Alessandra Adrover

Characterization of thin wall Pd–Ag rolled membranes

Abstract A thin wall Pd–Ag tube (thickness 50 μm ) obtained by a procedure of cold-rolling and annealing of thin metal foils has been characterized in long-term tests for determining the hydrogen permeability under operating condition of a temperature range from 300°C to 400°C and transmembrane differential pressure from 50 to 100 kPa . During testing, the physical and mechanical stability of the rolled membranes have been observed and high hydrogen fluxes have been measured. The long-term tests have also shown the modification of the surface structure of the membrane due to the hydrogen–metal interaction and the thermal cycling: as a consequence, an increase of the mass transfer properties of the hydrogen through the material (diffusivity and solubility) has been observed and the membrane tube has attained very high performances in about 3 months of operation in terms of hydrogen permeability. Furthermore, the tests have demonstrated that these Pd–Ag membranes have the capability to separate hydrogen from gas mixtures with a complete hydrogen selectivity and can be used to produce ultra-pure hydrogen for applications in energetic fields in membrane reactors by molecular reforming in membrane reactors (i.e. isotopic hydrogen separation, fuel cell, etc.).

The intermaterial area density generated by time- and spatially periodic 2D chaotic flows

Abstract This paper explores in some detail the spatial structure and the statistical properties of partially mixed structures evolving under the effects of a time-periodic chaotic flow. Numerical simulations are used to examine the evolution of the interface between two fluids, which grows exponentially with a rate equal to the topological entropy of the flow. Such growth is much faster than predicted by the Lyapunov exponent of the flow. As time increases, the partially mixed system develops into a self-similar structure. Frequency distributions of interface density corresponding to different times collapse onto an invariant curve by a simple homogeneous scaling. This scaling behavior is a direct consequence of the generic asymptotic directionality property characteristic of 2D time-periodic flows. Striation thickness distributions (STDs) also acquire a time-invariant shape after a few (∼5–10) periods of the flow and are collapsed onto a single curve by standardization. It is also shown that STDs can be accurately predicted from distributions of stretching values, thus providing an effective method for calculation of STDs in complex flows.

The geometry of mixing in time-periodic chaotic flows.: I. asymptotic directionality in physically realizable flows and global invariant properties

Abstract This paper demonstrates that the geometry and topology of material lines in 2D time-periodic chaotic flows is controlled by a global geometric property referred to as asymptotic directionality . This property implies the existence of local asymptotic orientations at each point within the chaotic region, determined by the unstable eigendirections of the Jacobian matrix of the n th iterative of the Poincare map associated with the flow. Asymptotic directionality also determines the geometry of the invariant unstable manifolds, which are everywhere tangent to the field of asymptotic eigendirections. This fact is used to derive simple non-perturbative methods for reconstructing the global invariant manifolds to any desired level of detail. The geometric approach associated with the existence of a field of invariant unstable subspaces permits us to introduce the concept of a geometric global unstable manifold as an intrinsic property of a Poincare map of the flow, defined as a class of equivalence of integral manifolds belonging to the invariant unstable foliation. The connection between the geometric global unstable manifold and the global unstable manifold of hyperbolic periodic points is also addressed. Since material lines evolved by a chaotic flow are asymptotically attracted to the geometric global unstable manifold of the Poincare map, in a sense that will be made clear in the article, the reconstruction of unstable integral manifolds can be used to obtain a quantitative characterization of the topological and statistical properties of partially mixed structures. Two physically realizable systems are analyzed: closed cavity flow and flow between eccentric cylinders. Asymptotic directionality provides evidence of a global self-organizing structure characterizing chaotic flow which is analogous to that of Anosov diffeomorphisms, which turns out to be the basic prototype of mixing systems. In this framework, we show how partially mixed structures can be quantitatively characterized by a nonuniform stationary measure (different from the ergodic measure) associated with the dynamical system generated by the field of asymptotic unstable eigenvectors.

Exact solution of linear transport equations in fractal media - I. Renormalization analysis and general theory

We develop in detail a renormalization analysis of transport equations on fractals by considering regular model structures represented by means of families of graphs G(n), each of which is characterized by its adjacency matrix. Particular attention is paid to the correct representation of boundary conditions relevant to specific transport problems. The extension theory for the solution of generic transport problems defined by positive functions in the algebra of a given adjacency matrix is also developed.

