Simulations of thixotropic liquids

In thixotropic liquids the rheological properties depend on the liquid’s deformation history. Clay suspensions (as encountered in oil sands mining) are a prominent example. Activated clay particles form a network. As a consequence of (ionic) transport limitations, the network is not an instantaneous feature; it takes time to build up, and also to break down, the latter as a result of deformation in the liquid. In this paper a procedure for detailed simulations of flow of viscous thixotropic liquids is outlined. The local viscosity of the liquid relates to the level of integrity of the network. The time-dependence of the liquid’s rheology is due to the finite rate with which the network in the liquid builds up or breaks down. This concept has been incorporated in a lattice-Boltzmann discretization of the flow equations. With this methodology the way thixotropic liquids are mobilized in mixing tanks and the drag force experienced by dense assemblies of coarse particles (e.g. sand) in thixotropic liquids have been studied.     

Confined and Agitated Swirling Flows with Applications in Chemical Engineering

Turbulent, swirling flows are encountered frequently in chemical engineering practice. In this article, experiments and simulations on two classes of swirling flows, viz. agitated flows (stirred tanks), and confined swirling flows are discussed. Results of large-eddy simulations of stirred tank flow are compared with experimental data, mainly phase-resolved LDA data of the flow in the vicinity of the impeller. Next to the average velocity field, also the turbulent kinetic energy, and the anisotropy of the Reynolds stress tensor have been assessed. An important application of confined swirling flow is the cyclone separator (hydrocyclones for the separation of liquids, gas cyclones for gas-solid separation). The flow in a swirl tube geometry exhibiting many of the typical features of swirl flows (e.g. vortex breakdown) is discussed. Furthermore, a large-eddy simulation of the gas flow in a high-efficiency Stairmand cyclone separator is presented. Two examples of process modeling based on flow simulations are briefly treated: orthokinetic agglomeration of crystals in a stirred tank, and particle separation in a cyclone. This revised version was published online in July 2006 with corrections to the Cover Date.     

Synthesis of Functional Polymers by Post‐Polymerization Modification

Post‐polymerization modification is based on the direct polymerization or copolymerization of monomers bearing chemoselective handles that are inert towards the polymerization conditions but can be quantitatively converted in a subsequent step into a broad range of other functional groups. The success of this method is based on the excellent conversions achievable under mild conditions, the excellent functional‐group tolerance, and the orthogonality of the post‐polymerization modification reactions. This Review surveys different classes of reactive polymer precursors bearing chemoselective handles and discusses issues related to the preparation of these reactive polymers by direct polymerization of appropriately functionalized monomers as well as the post‐polymerization modification of these precursors into functional polymers.     

The Order Completion Method for Systems of Nonlinear PDEs Revisited

In this paper we presents further developments regarding the enrichment of the basic Theory of Order Completion as presented in Oberguggenberger and Rosinger (Solution of continuous nonlinear PDEs through order completion, North-Holland, Amsterdam, 1994). In particular, spaces of generalized functions are constructed that contain generalized solutions to a large class of systems of continuous, nonlinear PDEs. In terms of the existence and uniqueness results previously obtained for such systems of equations (van der Walt, Acta Appl. Math. 103:1–17, 2008), one may interpret the existence of generalized solutions presented here as a regularity result. Furthermore, it is indicated how the methods developed in this paper may be adapted to solve initial and/or boundary value problems. In particular, we consider the Navier-Stokes equations in three spacial dimensions, subject to an initial condition on the velocity. In this regard, we obtain the existence of a generalized solution to a large class of such initial value problems.      

The synthesis,interfacial, and colloidal properties of waterborne cationic methacrylic co-polymers

Two cationic polymers with similar composition were prepared by two different polymerization methods. By monitoring the evolution of the molar mass and chemical composition during the reactions together with charge density measurements and calculations, it was concluded that the cationic polymer synthesized by emulsion polymerization had a less uniform compositional distribution than the cationic polymer prepared by solution polymerization. Contributing to the heterogeneity was the hydrolysis of one monomer (dimethylamino ethylmethacrylate (DMAEMA)) during the synthesis. As a result, the polymer prepared by emulsion polymerization had a more blocky structure and was more surface active as supported by static and dynamic surface tensions data. Fluorescence experiments showed that both polymers formed aggregates at very low concentrations of approximately 0.01 wt%. The aggregates of the polymer prepared by emulsion polymerization were compact, whereas the solution polymerization-based polymer aggregates exhibited a rather expanded geometry.     

Microextraction of Reseda luteola-Dyed Wool and Qualitative Analysis of Its Flavones by UHPLC-UV,NMR and MS

Detailed knowledge on natural dyes is important for agronomy and quality control as well as the fastness, stability, and analysis of dyed textiles. Weld (Reseda luteola L.), which is a source of flavone-based yellow dye, is the focus of this study. One aim was to reduce the required amount of dyed textile to ≤50 μg for a successful chromatographic analysis. The second aim was to unambiguously confirm the identity of all weld flavones. By carrying out the extraction of 50 μg dyed wool with 25 μL of solvent and analysis by reversed-phase UHPLC at 345 nm, reproducible chromatographic fingerprints could be obtained with good signal to noise ratios. Ten baseline separated peaks with relative areas ≥1% were separated in 6 min. Through repeated polyamide column chromatography and prepHPLC, the compounds corresponding with the fingerprint peaks were purified from dried weld. Each was unequivocally identified, including the position and configuration of attached sugars, by means of 1D and 2D NMR and high-resolution MS. Apigenin-4′-O-glucoside and luteolin-4′-O-glucoside were additionally identified as two trace flavones co-eluting with other flavone glucosides, the former for the first time in weld. The microextraction might be extended to other used dye plants, thus reducing the required amount of precious historical textiles.     

The Order Completion Method for Systems of Nonlinear PDEs: Pseudo-topological Perspectives

By setting up appropriate uniform convergence structures, we are able to reformulate the Order Completion Method of Oberguggenberger and Rosinger in a setting that more closely resembles the usual topological constructions for solving PDEs. As an application, we obtain existence and uniqueness results for the solutions of arbitrary continuous, nonlinear PDEs.      

Degree bounds for syzygies of invariants

Suppose that G is a linearly reductive group. Good degree bounds for generators of invariant rings were given in (Proc. Amer. Math. Soc. 129 (4) (2001) 955). Here we study minimal free resolutions of invariant rings. For finite linearly reductive groups G it was recently shown in (Adv. Math. 156 (1) (2000) 23, Electron Res. Announc. Amer. Math. Soc. 7 (2001) 5, Adv. Math. 172 (2002) 151) that rings of invariants are generated in degree at most the group order |G|. In characteristic 0 this degree bound is a classical result by Emmy Noether (see Math. Ann. 77 (1916) 89). Given an invariant ring of a finite linearly reductive group G, we prove that the ideal of relations of a minimal set of generators is generated in degree at most ?2|G|.