Shape Factor Correlations of Hydraulic Conductance in Noncircular Capillaries

In Part I of this paper, we introduced the Mason-Morrow shape factor and the corner half-angles to capture the part of geometry of angular capillaries essential in pore network calculations of single- and two-phase flow in drainage and imbibition. We then used this shape factor to obtain simple expressions for the hydraulic conductance in single-phase flow through triangular, rectangular, and oval capillaries. In Part II, we study two-phase fluid flow along angular capillaries. The nonwetting fluid occupies the central part of the capillary, whereas the wetting liquid fills the corners. First, we verify the numerical solution obtained by Ransohoff-Radke for concave corner menisci by using a high-resolution finite element method with zero and infinite surface shear viscosity. We present new numerical results for corner flow domains bounded by convex menisci, i.e., for pinned contact lines and forced imbibition. We also present numerical solutions for two-phase flow with momentum transfer across the interface. We introduce a dimensionless hydraulic conductance of wetting fluid in the corners and correlate it with the corner filament shape factor, corner half-angle, and contact angle. By appropriate scaling, we obtain an accurate universal curve for flow conductance in the corners of an arbitrary angular capillary and for arbitrary contact angles. We give error estimates of the Ransohoff-Radke flow resistance factors, of the Zhou et al. analytical expressions for the resistance factors, and of our universal curves for the hydraulic conductance with no-slip and perfect-slip boundary conditions at the interface. Our expressions for the hydraulic conductance in corner flow of wetting liquid not only are valid for both concave and convex fluid interfaces but also are more accurate than any other published correlation. Copyright 2001 Academic Press.     

Higher integrability of minimizing Young measures

We prove local higher integrability with large exponents for minimizers and Young measure minimizers of variational integrals of the form where F is a Carathéodory integrand that resembles the p-Dirichlet integrand at infinity. The result yields existence of minimizing sequences with higher equi-integrability properties locally in .Received: 5 April 2003, Accepted: 2 February 2004, Published online: 16 July 2004Mathematics Subject Classification (2000): 26B15,74N15Jan Kristensen: GD was supported by NSF through grant DMS0104118, and both authors were partially supported by EPSRC grant GR/R25002.     

Synthesis and binding studies of 2-arylapomorphines

From codeine, four different 2-aryl substituted apomorphines were synthesised in 6 steps each. Oxidation of codeine with IBX followed by acid catalysed rearrangement gave morphothebaine, which was selectively triflylated at the 2-position and subsequently O-acetylated at the 11-position. The resulting triflate was coupled in a Suzuki-Miyaura type reaction with a series of 4-substituted arylboronic esters which, after deprotection, gave the desired 2-aryl apomorphines. The analogues were tested for affinity towards a range of dopaminergic, serotonergic and adrenergic receptors. 2-(4-Hydroxyphenyl)-apomorphine exhibited high affinity for the dopamine D2 receptor. A putative ligand-receptor interaction was put forward.     

Non-differentiable functionals and singular sets of minima

We provide bounds for the Hausdorff dimension of the singular set of minima of functionals of the type ${\int }_{\Omega }F(x\text{,}v\text{,}Dv)$, where F is only Hölder continuous with respect to the variables $(x\text{,}v)$. To cite this article: J. Kristensen, G. Mingione, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

X-ray crystal structure, Raman spectroscopy, and Ab initio density functional theory calculations on 1,1,3,3-tetramethylguanidinium bromide

The salt 1,1,3,3-tetramethylguanidinium bromide, [((CH(3))(2)N)(2)C═NH(2)](+)Br(-) or [tmgH]Br, was found to melt at 135(5) °C, forming what may be referred to as a moderate temperature ionic liquid. The chemistry was studied and compared with the corresponding chloride compound. We present X-ray diffraction and Raman evidence to show that also the bromide salt contains dimeric ion pair "molecules" in the crystalline state and probably also in the liquid state. The structure of [tmgH]Br determined at 120(2) K was found to be monoclinic, space group P2(1)/n, with a = 7.2072(14), b = 13.335(3), c = 9.378(2) ?, β =104.31(3)°, Z = 2, based on 11769 reflections, measured from θ = 2.71-28.00° on a small colorless needle crystal. Raman and IR spectra are presented and assigned. When heated, both the chloride and the bromide salts form vapor phases. The Raman spectra of the vapors are surprisingly alike, showing, for example, a characteristic strong band at 2229 cm(-1). This band was interpreted by some of us to show that the [tmgH]Cl gas phase should consist of monomeric ion pair "molecules" held together by a single N-H(+)···Cl(-) hydrogen bond, the stretching vibration of which should be causing the band, based on ab initio molecular orbital density functional theory type calculations. It is not likely that both the bromide and chloride should have identical spectra. As explanation, the formation of 1,1-dimethylcyanamide gas is proposed, by decomposition of [tmgH]X leaving dimethylammonium halogenide (X = Cl, Br). The Raman spectra of all gas phases were quite identical and fitted the calculated spectrum of dimethylcyanamide. It is concluded that monomeric ion pair "molecules" held together by single N-H(+)···X(-) hydrogen bonds probably do not exist in the vapor phase over the solids at about 200-230 °C.     

Total synthesis of ascididemin via anionic cascade ring closure

A new and convergent synthesis of ascididemin is presented. Using an anionic cascade ring closure as the key step, this natural product is obtained in 45% overall yield in just 6 steps starting from 2'-fluoroacetophenone. This new approach was extended to the synthesis of a new isomer of ascididemin.