Two-layer shrinking-core model: parameter estimation for the reaction order in leaching processes

This article develops a modified version of the shrinking-core model accounting for the surface heterogeneity of solid particles. This model can be primarily used as a shortcut method for estimating the dependence of the kinetic rates on the concentration of fluid reactants and specifically the reaction order in the presence of a polydisperse solid mixture. This approach is tested numerically for model reactions involving polydisperse systems and is applied to the dissolution of MnO2 in sulphuric acid solutions containing glucose as the reductant agent.

A spectral approach to reaction/diffusion kinetics in chaotic flows

A classical spectral approach based on the set of eigenfunctions of the Laplacian operator is proposed for the numerical solution of advection/diffusion/reaction equations for reactive mixing in 2-D laminar chaotic flows. This approach overcomes numerical diffusion problems and provides accurate spatiotemporal concentration fields in reasonable computer time up to very high values of Pe, such as Pe=105 and higher. Moreover, a pseudo-spectral approach, combining spectral expansion with an FFT algorithm, provides an efficient computational strategy for both polynomial and non-polynomial nonlinearities such as those arising in non-isothermal reactive mixing problems with Arrhenius dependence of kinetic rates on temperature.

Feasibility, efficiency and transportability of short-horizon optimal mixing protocols

We consider, as a case study, the optimization of mixing protocols for a two-dimensional, piecewise steady, nonlinear flow, the sine flow, for both the advective-diffusive and purely advective cases. We use the mix-norm as the cost function to be minimized by the optimization procedure. We show that the cost function possesses a complex structure of local minima of nearly the same values and, consequently, that the problem possesses a large number of sub-optimal protocols with nearly the same mixing efficiency as the optimal protocol. We present a computationally efficient optimization procedure able to find a sub-optimal protocol through a sequence of short-time-horizon optimizations. We show that short-time-horizon optimal mixing protocols, although sub-optimal, are both feasible and efficient at mixing flows with and without diffusion. We also show that these optimized protocols can be derived, at lower computational cost, for purely advective flows and successfully transported to advective-diffusive flows with small molecular diffusivity. We characterize our results by discussing the asymptotic properties of the optimized protocols both in the pure advection and in the advection-diffusion cases. In particular, we quantify the mixing efficiency of the optimized protocols using the Lyapunov exponents and Poincare sections for the pure advection case, and the eigenvalue-eigenfunction spectrum for the advection-diffusion case. Our results indicate that the optimization over very short-time horizons could in principle be used as an on-line procedure for enhancing mixing in laboratory experiments, and in future engineering applications.

Analysis of controlled release in disordered structures: a percolation model

Abstract The analysis of controlled-release kinetics in disordered models (percolation clusters) of polymer matrices is developed in detail. It is shown that the “anomalous diffusion” experimentally found in the release kinetics from swollen gels, M t M x ∼ t″ , n> 1 2 , cannot possibly be related to hindered diffusive motion in disordered media, i.e. is not a consequence of the disordered structure of the matrix. A kinetic model is proposed to account for an exponent n greater than 1 2 . This is based on a two-phase kinetics which takes into account both field effects (deriving from potential interaction between solute and polymeric matrix) and entrapping effects due to geometric constraints.

Exact solution of linear transport equations in fractal media—II. Diffusion and convection

Renormalization analysis discussed in Giona et al. (1996a, Chem. Engng Sci., 51, 4717–4729) is applied to study diffusion and convection on fractals. Sorption properties and moment analysis are developed on fractals. Extension theory is applied to diffusion in the presence of multiple- length hopping. The case of diffusion in random and heterogeneous structures is also addressed. Finally, renormalization of diffusion with convective bias on fractals is developed.

Exact solution of linear transport equations in fractal media-III. Adsorption and chemical reaction

Absorption kinetics and first-order reaction models on fractal lattices are studied. Adsorption kinetics in macro/microporous fractal solids showing fractal scaling properties and a complex topological pore-network structure are developed by considering the coupling of two fractal graphs. For first-order reactions on fractal substrata, the exact determination of the behavior of the effectiveness factor vs the Thiele modulus is obtained. A model for analyzing the spatial concentration distribution in a fractal catalyst is proposed.