Reduced light-scattering properties for mixtures off spherical particles: a simple approximation derived from Mie calculations Graaff, R.; Aarnoudse, J.G.; Zijp, J.R.; Sloot, P.M.A.; de Mul, F.F.M.; Greve, J. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. The reduced scattering cross section per unit of volume ;' -,(1 -g) is an important parameter to describe light propagation in media with scattering and absorption. Mie calculations of the asymmetry factorg for nonabsorbing spheres and Q_, the ratio of the scattering cross section ;, and the particle cross section, show that Q_(1 -g) = 3.28x 037 (m -1)209 is true to within a few percent, when the Mie parameters for relative refractive index m and size x are in the ranges of 1 < m • 1.1 and 5 < x < 50, respectively. A ratio of reduced scattering cross sections for radiation at two wavelengths is also independent of the size within the range mentioned, even for mixtures of different size spheres. The results seem promising for biomedical applications.
The role of stagnant zones in hydrodynamic dispersion is studied for creeping flow through a fixed bed of spherical permeable particles, covering several orders of characteristic time and length scales associated with fluid transport. Numerical simulations employ a hierarchical model to cope with the different temporal and spatial scales, showing good agreement with our experimental results on diffusionlimited mass transfer, transient, and asymptotic longitudinal dispersion. These data demonstrate that intraparticle liquid holdup in macroscopically homogeneous porous media clearly dominates over contributions caused by the intrinsic flow field heterogeneity and boundary-layer mass transfer. DOI: 10.1103/PhysRevLett.88.234501 PACS numbers: 47.15.Gf, 05.60. -k, 47.55.Mh A detailed understanding of transport in porous media over the intrinsic temporal and spatial scales is important in many technological and environmental processes [1]. For example, natural and industrial materials such as soil, rock, filter cakes, or catalyst pellets often contain lowpermeability zones with respect to hydraulic flow of liquid through the medium or even stagnant regions which then remain purely diffusive. The relevance of stagnant zones stems from their influence on dispersion: Fluid molecules entrained in the deep diffusive pools cause a substantial holdup contribution and thereby affect the time scale of transient dispersion, as well as the value of the asymptotic dispersion coefficient (if the asymptotic long-time limit can be reached at all) [2][3][4]. Consequently, the associated kinetics of mass transfer between fluid percolating through the medium and stagnant fluid becomes rate limiting in a number of dynamic processes, including the separation and reaction efficiency of chromatographic columns and reactors, or economic oil recovery from a reservoir.In this respect, transport phenomena observed in model systems such as random packings of spheres may help to characterize materials with a higher disorder [5][6][7]. For random packings of nonporous (impermeable) particles, for example, the long-time longitudinal dispersion coefficient is dominated by the boundary-layer contribution (due to the no-slip condition at the solid-liquid interface) or by medium and large-scale velocity fluctuations in the flow field depending on the actual disorder of the medium and the Peclet number, Pe u ay d p D m (with u ay , the average velocity; d p , particle diameter; and D m , the molecular diffusivity) [6,8]. This behavior contrasts with random packings of porous (permeable) particles. In that case, liquid holdup associated with stagnant zones inside the particles may dominate dispersion when convective times t c uayt dp significantly exceed the dimensionless time for diffusion, t d. In many situations, however, both a macroscopic flow heterogeneity and solute trapping in stagnant zones contribute to transient and asymptotic dispersion [3,7,9].Despite numerous theoretical, experimental, and numerical studies (e.g., [1,7,8,[10][11][12]),...
Several articles have been written regarding the hydraulic permeability of ordered and disordered fibrous media. Here, we explore wall effects on hydraulic permeabilities for ordered and disordered media using the lattice Boltzmann (LB) simulation method. Simulation results are found to be in excellent agreement with the semi analytic result of Sangani and Acrivos, and simulation results for disordered media are in good agreement with the results of Jackson and James and Higdon and Ford's fcc lattice. The macroscopic behavior, the hydraulic permeability, shows a distinct connection with the geometry of the system. This connection is explored and elucidated for ordered and disordered media. Finally, hydraulic permeabilities for bounded media at various wall separations are presented for both ordered and disordered media and results are compared with hydraulic permeabilities calculated for the unbounded media, and a phenomenological correlation is presented to facilitate rapid prediction of hydraulic permeabilities for both unbounded and bounded fibrous media.
We describe a method for modeling aggregation in a flowing fluid. In the model, aggregation proceeds by the accumulation of a "nutrient." The nutrient is modeled using a lattice Boltzmann model of transport. The aggregate absorbs the nutrient, and the amount absorbed determines the local growth probability. This model contains some of the essential features of growth of stony corals. We find that the morphology of the aggregates changes drastically as we increase the Péclet number from a regime where nutrient transport is diffusion controlled to a regime where hydrodynamic transport dominates. This is in qualitative agreement with the morphogenesis of stony corals. [S0031-9007(96)
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