1,721,109 research outputs found
Granular gases
No full textThe dynamic evolution of granular gases is fundamentally different from molecular gases due to the energy loss during collisions. Nevertheless techniques of kinetic theory are useful in a regime, when the granular particles are moving rapidly and the gas is sufficiently dilute. In these lecture notes we analyse in detail the collision of two rough particles which is inelastic due to incomplete normal and tangential restitution as well as Coulomb friction. Based on the Walton model a time evolution operator for the many particle system is introduced, a formalism which is well suited for simple approximations. We discuss free cooling of granular particles with particular emphasis on the exchange of energy between rotational and translational degrees of freedom. (c) 2006 Elsevier B.V. All rights reserved
Liquid Fluidized Beds of Granular Particles
No full textAbstract We suggest a simple model for the dynamics of granular particles in suspension which is suitable for an event driven algorithm, allowing to simulate N = O(106) particles or more. As a first application we consider a dense granular packing which is fluidized by an upward stream of liquid, i.e. a fluidized bed. In the stationary state, when all forces balance, we always observe a well defined interface whose width is approximately independent of packing fraction. We also study the dynamics of expansion and sedimentation after fast and slow changes in flow rate and determine the timescales to reach a stationary state
Amoeboid propulsion of active solid bodies, vesicles and droplets: a comparison
No full textRace between micro swimmers: droplets (blue), vesicles (orange) and deformable solids (green), driven by the same swim stroke, exhibit very different velocities and efficiencies.We present a unified discussion of three types of near-spherical amoeboid microswimmers, driven by periodic, axially symmetric, achiral deformations (swim strokes): a solid deformable body, a vesicle with incompressible fluid membrane, and a droplet. Minimal models are used, which characterize the swimmer type only by boundary conditions. We calculate the swimming velocities, the dissipated power and the Lighthill efficiencies within a second order perturbation expansion in the small deformation amplitudes. For solid bodies, we reproduce older results by Lighthill and Blake, for vesicles and for droplets we add new results. The unified approach allows for a detailed comparison between the three types of microswimmers. We present such comparisons for swim strokes made up of spherical harmonics of adjacent orders l and l + 1, as well as for a manifold of swim strokes, made up of spherical harmonics up to order l = 4, which respect volume- and surface-incompressibility. This manifold is two-dimensional, which allows to present swimming velocities and efficiencies in compact graphical form. In a race in which each swimmer can choose the stroke that maximizes its speed, the droplet always comes in first, the vesicle comes in second, while the particle finishes third. However, if the three swimmers perform the same stroke, other order of rankings become possible. The maximum of the total efficiency of a droplet is greater than that of a vesicle if the internal dissipation is small. The efficiency of the solid body turns out to be typically two orders of magnitude smaller than that of vesicles and droplets. Optimizing the Lighthill efficiency and optimizing the swimming velocity result in different optimal swim strokes.Race between micro swimmers: droplets (blue), vesicles (orange) and deformable solids (green), driven by the same swim stroke, exhibit very different velocities and efficiencies.We present a unified discussion of three types of near-spherical amoeboid microswimmers, driven by periodic, axially symmetric, achiral deformations (swim strokes): a solid deformable body, a vesicle with incompressible fluid membrane, and a droplet. Minimal models are used, which characterize the swimmer type only by boundary conditions. We calculate the swimming velocities, the dissipated power and the Lighthill efficiencies within a second order perturbation expansion in the small deformation amplitudes. For solid bodies, we reproduce older results by Lighthill and Blake, for vesicles and for droplets we add new results. The unified approach allows for a detailed comparison between the three types of microswimmers. We present such comparisons for swim strokes made up of spherical harmonics of adjacent orders l and l + 1, as well as for a manifold of swim strokes, made up of spherical harmonics up to order l = 4, which respect volume- and surface-incompressibility. This manifold is two-dimensional, which allows to present swimming velocities and efficiencies in compact graphical form. In a race in which each swimmer can choose the stroke that maximizes its speed, the droplet always comes in first, the vesicle comes in second, while the particle finishes third. However, if the three swimmers perform the same stroke, other order of rankings become possible. The maximum of the total efficiency of a droplet is greater than that of a vesicle if the internal dissipation is small. The efficiency of the solid body turns out to be typically two orders of magnitude smaller than that of vesicles and droplets. Optimizing the Lighthill efficiency and optimizing the swimming velocity result in different optimal swim strokes
