Numerical methods for the simulation of a coalescence-driven droplet size distribution

The droplet size distribution in a turbulent flow field is considered and modeled by means of a population balance system. This paper studies different numerical methods for the 4D population balance equation and their impact on an output of interest, the time-space-averaged droplet size distribution at the outlet, which is known from experiments. These methods include different interpolations of the experimental data at the inlet, various discretizations in time and space, and different schemes for computing the coalescence integrals. It will be shown that noticeable changes in the output of interest might occur. In addition, the computational efficiency of the studied methods is discussed.     

High‐molecular‐weight symmetrical multiblock copolymers: Synthesis by RAFT polymerization and characterization

High‐molecular‐weight (MW) symmetrical multiblock copolymers, based on the hydrophobic monomers styrene (Sty) and methyl methacrylate (MMA), and the more polar monomer, 2‐vinyl pyridine (2VPy), were prepared using stepwise reversible addition‐fragmentation chain transfer polymerization. All copolymers shared a common poly(ethylene glycol) (PEG) midblock, introduced as a bifunctional macromolecular chain transfer agent. In total, five ABA triblock copolymers, five ABCBA pentablock terpolymers, and two ABCDCBA heptablock quaterpolymers (comprising four different monomer types) were synthesized. The MWs of the multiblock polymers were determined using gel permeation chromatography (GPC) and proton nuclear magnetic resonance (¹H NMR) spectroscopy, with the latter values being closer to the theoretically expected, whereas GPC MW distributions were relatively narrow, broadening with the number of blocks. The compositions of the synthesized polymers, as determined by ¹H NMR spectroscopy, were also close to the expected values. Finally, films cast from chloroform solutions of the pentablock terpolymers P2VPy‐b‐PSty‐b‐PEG‐b‐PSty‐b‐P2VPy, PSty‐b‐PMMA‐b‐PEG‐b‐PMMA‐b‐PSty, and P2VPy‐b‐PMMA‐b‐PEG‐b‐PMMA‐b‐P2VPy examined using transmission electron microscopy exhibited PSty and PMMA cylinders (first two) and lamellae (third terpolymer). © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4957–4965     

An algebraic variational multiscale–multigrid method for large-eddy simulation of turbulent variable-density flow at low Mach number

An algebraic variational multiscale–multigrid method is proposed for large-eddy simulation of turbulent variable-density flow at low Mach number. Scale-separating operators generated by level-transfer operators from plain aggregation algebraic multigrid methods enable the application of modeling terms to selected scale groups (here, the smaller of the resolved scales) in a purely algebraic way. Thus, for scale separation, no additional discretization besides the basic one is required, in contrast to earlier approaches based on geometric multigrid methods. The proposed method is thoroughly validated via three numerical test cases of increasing complexity: a Rayleigh–Taylor instability, turbulent channel flow with a heated and a cooled wall, and turbulent flow past a backward-facing step with heating. Results obtained with the algebraic variational multiscale–multigrid method are compared to results obtained with residual-based variational multiscale methods as well as reference results from direct numerical simulation, experiments and LES published elsewhere. Particularly, mean and various second-order velocity and temperature results obtained for turbulent channel flow with a heated and a cooled wall indicate the higher prediction quality achievable when adding a small-scale subgrid-viscosity term within the algebraic multigrid framework instead of residual-based terms accounting for the subgrid-scale part of the non-linear convective term.     

Reactivity of a Cyclopentadienyl Containing Heterobimetallic Alkoxide

The synthesis of the new heteroleptic heterotrimetallic cluster, [(C₅H₅)Sn(μ-OBu^t)₂Ge(OBu^t)Mo(CO)₅] (1) has been achieved by a thermally induced CO substitution of the transition metal derivative, Mo(CO)₆, by the basic germanium atom of the cyclopentadienyl heterobimetallic alkoxide, [(C₅H₅)Sn(μ-OBu^t)₂Ge(OBu^t)]. The microanalysis, molecular weight (monomer in benzene), IR and multinuclear NMR data and X-ray diffraction study is consistent with the formulation of 1. The Sn atom has a trigonal pyramidal coordination environment formed by a aysmmterically π-bonded terminal C₅H₅ ring and two symmetrically bridged tert-butoxy groups. The four-coordinate Ge atom lies at the centre of a distorted tetrahedron and is terminally attached to a tert-butoxy group and a Mo(CO)₅5^? fragment.     

Vertical Electronic Spectra of the Isovalent Molecules H2CNH,H2SiNH,H2CPH and H2SiPH on the Basis of MRD-CI Calculations

Abstract

Large-scale multi-reference single and double-excitation configuration interaction (MRD-CI) calculations are employed for the study of the isovalent compounds H₂CNH, HLSiNH, hLCPH and H₂SiPH in their ground state equilibrium geometry. The dipole moments and charge distributions are given. The vertical excitation energies to the intravalence states ^3,1 (n, π*) and ^3,1(π,π*) and to the first members of the Rydberg series originating from n and - MO's respectively are predicted; the first two ionization potentials and the Rydberg term values are also calculated. In H₂CNH, mixing of Rydberg and valence-shell states with CN stretching is analyzed. The trends in relative stability of electronic and ionized states can be directly related to increased orbital stability of n relative to π as soon as a first-row constituent is replaced by a second-row atom. The calculations explain the diffuse character of the uv spectrum of imines; they treat the molecules H₂SiNH and H₂SiPH for the first time and present a large number of data for all four molecules which can serve as a basis for future experimental investigations on these and related compounds.