Homogenization of a locally-periodic medium with areas of low and high diffusivity

We aim at understanding transport in porous materials including regions with both high and low diffusivities. For such scenarios, the transport becomes structured (here: micro- macro). The geometry we have in mind includes regions of low diffusivity arranged in a locally-periodic fashion. We choose a prototypical advection-diffusion system (of minimal size), discuss its formal homogenization (the heterogenous medium being now assumed to be made of zones with circular areas of low diffusivity of x-varying sizes), and prove the weak solvability of the limit two-scale reaction-diffusion model. A special feature of our analysis is that most of the basic estimates (positivity, L^inf-bounds, uniqueness, energy inequality) are obtained in x-dependent Bochner spaces. Keywords: Heterogeneous porous materials, homogenization, micro-macro transport, two-scale model, reaction-diffusion system, weak solvability

New algorithms for parameter-swing reactors

Bliek, A. [Promotor]Verduyn Lunel, S.M. [Promotor

Crystal dissolution and precipitation in porous media : L1L^1-contraction and uniqueness

In this note we continue the analysis of the pore-scale model for crystal dissolution and precipitation in porous media proposed in [C. J. van Duijn and I. S. Pop, Crystal dissolution and precipitation in porous media: pore scale analysis, J. Reine Angew. Math. 577 (2004), 171–211]. There the existence of weak solutions was shown. We prove an L1-contraction property of the pore-scale model. As a direct consequence we obtain the uniqueness of (weak) solutions

Image Recognition of Shape Defects in Hot Steel Rolling

A frequently occurring issue in hot rolling of steel is so-called tail pinching. Prominent features of a pinched tail are ripple-like defects and a pointed tail. In this report two algorithms are presented to detect those features accurately in 2D gray scale images of steel strips. The two ripple detectors are based on the second order Gaussian derivative and the Gabor transform, a localized Fourier transform, yielding the so-called rippleness measures. Additionally a parameter called tail length is defined which indicates to what extent the overall shape of the tail deviates from an ideal rectangular shape. These methods are tested on images from the surface inspection system at Tata Hot Strip Mill 2 in IJmuiden, it is shown that by defining a simple criterion in the feature space spanned by these two parameters a given set of strips can correctly be classified into pinched and non-pinched strips. These promising results open the way for the development of an automatic pinch detection system

Semi-discrete finite difference multiscale scheme for a concrete corrosion model: approximation estimates and convergence

We propose a semi-discrete finite difference multiscale scheme for a concrete corrosion model consisting of a system of two-scale reaction-diffusion equations coupled with an ode. We prove energy and regularity estimates and use them to get the necessary compactness of the approximation estimates. Finally, we illustrate numerically the behavior of the two-scale finite difference approximation of the weak solution.Comment: 22 pages, 1 figure, submitted to Japan Journal of Industrial and Applied Mathematic

Crystal precipitation and dissolution in a thin strip

We present a two-dimensional micro-scale model for crystal dissolution and precipitation in a porous medium. The local geometry of the pore is represented as a thin strip and the model allows for changes in the pore volume. A formal limiting argument, for the limit of the width of the strip going to zero, leads to a system of one-dimensional effective upscaled equations. We show that the effective equations allow for travelling-wave solutions and prove the existence and uniqueness of these. Numerical solutions of the effective equations are compared with numerical solutions of the original equations on the thin strip and with analytical results. We also show that a model from the literature that does not allow changes in the pore volume can be obtained from the present model as a formal limit