Mobilities of a drop and an encapsulated squirmer
No full textAbstract We have analyzed the dynamics of a spherical, uniaxial squirmer which is located inside a spherical liquid drop at general position 1487911\varvec{r}_s1487911 r s . The squirmer is subject to an external force and torque in addition to the slip velocity on its surface. We have derived exact analytical expressions for the linear and rotational velocity of the squirmer as well as the linear velocity of the drop for general, non-axisymmetric configurations. The mobilities of both, squirmer and drop, are in general anisotropic, depending on the orientation of 1487911\varvec{r}_s1487911 r s , relative to squirmer axis, external force or torque. We discuss their dependence on the size of the squirmer, its distance from the center of the drop and the viscosities. Our results provide a framework for the discussion of the trajectories of the composite system of drop and enclosed squirmer. Graphical AbstractGeorg-August-Universität Göttinge
Singular energy distributions in driven and undriven granular media
No full textWe study the kinetic theory of driven and undriven granular gases, taking into account both translational and rotational degrees of freedom. We obtain the high-energy tail of the stationary bivariate energy distribution, depending on the total energy E and the ratio x = root E-w/ E of rotational energy E-w to total energy. Extremely energetic particles have a unique and well-defined distribution f(x) which has several remarkable features: x is not uniformly distributed as in molecular gases; f(x) is not smooth but has multiple singularities. The latter behavior is sensitive to material properties such as the collision parameters, the moment of inertia and the collision rate. Interestingly, there are preferred ratios of rotational-to-total energy. In general, f(x) is strongly correlated with energy and the deviations from a uniform distribution grow with energy. We also solve for the energy distribution of freely cooling Maxwell Molecules and find qualitatively similar behavior
Dynamics of gelling liquids: a short survey
No full textThe dynamics of randomly crosslinked liquids is addressed via Rouse-type and Zimm-type models with crosslink statistics taken either from bond percolation or Erdos-Renyi random graphs. While the Rouse-type model isolates the effects of the random connectivity on the dynamics of molecular clusters, the Zimm-type model also accounts for hydrodynamic interactions on a preaveraged level. The incoherent intermediate scattering function is computed in thermal equilibrium; its critical behaviour near the: sol-gel transition is analysed and related to the scaling of cluster diffusion constants at the critical point. Second, non-equilibrium dynamics is studied by. looking at stress relaxation in a simple shear flow. Anomalous stress relaxation and critical rheological properties are derived. Some of the results contradict long-standing scaling arguments, which are shown to be flawed by inconsistencies
Local heat flux and energy loss in a two-dimensional vibrated granular gas
No full textWe performed event-driven simulations of a two-dimensional granular gas between two vibrating walls and directly measured the local heat flux and local energy dissipation in the stationary state. Describing the local heat flux as a function of the coordinate x in the direction perpendicular to the driving walls, we test a generalization of Fourier's law, q(x)=-kappa del T(x)+mu del rho(x), by relating the local heat flux to the local gradients of the temperature and density. This ansatz accounts for the fact that heat flux can also be generated by density gradients, not only by temperature gradients. Assuming the transport coefficients kappa and mu to be independent of x, we check the validity of this assumption and test the generalized Fourier law in the simulations. Both kappa and mu are determined for different system parameters, in particular, for a wide range of coefficients of restitution. We also compare our numerical results to existing hydrodynamic theories. Agreement is found for kappa for very small inelasticities only, i.e., when the gradients are small. Beyond this region, kappa and mu exhibit a striking nonmonotonic behavior. This may hint that hydrodynamics to Navier-Stokes order cannot be applied to moderately inelastic vibrated systems
- …
