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.     

ORGANISCHE PHOSPHORVERBINDUNGEN 80 HERSTELLUNG VON TRIAZOLYLMETHYL-PHOSPHONATEN UND VON TRIAZOLYL-METHYLPHOSPHONIUMSALZEN UND DEREN VERWENDUNG IN DER WITTIG-HORNER REAKTION

Abstract

Attempts to prepare 1H-1,2,4-triazol-1-ylmethylphosphonates (4 and 5) by a Mannichtype reaction or by transesterification of 1-hydroxymethyl-1H-1,2,4-triazol 1 with tertiary phosphites failed. On the other hand 4 and 5 are obtained by a Michaelis-Becker reaction from 1-chloromethyl-1H-1,2,4-triazol 3 and sodium phosphites in high yield. The Michaelis-Arbuzov reaction is less suited for the preparation of 4 and 5. 3 is obtained in good yield as a water clear liquid, b.p. 52–54°C/0.2 torr, from the interaction of 1 with thionyl chloride followed by treatment with a base. On standing at 0° or 20°C it decomposes within hours and yields the unsymmetrical methylen-bis(triazol) 3a in addition to other products. However an acetonitrile solution of 3 is stable for months. Heating this solution with tertiary phosphines gives triazolylsubstituted phosphoniumsalts 6 to 8. The Wittig-Horner reaction with 4 to 6 gives the olefinically substituted triazols 9–12 as a Z/E mixture in high yield. Alkylation of 4 with methyl-and ethyl iodide gives the corresponding alkylated diethyl-1H-1,2,4-triazol-1-yl-ethyl-1-and-propyl-1-phosphonates 14 and 15 which on hydrolysis with HCI yield 1H-1,2,4-triazol-1-yl-ethyl-1-and propyl-1-phosphonic acids 17 and 18, respectively. Hydrolysis of 4 gives the unsubstituted 1H-1,2,4-triazol-1-ylmethyl-phosphonic acid, 16.     

Phosphoranylidenephines (R3P=Pr) as Phospha-Wittig Reagents

Abstract

We have recently discovered direct and high yielding routes to phosphoranylidenephosphines ArP=PMe₃ (la, Ar = Dmp; lb, Ar = Mes*, eq. l).¹     

Acid-Catalysed Hydrolysis of Some Aromatic Cyclic Sulfamates

The acid catalysed hydrolysis of some cyclic sulfamates, X-3-(p-tolylsulfonyl)-1,2,3-benzoxathiazole 2,2-dioxides ( 1a , X = Me; 1b , X = H; 1c , X = Cl; 1d , X = NO 2 ) have been studied in concentrated aqueous sulfuric and perchloric acid solutions. Analysis of the data by the Excess Acidity Method, activation parameters, substituent, solvent deuterium isotope effect and order of the catalytic effects of the acids are all in agreement with an A-1 mechanism in the studied range.     

THE STRUCTURE OF myo-INOSITOL HEXAPHOSPHATE IN SOLUTION: 31P N.M.R. INVESTIGATION

Abstract

Changes in the ³¹P n.m.r. spectrum of myo-inositol hexaphosphate at different pH reveal that the conformation of this molecule varies with its degree of protonation. Above pH 12 it has the equatorial structure (Ie), below it has the axial conformation (Ia) which it retains to pH 5 when it reverts to le on the addition of a seventh proton. These changes are explained by strong hydrogen bonding between phosphate groups. There is also evidence that at low pH (2) the molecule again reverts to la.     

Novel,highly polarizable thiophene derivatives for use in nonlinear optical applications

The synthesis of a variety of thiophene-containing materials for use in electro-optic devices requiring highly birefringent materials is reported. The refractive indices were measured with the use of an Abbé refractometer, and from these results the optical anisotropies, polarizabilities and order parameters were determined. The replacement of a phenyl ring by thiophene leads to large enhancements of polarizability. The most significant increases in polarizability anisotropy were observed when the rigid core was a collinear 5,5′-disubstituted-2,2′-dithienyl unit. The changes in the optical properties are discussed in terms of the structural units (thiophene, phenyl, isothiocyanate, nitrile, butylsulfanyl, alkoxy and alkyl moieties) used and their positions with respect to the molecular core.