1,721,245 research outputs found
L'articolo Taming Axial Dispersion in Hydrodynamic Chromatographic Columns through Wall Patterning, Physics of Fluids 30, 042002 (2018); doi: 10.1063/1.5022257 di A. Adrover, S. Cerbelli, M Giona e' stato selezionato come Top papers in Physics of Fluids 2018
No full textA well-known limitation of hydrodynamic chromatography arises from the synergistic interaction
between transverse diffusion and streamwise convection, which enhances axial dispersion through
the Taylor-Aris mechanism. We show that a periodic sequence of slip/no-slip conditions at the channel
walls (e.g., representing wall indentations hosting stable air pockets) can significantly reduce axial
dispersion, thus enhancing separation performance. The theoretical/numerical analysis is based on a
generalization of Brenner’s macrotransport approach to solute transport, here modified to account for
the finite-size of the suspended particles. The most effective dispersion-taming outcome is observed
when the alternating sequence of slip/no-slip conditions yields non-vanishing cross-sectional flow
components. The combination of these components with the hindering interaction between the chan-
nel boundaries and the finite-sized particles gives rise to a non-trivial solution of Brenner’s problem
on the unit periodic cell, where the cross-sectional particle number density departs from the spa-
tially homogeneous condition. In turn, this effect impacts upon the solution of the so-called b-field
defining the large-scale dispersion tensor, with an overall decremental effect on the axial disper-
sion coefficient and on the Height Equivalent of a Theoretical Plate. Published by AIP Publishing
On the hyperbolic behavior of laminar chaotic flows
No full textInternational centre for mechanical sciences CISM courses and lectures no. 51
Critical dispersion of advecting-diffusing tracers in periodic landscapes of hard-wall symmetric potentials
No full textLarge-scale, time-asymptotic dispersion properties of diffusing tracers dragged by a uniform drive through a two-dimensional periodic lattice of hard-wall symmetric potentials are investigated. Dispersion is quantified by a typically anisotropic effective diffusivity tensor D, whose eigenvalues and eigenvectors depend on the dimensionless bare diffusivity 1/Pe for each given lattice geometry. Attention is focused on critical lattice geometries yielding sustained macroscale dispersion D-perpendicular to along the direction orthogonal to the uniform drive in the limit where Pe -> infinity. A simple one-dimensional model is proposed, which predicts the anomalous scaling D-perpendicular to similar to 1/[A(1) + A(2) log(Pe)]
Separation of polydisperse particle mixtures by deterministic lateral displacement. the impact of particle diffusivity on separation efficiency
No full textDeterministic lateral displacement (DLD) has been recently proposed as a simple and efficient method to separate a polydisperse mixture of particles based on particle size. The separation device consists of a shallow rectangular channel filled with a periodic lattice of micrometer-sized obstacles, whose principal direction forms an angle with the channel walls. Particles are dragged by a carrier flow stream through the device. Experiments have shown that particles larger than a critical size depart from the average direction of the carrier flow, as they are systematically deflected by the obstacles while being dragged downstream. Theoretical models based on the geometric structure of the Stokes flow through the obstacle lattice have been proposed to predict the average direction of particle current flux. Besides, little is known about the dispersion of diffusing particles about the average particle current. In this article, we show that the interaction between the deterministic and stochastic components of particle motion results in a large-scale, possibly anisotropic, convection-enhanced dispersion process, which may hinder separation far beyond what could be predicted from the value of the bare particle diffusivity. The prediction of dispersion regimes results therefore essential for an optimal design of DLD devices. Copyright © 2012 Curtin University of Technology and John Wiley & Sons, Ltd
Cerbelli and Giona's map is pseudo-Anosov and nine consequences
No full textIt is shown that a piecewise affine area-preserving homeomorphism of the 2-torus studied by Cerbelli and Giona is pseudo-Anosov. This enables one to prove various of their conjectures, quantify the multifractality of its "w-measures," calculate many other quantities for its dynamics, and construct an exact area-preserving tilt map of the cylinder with proved diffusive behaviour
Laminar dispersion at low and high Peclet numbers in finite-length patterned microtubes
