Modeling Geometric State for Fluids in Porous Media: Evolution of the Euler Characteristic

Multiphase flow in porous media is strongly influenced by the pore-scale arrangement of fluids. Reservoir-scale constitutive relationships capture these effects in a phenomenological way, relying only on fluid saturation to characterize the macroscopic behavior. Working toward a more rigorous framework, we make use of the fact that the momentary state of such a system is uniquely characterized by the geometry of the pore-scale fluid distribution. We consider how fluids evolve as they undergo topological changes induced by pore-scale displacement events. Changes to the topology of an object are fundamentally discrete events. We describe how discontinuities arise, characterize the possible topological transformations and analyze the associated source terms based on geometric evolution equations. Geometric evolution is shown to be hierarchical in nature, with a topological source term that constrains how a structure can evolve with time. The challenge associated with predicting topological changes is addressed by constructing a universal geometric state function that predicts the possible states based on a non-dimensional relationship with two degrees of freedom. The approach is validated using fluid configurations from both capillary and viscous regimes in ten different porous media with porosity between 0.10 and 0.38. We show that the non-dimensional relationship is independent of both the material type and flow regime. We demonstrate that the state function can be used to predict history-dependent behavior associated with the evolution of the Euler characteristic during two-fluid flow.

     

The platinum benzole acid blues — a new class of blue platinum compounds

Summary The preparation of platinum blues from Pt(NH₃)₂(H₂O) ₂ ²⁺ and benzoic or phthalic acids is described. The compounds were characterised by e.p.r., u.v./vis. and x-ray photoelectron spectroscopy. Unlike pyrimidine blues, the platinum blues reported here appear to be non-ionic.     

Electrosorptive detection in liquid chromatography of simple charged organic compounds

Summary The applicability of electrosorptive (ES) detection in liquid chromatography to charged organic species, specifically amines, alkanolamines, and alkylsulfonates is demonstrated. Separations can be carried out using ion-pair chromatography, and detection acieved by measuring changes in differential double-layer capacitance (DLC), C_d, brought about by analyte adsorption at potentials either well negative or positive of the potential of zero charge (pzc), depending on whether cationic or anionic forms, respectively, are being determined. The C_d-analyte concentration response curves are linear over a limited range. A welcome feature of the technique is that organic modifiers may be used in the mobile phase without deleterious consequence to the detection. Attempts were also made to detect these charged species as ion pairs by DLC at potentials close to the pzc. This approach, however, appears to have less practical utility.     

Method for enantiomeric purity of a quinuclidine candidate drug by capillary electrophoresis

A chiral procedure based on EKC was developed and validated for determination of the enantiomeric purity of PHA-543613, a drug candidate that was under development for treatment of the cognitive deficits of Alzheimer's disease and schizophrenia. Separation of enantiomers is accomplished via differential, enantiospecific complexation with a single-isomer, precisely sulfated beta-CD and heptakis-6-sulfato-beta-CD (HpS-beta-CD). Both neutral and sulfated CDs were screened before selecting HpS-beta-CD as the chiral selector. The separation is conducted in a 61 cm x 50 microm uncoated fused silica capillary with 25 mM HpS-beta-CD in pH 2.50, 25 mM lithium phosphate as the separation buffer with detection at 220 nm. Application of reverse polarity at -30 kV results in an elution time of about 12 min for PHA-543613 and 13 min for the undesired S-enantiomer. Quantification is versus an authentic reference S-enantiomer as an external standard in combination with an internal standard. The procedure was validated over the range 0.1-2.0% w/w. The detection limit is 0.01-0.02%. The amount of distomer intrinsic to the drug substance is about 0.1% or less. The developed method was used to generate stability data on multiple lots: in one case for up to 3 years.     

A CD-MEKC Method Utilizing a Neutral Surfactant for Enantiomeric Purity Determination of an Oxazolidinone Drug Candidate

A method based on cyclodextrin-mediated micellar electrokinetic chromatography (CD-MEKC) was developed and validated for quantification of the minor, undesired enantiomer (distomer) in the drug candidate PHA-549184, an oxazolidinone that was under development as an antibiotic. The low intrinsic solubility of the compound (0.24 mg mL⁻¹), combined with the poor solution concentration sensitivity of capillary electrophoresis, required extensive method development to enhance the solubility of PHA-549184 while minimally degrading electrophoretic performance. A number of approaches were investigated, including inclusion of neutral and charged cyclodextrins in the background electrolyte (BGE) and addition of both charged and neutral surfactants. The final BGE contains the nonionic surfactant Brij 35: pH 2.5, 18.8 mM lithium phosphate buffer/5% highly sulfated-γ-CD/7.5 mM Brij 35. Quantitation is versus an external standard in the presence of an internal standard. The assay is selective for the distomer and proved linear with a mean recovery of 104.0% over the range 0.25–2.0%. The LOD was 0.1, and the LOQ 0.2%, both slightly higher than customary in chiral analysis, a consequence of an upper bound of 1.5 mg mL⁻¹ placed on the sample concentration in order to maintain high efficiency for the system. Precision examined over the range 0.2–1.0% varied between 3.8% and 8.0%. No batch of drug substance registered above the detection limit for the distomer.     

Electrosorptive detection based on double-layer capacitance for selective anion monitoring in ion chromatography : Part 1. Mercury Electrodes

A novel scheme is presented for the detection of selected anions in ion chromatography, based on changes in differential double-layer capacitance, ΔC_d, for a metal electrode at a suitable electrode potential induced by specific anion adsorption. The detector in this liquid chromatography/double-layer capacitance (LC/DLC) arrangement is a hanging or dropping mercury electrode in a large-volume wall-jet configuration. The anions observed to be detected readily by this approach include chloride, bromide, iodide, azide, thiocyanate, and thiosulfate. The relationship between ΔC_d and the analyte concentration can be arranged to be approximately linear at least over the range 1–100 mg l^?1. An attractive feature of the technique is its insensitivity to ionic concentration gradients in the flowing stream. Another virtue of LC/DLC is its selectivity, although it is less sensitive for the detection of complexing anions than amperometric detection based on mercury oxidation. Dual detection schemes are also devised, involving monitoring double-layer capacitance at two potentials or combined with amperometric detection.