1,721,114 research outputs found
Probabilistic analysis of the dual site-bond model: the self-consistent case
No full textA probabilistic analysis of the generation of dual site-bond models for the energy landscape of adsorbents is presented, focusing attention on the self-consistent case. To generate an uncorrelated site-bond energy landscape with prescribed distribution functions FS*(E) and FB*(E) consistent with the two basic laws of the dual site-bond model, the random variables associated with the site and bond energies should possess the local distribution functions FS(E) and FB(E), which are related to FS*(E) and FB*(E) through a nonlinear integral equation. In particular, the inverse problem in two dimensions is solved in closed form. The analytical solution for the inverse problem provides a clear description of the intrinsic correlation in the energy landscape induced by the fulfillment of the construction principle
Convection-dominated dispersion in channels with fractal cross-section
No full textWe focus on the characterization of dispersion processes in microchannels with fractal boundaries (and translational symmetry in the longitudinal direction) in the presence of laminar axial velocity field. This article extends the theory of laminar dispersion in finite-length channel flows at high Peclet numbers by analyzing the role of the fractal cross-section in the convection-dominated transport regime. In this regime, the properties of the dispersion boundary layer and the values of the scaling exponents controlling the dependence of the moment hierarchy on the Peclet number are determined by the local near-wall behavior of the axial velocity. Specifically, different scaling laws in the behavior of the moment hierarchy occur, depending whether the cross-sectional boundary is smooth or nonsmooth (e.g., presenting corner points or cusps). The limit case of a fractal boundary is analyzed in detail. Analytical and numerical results are presented for two fractal cross-sections (the classical Koch curve and the Koch snowflake) in the Stokes regime. © 2011 American Institute of Physics
Laminar convective heat transfer across fractal boundaries
No full textWe focus on the characterization of heat-transfer processes in microchannels with fractal boundaries (and translational symmetry in the longitudinal direction) in the presence of a laminar axial velocity field. This corresponds to the generalization of the classical Leveque problem to investigate the role of fractal boundaries. We show that the thickness delta of the thermal boundary layer scales with the thermal Peclet number as delta similar to Pe(eff)(-1/(n+2)), n being the exponent characterizing the local behaviour of the laminar velocity field at the no-slip fractal wall. Correspondingly, the normalized thermal flux F is controlled by the boundary fractal dimension D(f) and the velocity exponent n according with the scaling law Phi similar to Pe(eff)(Df/(n+2)). Numerical results are presented for two different structures having different fractal dimensions: the Koch microchannel of fractal dimension D(f) = 3/2 and the Koch snowflake microchannel of fractal dimension D(f) = ln(4)/ln(3). Copyright (C) EPLA, 201
Effect of secondary flows on dispersion in finite-length channels at high Peclet numbers
No full textWe investigate the effects of secondary (transverse) flows on convection-dominated dispersion of pressure driven, open column laminar flow in a conduit with rectangular cross-section. We show that secondary flows significantly reduce dispersion (enhancing transverse diffusion) in Taylor-Aris regime [H. Zhao and H. H. Bau, "Effect of secondary flows on Taylor-Aris dispersion," Anal. Chem. 79, 7792-7798 (2007)], as well as in convection-controlled regime. In the convection-controlled dispersion regime (i.e., laminar dispersion in finite-length channel with axial flow at high Peclet numbers) the properties of the dispersion boundary layer and the values of the scaling exponents controlling the dependence of the moment hierarchy on the Peclet number m(n) out ∼ P e θn eff are determined by the local near-wall behaviour of the axial velocity. The presence of transverse flows strongly modify the localization properties of the dispersion boundary layer and consequently the moment scaling exponents. Different secondary flows, electrokinetically induced and independent of the primary axial flow are considered. A complete scaling theory is presented for the nth order moment of the outlet chromatogram as a function of the axial Peclet number, the secondary flow's pattern and intensity. We show that some secondary flows (the corotating and the counter-rotating cavity flows) significantly reduce dispersion and m(n) out ∼ P e (n-1)/3 eff. No significant dispersion reduction is obtained with the cavity cross-flow m(n) out ∼ P e (n-1)/2 eff. The best result is obtained with the two full-motion counter-rotating cross-flows because m(n) out saturates towards a constant value. Theoretical results from scaling theory are strongly supported by numerical results obtained by Finite Element Method. © 2013 AIP Publishing LLC
Swelling kinetics of HPMC tablets
No full textHydroxypropyl methylcellulose (HPMC) is a cellulosic polymer widely employed in tablets formulation. In contact with biological fluids, it undergoes a glassy-rubbery transition and drug release is strongly influenced by swelling. We study the kinetic parameters of a classical phenomenological model (Astarita and Sarti), which describes the velocity of a glassy-rubbery interface as a function of the local solvent concentration. One dimensional mass transport equations with moving boundaries are numerically solved by finite elements method (FEM) in order to fit Astarita-Sarti parameters k and n on experimental swelling fronts and concentration profiles taken from literature for HPMC K4 M, HPMC K15 M and HPMC K100 M
Experimental validation of a correlation-based model for permeability
No full text[No abstract available
A versatile lattice simulator for fluid-solid noncatalytic reactions in complex media
No full textA versatile lattice simulator for fluid-solid noncatalytic reactions is developed in detail in order to study linear, nonlinear, and nonisothermal kinetics in complex media, in the presence of multicomponent diffusion and n-solid reactant species. The simulator is based on a time-splitting algorithm for the diffusion and for the reaction steps. The simulator is quantitatively checked in many different cases involving initially nonporous particles constituted by a solid reactant dispersed in an inert matrix. The influence of spatial correlation properties in the case of uniform and nonuniform solid reactant distribution is analyzed in detail
Multicomponent percolation: Probabilistic properties and application to nonisothermal reactions in granular materials
No full textMulticomponent percolation schemes are introduced and discussed. They represent a generalization of usual percolation models to an arbitrary number of species. A detailed analysis of the probabilistic properties of multicomponent percolation is developed and extended to a non-numerable (continuous) distribution of species. Some initial results on transport properties are presented. The connection between multicomponent percolation models and (chemical) reaction schemes in granular materials is analyzed in detail and an application to exothermal self-propagating reactions proposed. © 1994 The American Physical Society
Invariant geometric properties of a class of 3D chaotic flows
No full textThis article extends the analysis developed by Giona and Adrover [M. Giona, A. Adrover, Phys. Rev. Lett. 81 (1998) 3864] for 2D area-preserving diffeomorphisms to 3D volume-preserving C-infinity-diffeomorphisms of the 3D torus topologically conjugate to a linear map. The article analyzes the invariant geometric properties of vector dynamics and surface element evolution in 3D systems and provides an analytic expression for the probability measure describing pointwise statistical properties of the unstable foliations in the hyperbolic case. The convergence propel ties of this measure are addressed starting from the dynamics of surface elements. The application of the methods developed to physically realizable 3D chaotic flows such as ABC flow is discussed in detail. (C) 2000 Elsevier Science B.V. All rights reserved
Modified model for the regulation of the tryptophan operon in Escherichia coli
No full textThis article proposes a modification of the model developed by Sinha (1988) and Sen and Liu (1990) for the regulation dynamics of the tryptophan operon in E. coli based on a consistent overall balance of the agent repressing the mRNA transcription. The dynamics of the model are analyzed by means of continuation techniques and the influence of periodic fluctuations in the intracellular demand for tryptophan is addressed. The analysis provides deeper insight into the dynamics of this operon system and the results obtained may be a useful starting point for the optimization of tryptophan yield in bacterial cultures. (C) 2002 Wiley Periodicals, Inc
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