No full textLaminar dispersion of solutes in finite-length patterned microtubes is investigated at values of the Reynolds number below unity. Dispersion is strongly influenced by axial flow variations caused by patterns of periodic pillars and gaps in the flow direction.We focus on the Cassie-Baxter state, where the gaps are filled with air pockets, therefore enforcing free-slip boundary conditions at the flat liquidair interface. The analysis of dispersion is approached by considering the temporal moments of solute concentration. Based on this approach, we investigate the dispersion properties in a wide range of values of the Peclet number, thus gaining insight into how the patterned structure of the microtube influences both the Taylor-Aris and the convection-dominated dispersion regimes. Numerical results for the velocity field and for the moment hierarchy are obtained by means of finite element method solution of the corresponding transport equations.We show that for different patterned geometries, in a range of Peclet values spanning up to six decades, the dispersion features in a patterned microtube are equivalent to those of a microtube characterized by a uniform slip velocity equal to the wallaverage velocity of the patterned case. This suggests that two patterned micropipes with different geometry yet characterized by the same flow rate and average wall velocity will exhibit the same dispersion features as well as the same macroscopic pressure drop
A continuous archetype of nonuniform chaos in area-preserving dynamical systems
No full textWe propose a piecewise linear, area-preserving, continuous map of the two-torus as a prototype of nonlinear two-dimensional mixing transformations that preserve a smooth measure (e.g., the Lebesgue measure). The model lends itself to a closed-form analysis of both statistical and geometric properties. We show that the proposed model shares typical features that characterize chaotic dynamics associated with area-preserving nonlinear maps, namely, strict inequality between the line-stretching exponent and the Lyapunov exponent, the dispersive behavior of stretch-factor statistics, the singular spatial distribution of expanding and contracting fibers, and the sign-alternating property of cocycle dynamics. The closed-form knowledge of statistical and geometric properties (in particular of the invariant contracting and dilating directions) makes the proposed model a useful tool for investigating the relationship between stretching and folding in bounded chaotic systems, with potential applications in the fields of chaotic advection, fast dynamo, and quantum chaos theory
On the estimate of mixing length in interdigital micromixers
No full textThe multilamination process that characterizes interdigital micromixers is an efficient and technologically feasible method for maximizing and controlling mass and/or heat transfer between two or more segregated fluid streams. We analyze the dynamics of mixing that takes place in the mixing channel downstream the interdigital apparatus. Specifically, we investigate, for different flow profiles, how the channel length necessary to achieve a prescribed level of mixedness depends on the degree of lamination (number and thickness of lamellae) of the feed stream. As a case study, we consider plug, shear and Poiseuille flow, and compare steady-state profiles resulting from the numerical simulation of the full advection-diffusion problem with the analytical solution stemming from the one-dimensional Sturm-Liouville eigenvalue problem along the spanwise coordinate, obtained neglecting streamwise diffusion. We find that (i) the mixing length can be significantly affected by the flow profile, especially at high degree of lamination of the feed stream, and (ii) in general, no obvious scaling between mixing length and lamellar thickness can be assumed. A rigorous way to approach the design of these micromixers is proposed. © 2007 Elsevier B.V. All rights reserved
Characterization of nonuniform chaos in area-preserving nonlinear maps through a continuous archetype
No full textNumerical investigations conducted over a wealth of nonlinear area-preserving smooth maps (e.g. the Standard Map) showed that these systems possess physically relevant features that are not captured by any continuous archetype of two-dimensional conservative dynamics. Among these properties are the dispersive behavior of stretch factor statistics, the multifractal character of the measure associated with invariant foliations, the sign-alternating property, accounting for the nestedly bent structure of invariant foliations, and the strict inequality between the topological entropy, ht.p, and the Lyapunov exponent, A. We refer to systems possessing all of these properties as nonuniformly chaotic. In this article, we present a globally continuous, piecewise-smooth area-preserving transformation, the total homeomorphism H, as an archetype of nommiformly chaotic behavior. The relatively simple structure of point set dynamics and the closed-form knowledge of the pointwise expanding and contracting invariant directions associated with V, permits to derive either analytically, or with arbitrary numerical precision, the standard chaotic properties as well as the dynamics of the physically relevant properties that define nonuniform chaos. Potentialities and limitations of the model proposed in representing geometric and statistical properties of physically relevant smooth systems are discussed in detail. (c) 2006 Elsevier Ltd. All rights reserved
Connecting the spatial structure of periodic orbits and invariant manifolds in hyperbolic area-preserving systems
No full textThis Letter discusses the equivalence between the Bowen measure associated with the set Per(n) of periodic points of period n of hyperbolic area-preserving maps of a smooth manifold, and the measure associated with the intersections between stable and unstable manifolds of hyperbolic points. In typical cases of physical interest (i.e., nonuniformly hyperbolic systems) these measures are found to be highly nonuniform (multifractal). (c) 2005 Elsevier B.V. All rights reserved
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