Continuum modelling of granular particle flow with inelastic inter-particle collisions

The kinetic theory of granular flow is a successful model for gas-solid flows. However, inelastic collisions between particles, among other mechanisms, cause agglomeration of particles, which may be the reason why undue sensitivity of the model to any slight inelasticity in inter-particle collisions has been seen previously. In contrast to a dry (i.e. no interstitial gas) granular system, this tendency to agglomerate in a gas driven two-phase system may be countered by the carrier gas turbulence. In this paper, a heuristic model for particle gas turbulence interaction is introduced within the scope of a generalized kinetic theory model which incorporates the carrier fluid effect on particulate stresses. The numerical results for the flow of granular particles in vertical pipes, which considers slightly inelastic inter-particle collisions, are in reasonably good agreement with published experimental data. Even in this relatively simple model, the results indicate that the interactions between the particle phase and gas turbulence need to be appropriately addressed in any kinetic theory based model for gas solid flows

Stochastic suspensions of heavy particles

Turbulent suspensions of heavy particles in incompressible flows have gained much attention in recent years. A large amount of work focused on the impact that the inertia and the dissipative dynamics of the particles have on their dynamical and statistical properties. Substantial progress followed from the study of suspensions in model flows which, although much simpler, reproduce most of the important mechanisms observed in real turbulence. This paper presents recent developments made on the relative motion of a pair of particles suspended in time-uncorrelated and spatially self-similar Gaussian flows. This review is complemented by new results. By introducing a time-dependent Stokes number, it is demonstrated that inertial particle relative dispersion recovers asymptotically Richardson's diffusion associated to simple tracers. A perturbative (homogeneization) technique is used in the small-Stokes-number asymptotics and leads to interpreting first-order corrections to tracer dynamics in terms of an effective drift. This expansion implies that the correlation dimension deficit behaves linearly as a function of the Stokes number. The validity and the accuracy of this prediction is confirmed by numerical simulations.Comment: 15 pages, 12 figure

Gas turbulence modulation in a two-fluid model for gas-solid flows

Recent rapid progress in the theoretical and experimental study of turbulence modulation has led to greater understanding of the physics of particle-gas turbulence interactions. A new two-fluid model incorporating these advances for relatively dilute gas-solid flows containing high-inertia particles is established. The effect of aerodynamic forces upon the particulate stresses is considered in this kinetic theory-based model, and the influence of the particles on the turbulent gas is addressed: the work associated with drag forces contributes to the gas turbulent energy, and the space occupied by particles restricts the turbulent length scale. The interparticle length scale, which is usually ignored, has been incorporated into a new model for determining the turbulent length scale. This model also considers the transport effect on the turbulent length scale. Simulation results for fully developed steady flows in vertical pipes are compared with a wide range of published experimental data and, generally, good agreement is shown. This comprehensive and validated model accounts for many of the interphase interactions that have been shown to be important

In vivo evaluation of an oral self-emulsifying drug delivery system (SEDDS) for exenatide

Background The aim of the study was to develop an oral self-emulsifying drug delivery system (SEDDS) for exenatide and to evaluate its in vivo efficacy. Methods Exenatide was lipidised via hydrophobic ion pairing with sodium docusate (DOC) and incorporated in SEDDS consisting of 35% Cremophor EL, 25% Labrafil 1944, 30% Capmul-PG 8 and 10% propylene glycol. Exenatide/DOC was characterized in terms of lipophilicity evaluating the octanol/water phase distribution (logP). Exenatide/DOC SEDDS were characterized via droplet size analysis, drug release characteristics (log DSEDDS/release medium determination) and mucus permeation studies. Furthermore, the impact of orally administered exenatide/DOC SEDDS on blood glucose level was investigated in vivo on healthy male Sprague-Dawley rats. Results Hydrophobic ion pairing in a molar ratio of 1:4 (exenatide:DOC) increased the effective logP of exenatide from −1.1 to 2.1. SEDDS with a payload of 1% exenatide/DOC had a mean droplet size of 45.87 ± 2.9 nm and a Log DSEDDS/release medium of 1.9 ± 0.05. Permeation experiments revealed 2.7-fold improved mucus diffusion for exenatide/DOC SEDDS compared to exenatide in solution. Orally administered exenatide/DOC SEDDS showed a relative bioavailability (versus s.c.) of 14.62% ± 3.07% and caused a significant (p < .05) 20.6% decrease in AUC values of blood glucose levels. Conclusion According to these results, hydrophobic ion pairing in combination with SEDDS represents a promising tool for oral peptide delivery

Perturbation theory for large Stokes number particles in random velocity fields

We derive a perturbative approach to study, in the large inertia limit, the dynamics of solid particles in a smooth, incompressible and finite-time correlated random velocity field. We carry on an expansion in powers of the inverse square root of the Stokes number, defined as the ratio of the relaxation time for the particle velocities and the correlation time of the velocity field. We describe in this limit the residual concentration fluctuations of the particle suspension, and determine the contribution to the collision statistics produced by clustering. For both concentration fluctuations and collision velocities, we analyze the differences with the compressible one-dimensional case.Comment: Latex, 12 pages, 2 eps figures include

Relating the microscopic rules in coalescence-fragmentation models to the macroscopic cluster size distributions which emerge

Coalescence-fragmentation problems are of great interest across the physical, biological, and recently social sciences. They are typically studied from the perspective of the rate equations, at the heart of such models are the rules used for coalescence and fragmentation. Here we discuss how changes in these microscopic rules affect the macroscopic cluster-size distribution which emerges from the solution to the rate equation. More generally, our work elucidates the crucial role that the fragmentation rule can play in such dynamical grouping models. We focus on two well-known models whose fragmentation rules lie at opposite extremes setting the models within the broader context of binary coalescence-fragmentation models. Further, we provide a range of generalizations and new analytic results for a well-known model of social group formation [V. M. Eguiluz and M. G. Zimmermann, Phys. Rev. Lett. 85, 5659 (2000)]. We develop analytic perturbation treatment of the original model, and extend the mathematical to the treatment of growing and declining populations

Statistical Microhydrodynamics

Written by experienced practitioners and teachers, this concise and comprehensive treatment on particulate flow covers both the theory as well as applications and examples from the oil and chemical industry. Following a look at the basic concepts of probability theory, the authors goe on to examine the elements of microhydrodynamics, Brownian motion, and real liquids in turbulent flow. Of interest for lecturers in physics, theoretical physicists and chemists, as well as chemical engineers