drainage of particulate foams is studied under conditions where the particles are not trapped individually by constrictions of the interstitial pore space. The drainage velocity decreases continuously as the particle volume fraction $phi_{p}$ increases. The suspensions jam - and therefore drainage stops - for values $phi_{p}^{*}$ which reveal a strong effect of the particle size. In accounting for the particular geometry of the foam, we show that $phi_{p}^{*}$ accounts for unusual confinement effects when the particles pack into the foam network. We model quantitatively the overall behavior of the suspension - from flow to jamming - by taking into account explicitly the divergence of its effective viscosity at $phi_{p}^{*}$. Beyond the scope of drainage, the reported jamming transition is expected to have a deep significance for all aspects related to particulate foams, from aging to mechanical properties.
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