Two phase flow through vertical capillaries—existence of a stratified flow pattern

Two phase downflows were investigated in vertical capillaries with internal diameters in the range 0.5–7.1 mm. Flow pattern regime maps were developed for water-air, distillate-air and water-distillate systems. Over the range of flowrates studied, stratified flow was found to occur in the smaller diameter ($\text{<3}\text{mm}$) capillaries where interfacial tension forces dominate. A modified Hagen-Poiseuille model, which incorporated surface tension effects and which employed the concept of an effective hydraulic diameter, was developed for each of the phases. These equations were used to predict pressure drop and holdup for laminar flow of the two phases in the capillaries. Comparison of pressure drop predictions and measurements gave an RMS error of 14% for the water-distillate system and 8% for the water-air system.     

On the Wronskian combinants of binary forms

Given a sequence A=(A₁,…,A_r) of binary d-ics, we construct a set of combinants C={C_q:0≤q≤r,q≠1}, to be called the Wronskian combinants of A. We show that the span of A can be recovered from C as the solution space of an SL(2)-invariant differential equation. The Wronskian combinants define a projective imbedding of the Grassmannian G(r,S_d), and, as a corollary, any other combinant of A is expressible as a compound transvectant in C.Our main result characterises those sequences of binary forms that can arise as Wronskian combinants; namely, they are the ones such that the associated differential equation has the maximal number of linearly independent polynomial solutions. Along the way we deduce some identities which relate Wronskians to transvectants. We also calculate compound transvectant formulae for C in the case r=3.     

De novo synthesis of 2,2-bis(dimethylamino)-3-alkyl or benzyl 2,3-dihydroquinazolin-4(1H)-one compounds

A new versatile and efficient strategy for the synthesis of 2,2-bis(dimethylamino)-3-alkyl or benzyl 2,3-dihydroquinazoline-4(1H)-one compounds has been developed by one-pot multicomponent reaction with isatoic anhydride, amines followed by in situ-generated Vilsmeier reagent. The reaction has also been studied with different amines and solvents.     

Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, here methods were developed to model several important surface formulations using exact surface discretizations. Following and refining Zauhar's work [J. Comput.-Aided Mol. Des. 9, 149 (1995)], two classes of curved elements were defined that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. Numerical integration techniques are presented that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, a set of calculations are presented that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planar-triangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute-solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that the methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online as supplemental material.     

Synthesis of planar poly(p-phenylene) derivatives for maximization of extended π-conjugation

Described is the synthesis of a ladder polymer with a poly(p-phenylene) (PPP) backbone. The main PPP backbone was synthesized via palladium-catalyzed coupling of an arylbis(boronic ester) with an aryl dibromide. Imine bridges, formed by exposure of the polymer to trifluoroacetic acid, are used to force the consecutive units into planarity. The bridging units are sp² hybridized thus allowing for greater π-electron flow between the consecutive phenyl units by lowering the band gap between the hydroquinoidal and the quinoidal forms of the phenylene backbone. When the bridges are n-dodecyl substituted, the fully planar structures (with Mn < 5 000) are soluble in hot chlorobenzene from which flexible free standing films can be cast. The n-butyl substituted polymers and the higher molecular weight n-dodecyl substituted polymers are soluble in CH₂Cl₂/trifluoroacetic acid mixtures. The optical spectra of the planar systems are compared to that of the parent nonplanarized polymers, some analogous planar oligomers, and oligo(p-phenylenes).