Analytical considerations and dimensionless analysis for a description of particle interactions in high pressure processes

High pressures of up to several hundreds of MPa are utilized in a wide range of applications in chemical, bio-, and food engineering, aiming at selective control of (bio-)chemical reactions. Non-uniformity of process conditions may threaten the safety and quality of the resulting products because processing conditions such as pressure, temperature, and treatment history are crucial for the course of (bio-)chemical reactions. Therefore, thermofluid-dynamical phenomena during the high pressure process have to be examined, and numerical tools to predict process uniformity and to optimize the processes have to be developed. Recently applied mathematical models and numerical simulations of laboratory and industrial scale high pressure processes investigating the mentioned crucial phenomena are based on continuum balancing models of thermofluid dynamics. Nevertheless, biological systems are complex fluids containing the relevant (bio-)chemical compounds (enzymes and microorganisms). These compounds are particles that interact with the surrounding medium and between each other. This contribution deals with thermofluid-dynamical interactions of the relevant particulate (bio-)chemical compounds (enzymes and microorganisms) with the surrounding fluid. By consideration of characteristic time and length scales and particle forces, the motion of the (bio-)chemical compounds is characterized.     

An analytical formula for pricing m-th to default swaps

The computational effort of pricing an m-th to default swap depends highly on the size n of the underlying basket. Usually, n different default times are modeled, but in fact the valuation only depends on the m-th smallest default time of this tuple. In this paper we attain an analytical formula for the distribution of this m-th default time. With the help of this distribution we simplify the valuation problem from an n-dimensional quadrature to a one-dimensional quadrature and break the curse of dimensionality. Applications of this modification are efficient pricing of m-th to default swaps, estimation of sensitivities and pricing of European max/min options.     

Central extensions of semidirect products and geodesic equations

We express the equation for stratified fluid and the superconductivity equation as geodesic equations on Lie group central extensions of semidirect products. We study the existence of stream functions.     

Numerical calculation of the tangent stiffness matrix in materials modeling

The Finite Element Method in the field of materials modeling is closely connected to the tangent stiffness matrix of the constitutive law. This so called Jacobian matrix is required at each time increment and describes the local material behavior. It assigns a stress increment to a strain increment and is of fundamental importance for the numerical determination of the equilibrium state. For increasingly sophisticated material models the tangent stiffness matrix can be derived analytically only with great effort, if at all. Numerical methods are therefore widely used for its calculation. We present our method to calculate the tangent stiffness matrix for the logarithmic strain measure. The approach is compared with other commonly used procedures. A significant increase in accuracy can be achieved with the proposed method. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An improved mixed finite element based on a modified least-squares formulation for hyperelasticity

The present work deals with the solution of geometrically nonlinear elastic problems solved by the least-squares finite element method (LSFEM). The main goal is to obtain an improved performance and an accurate approximation in particular for lower-order elements. Basis for the mixed element is a first-order stress-displacement formulation resulting from a classical least-squares method. Similar to the ideas in SCHWARZ ET AL. [1] a modified weak form is derived by the introduction of an additional term controlling the stress symmetry condition. The approximation of the unknowns follows the same procedures as for a conventional least-squares method, see e.g. CAI & STARKE [2]. The proposed modified formulation is compared to recently developed classical LSFEMs, in order to show the improvement of performance and accuracy. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical Simulation of Bubbles in Shear Flow

To gain a basic understanding of foam flow, as it can be found e.g. in transport of aerated food, simulation tools can help to provide better insight. Shearing of the bubbles appears in different flow geometries and is for a bubble assembly not captured analytically. Also experimentally, those flow fields are hard to observe so that simulations are the method of choice. Our method to simulate foams uses a volume of fluid approach that is based on the free surface algorithm by Körner et al. [1]. Different from classical multiphase methods, only the liquid phase is simulated and special boundary conditions at the liquid-gas interface account for the gas phase. With this approach high density ratios, e.g. in water-air systems, are easier to realize than in other methods. High density ratios are even necessary to physically justify the model, where the dynamics of the lighter phase are partially neglected. This method is integrated in the Lattice Boltzmann software framework waLBerla [3] (widely applicable Lattice Boltzmann solver from Erlangen†) that can be used on massively parallel computers and thus allows to simulate even large bubble assemblies. As first validation, single bubbles are sheared with different capillary numbers and the simulation results are compared to literature [2] and show good agreement. The next step is shearing a bubble assembly which is arranged like a dense sphere packing. In order to investigate the geometrical configuration of the assembly and its impact on the behavior during a shear deformation, the bubble assembly is rotated with different angles with respect to the shear direction. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Density functional theory study with and without COSMO of H2SO4 reactions in an aqueous environment for metal extraction

