08 Fakultät Mathematik und Physik

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Author: search.filters.author.Holm, ChristianSubject: search.filters.subject.620

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    Permeability estimation of regular porous structures : a benchmark for comparison of methods
    (2021) Wagner, Arndt; Eggenweiler, Elissa; Weinhardt, Felix; Trivedi, Zubin; Krach, David; Lohrmann, Christoph; Jain, Kartik; Karadimitriou, Nikolaos; Bringedal, Carina; Voland, Paul; Holm, Christian; Class, Holger; Steeb, Holger; Rybak, Iryna
    The intrinsic permeability is a crucial parameter to characterise and quantify fluid flow through porous media. However, this parameter is typically uncertain, even if the geometry of the pore structure is available. In this paper, we perform a comparative study of experimental, semi-analytical and numerical methods to calculate the permeability of a regular porous structure. In particular, we use the Kozeny-Carman relation, different homogenisation approaches (3D, 2D, very thin porous media and pseudo 2D/3D), pore-scale simulations (lattice Boltzmann method, Smoothed Particle Hydrodynamics and finite-element method) and pore-scale experiments (microfluidics). A conceptual design of a periodic porous structure with regularly positioned solid cylinders is set up as a benchmark problem and treated with all considered methods. The results are discussed with regard to the individual strengths and limitations of the used methods. The applicable homogenisation approaches as well as all considered pore-scale models prove their ability to predict the permeability of the benchmark problem. The underestimation obtained by the microfluidic experiments is analysed in detail using the lattice Boltzmann method, which makes it possible to quantify the influence of experimental setup restrictions.
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    Renormalized charge and dielectric effects in colloidal interactions : a numerical solution of the nonlinear Poisson-Boltzmann equation for unknown boundary conditions
    (2023) Schlaich, Alexander; Tyagi, Sandeep; Kesselheim, Stefan; Sega, Marcello; Holm, Christian
    The Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, introduced more than 70 years ago, is a hallmark of colloidal particle modeling. For highly charged particles in the dilute regime, it is often supplemented by Alexander’s prescription (Alexander et al. in J Chem Phys 80:5776, 1984) for using a renormalized charge. Here, we solve the problem of the interaction between two charged colloids at finite ionic strength, including dielectric mismatch effects, using an efficient numerical scheme to solve the nonlinear Poisson-Boltzmann (NPB) equation with unknown boundary conditions. Our results perfectly match the analytical predictions for the renormalized charge by Trizac and coworkers (Aubouy et al. in J Phys A 36:5835, 2003). Moreover, they allow us to reinterpret previous molecular dynamics (MD) simulation results by Kreer et al. (Phys Rev E 74:021401, 2006), rendering them now in agreement with the expected behavior. We furthermore find that the influence of polarization becomes important only when the Debye layers overlap significantly.