1,721,042 research outputs found
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
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)]
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
50-Fold reduction of separation time in open-channel hydrodynamic chromatography via lateral vortices
No full textDespite its relatively long history, open-channel hydrodynamic chromatography (OC-HDC) still represents a niche technique for determining the size distribution of particle suspensions. Practical limitations of this separation method ultimately arise from the low eluent velocity that is necessary to contain the adverse increase of analyte bandwidth caused by Taylor-Aris dispersion. Because of the micrometric size of the channel cross section, the low eluent velocity translates into order of pL-per-minute flow rates, which introduce a challenge for both the injection and the detection systems. In this article, we provide theoretical/numerical evidence illustrating how a sizable reduction of the Taylor-Aris effect can be obtained by triggering cross-sectional vortices alongside the main pressure-driven axial flow. As a case study, we consider a square channel geometry where the lateral vortices are created by DC-induced electroosmosis. The analysis of particle separation is based on the classical excluded-volume macrotransport approach, which allows to derive the average particle velocity and the axial dispersion coefficient from the solution of two stationary advection-diffusion problems defined onto the channel cross section. We find that lateral vortices can enhance the separation efficiency quantitatively, e.g., by reducing the separation time of a two-species mixture by a 50-fold factor compared to standard OC-HDC
On the connection between reaction efficiency and interface structure in open laminar flows
No full textWe investigate numerically the steady-state properties of a mixing-controlled reaction between segregated reactants continuously inflowing-outflowing the annular region between counter-rotating coaxial cylinders in the Stokes regime. This system provides a prototypical example of an open nonchaotic flow generating steady-state kinematic mixing structures of arbitrarily fine lengthscales which can be characterized analytically. The kinematic interface structure is compared and contrasted to that of the reaction interface associated with the presence of a small but finite diffusivity. Results of accurate numerical simulations show that reaction efficiency and mixing performance are only weakly correlated with the global measure of both the kinematic and the reaction interface. Relevant information oil reaction regimes at low diffusivity can instead be obtained from the analysis of the spatial distribution of the kinematic interface, which controls the localization properties of unreacted species. The generality of the results is tested for several prototypical open and closed channel flows. (C) 2008 Elsevier Ltd. All rights reserved
Localization and spectral phase transition in an open advecting-diffusing three-dimensional Stokes flow
No full textWe study the steady-state characterization of an advecting-diffusing three-dimensional flow defined in the annular region between coaxial cylinders of finite length that can rotate independently. A phase transition occurs when the cylinder velocities vary, which controls the spectral properties of the dominant eigenvalue and eigenfunction of the advection-diffusion equation for high Péclet numbers. The localization abscissa of the dominant eigenfunction can be used as the order parameter of the transition, and is a continuous function of the wall velocity. Conversely, the exponent characterizing the scaling of the real part of the dominant eigenvalue displays a discontinuous behavior at the critical point. Theoretical arguments support the localization properties observed numerically and provide a simple explanation of this phenomenon. © 2008 The American Physical Society
Perturbation analysis of mixing and dispersion regimes in the low and intermediate Péclet number region
No full textThe object of this paper is to show that a variety of dispersion and mixing phenomena induced by laminar convection and diffusion can be approached by perturbation analysis of the spectrum associated with the corresponding advection-diffusion operator. As a case study for dispersion, we consider the classical Taylor-Aris problem, whereas a prototypical model of Sturm-Liouville generalized eigenvalue problem is considered for describing mixing in open or closed bounded flows. For both cases, we show how a simplified (low-order) perturbative approach defines quantitatively the range of different mixing regimes and the associated time scales. Furthermore, we show how a complete higher-order approach cannot improve significantly the simplified low-order analysis due to the lack of analyticity of the eigenvalue branches. The perturbation analysis is also extended to models of physically realizable mixing systems (lid-driven cavity flow). © 2010 The American Physical Society
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