In a recent study investigating the suitability of solvent extraction (SX) for the separation of Ta and Nb, it was shown that speciation data would be required to help explain the data obtained. As traditional speciation techniques cannot be readily applied for Ta and Nb, it was decided to determine the suitability of molecular modeling for this purpose. During the SX experiments the aqueous phase consisted of sulfuric acid (H₂SO₄), water, and metal species. In this study density functional theory (DFT) modeling was used to calculate the formation energy of five possible reactions of H₂SO₄ and H₂O. Different functional and basis set combinations were compared as well as the effect of infinite dilution by using the conductor-like screening model (COSMO), which simulates infinite dilution of solvents of varying polarity and includes the short-range interactions of the solute particles. The results obtained were used to determine whether it is possible to predict the reactions and mechanism when H₂SO₄ and H₂O interact during SX. According to the results, the deprotonation of H₂SO₄ was endothermic in a 1:1 acid–water ratio, while being both exothermic in the 1:5 and 1:10 acid–water ratio forming HSO₄⁻ and SO₄²⁻ respectively. Furthermore, it was seen that the hydration and dehydration of H₂SO₄ in a bulk H₂O solution was a continuous process. From the energy calculations it was determined that although the H₂SO₄●H₂O, HSO₄⁻●H₂O, and H₂SO₄●2H₂O species could form, they would most likely react with H₂O molecules to form HSO₄⁻, H₃O⁺, and H₂O. © 2018 Wiley Periodicals, Inc.     

Review: the multicolored coordination chemistry of violurate anions

This review provides a comprehensive overview on the coordination chemistry of violuric acid, C₄H₃N₃O₄ (= H₃Vio), and its derivatives (e.g. 1,3-diorganovioluric acids and thiovioluric acid). The most remarkable property of these colorless compounds is the formation of brightly colored (pantochromic/polychromic) salts with colorless cations such as alkali metal and alkaline earth metal ions and organoammonium ions. These magnificent colors have fascinated chemists for more than a century. Only in recent years it has been fully recognized that the structural chemistry of violurates is rather interesting and diverse. Violurate anions are excellent building blocks for new supramolecular assemblies in the crystalline state. Various organoammonium violurates and transition metal violurate complexes have been structurally characterized through single-crystal X-ray diffraction. Highly characteristic for these structures is the formation of 1D, 2D, or 3D hydrogen-bonded assemblies in the crystalline state. This review provides a comprehensive overview on the multicolored coordination chemistry of violurate anions, with the focus being on structurally characterized species.     

Tenfold Metalation of Ferrocene: Synthesis,Structures, and Metallophilic Interactions in FeC10(HgX)10

The permercuration of ferrocene was achieved by reacting ferrocene with 10 equivalents of mercury(II) butyrate Hg(O₂CC₃H₇)₂ in a facile one-pot reaction in multi-gram scale and high yields. The butyrate groups in FeC₁₀(HgX)₁₀ (X=O₂CC₃H₇) can be exchanged by treatment with trifluoro- or trichloroacetic acid (X=O₂CCF₃, O₂CCCl₃). Substitution of the trifluoroacetate groups by halides (X=Cl, F) proceeds easily in aqueous THF. The completeness of metalation was confirmed by NMR and vibrational spectroscopy, mass spectrometry, as well as elemental analysis. Additionally, the first crystal structures of permetallated metallocenes are presented: FeC₁₀(HgX)₁₀ (X=Cl, O₂CCF₃, O₂CCCl₃).