Zeros of the Whittaker function associated to Coulomb waves

The zeros in the complex z plane of the Whittaker function W_c/z,µ(z),closely related to spherical waves in the quantum-mechanicalCoulomb problem, are investigated for varying real values ofthe parameters c and µ     

Determination of total sulfite in wine. Zone electrophoresis-isotachophoresis quantitation of sulfate on a chip after an in-sample oxidation of total sulfite

This work deals with the determination of total sulfite in wine. The determination combines an in-sample hydrogen peroxide oxidation of total sulfite in alkalized wine to sulfate with the separation and quantitation of the latter anion by zone electrophoresis (ZE) on-line coupled with isotachophoresis (ITP) on a column-coupling chip. Sample clean up, integrated into the ITP-ZE separation, eliminated wine matrix in an extent comparable to that provided by a highly selective distillation isolation of sulfite. At the same time, conductivity detection, employed to the detection of sulfate in the ZE stage of the ITP-ZE combination, provided for sulfate the concentration limit of detection corresponding to a 90 microg/l concentration of sulfite in the loaded sample (0.9 microl). Such a detectability allowed a reproducible quantitation of total sulfite when its concentration in wine was 15 mg/l. Formaldehyde binding of free sulfite in wine, included into the pre-column sample preparation, prevented an uncontrolled oxidation of this sulfite form. This step contributed to an unbiased determination of sulfate present in the original wine sample (this determination corrected for the concentration of sulfate determined in the sample after the peroxide oxidation of sulfite to the value equivalent to the total sulfite). The 99-101% recoveries of sulfite, determined for appropriately spiked wine samples, indicate a very good accuracy of the present method. Such a statement also supports excellent agreements of the results of quantitation based on the in-sample peroxide oxidation of the total sulfite (bound sulfite released at a high pH) with those in which this analyte was isolated from wine by distillation (bound sulfite released at a very low pH).     

An integrated multiphase flow sensor for microchannels

The flow regimes of microscale multiphase flows affect the yield and selectivity of microchemical systems, and the heat transfer properties of micro heat exchangers. We describe an integrated optical sensor that uses total internal reflection to detect the structure of multiphase flows in microchannels. The non-intrusive sensor enables detection of individual slugs, bubbles, or drops, and can be used to continuously determine their number and velocity. The sensor performance is modeled using ray-tracing techniques, and tested for several channel geometries. Both gas-liquid and liquid-liquid flows are investigated in microchannels with rectangular and triangular cross-sections. Statistical properties of the flow, derived from the sensor signal, compare favorably to commonly-used dynamic pressure measurements. We demonstrate the integration of the sensor into a planar multichannel microreactor. An existing glass layer used as a waveguide allows us to monitor flows in optically inaccessible channels. This sensor configuration can be integrated into layers of vertically-stacked multichannel microreactors.

List of symbols

Roman symbols a Radius of largest sphere inscribed in channel [m] - A_ch Channel cross-sectional area [m²] - Ca Capillary number [-] - Critical capillary number [-] - d_h Hydraulic diameter [m] - d_sensor Distance prism surface-sensor origin [m] - E₀ Incident light energy [J] - E_r Emerging light energy [J] - f(t_pass) Probability density function (PDF) of slug dwell times [1/s] - f Focal length [m] - f_slug Slug frequency [Hz] - F(t_pass) Probability distribution of slug dwell times [-] - g(t) Arbitrary function of time [-] - h Liquid film thickness [m] - j_G Superficial gas velocity [m/s] - j_L Superficial liquid velocity [m/s] - l Slug length [m] - N Number of samples [-] - n Refractive index [-] - N_c Number of channel corners [-] - n_i Refractive index of incident medium [-] - n_r Number of reflections [-] - n_t Refractive index of transmitting medium [-] - n_slug Number of slugs [-] - p Gas inlet pressure [Pa] - r Reflectance [-] - R_XX(x,) Autocorrelation function [-] - R_Xp(x,) Cross correlation function [-] - r Slug radius at infinite distance from leading slug tip [m] - s Standard deviation of measured slug dwell times [s] - t Time [s] - t Measurement time interval [s] - t_pass Slug dwell time [s] - U_b Slug (bubble) velocity [m/s] - W Bin size of slug dwell time histogram [-] - x Streamwise coordinate [m] - X(x,t) Phase density function [-] - Y Surface tension of the gas-liquid interface [N/m] - Volumetric gas flow rate [m³/s] - Volumetric liquid flow rate [m³/s] - Volumetric oil flow rate [m³/s] - Volumetric water flow rate [m³/s] - z Normal coordinate [m]Greek symbols Void fraction [-] - _c Critical angle for total internal reflection [^°] - _i Incident angle [^°] - Laser wavelength [m] - µ Liquid viscosity [Pa s] - Normalization factor [-] - _h Dimensionless liquid film thickness [-] - _r Dimensionless radius [-] - _x Dimensionless streamwise position [-] - _r Dimensionless slug radius at infinite distance from leading slug end [-] - Standard deviation of the slug dwell time distribution [s] - Time shift [s] - Contact angle [^°]     

Evaluation of capillary gas chromatography columns for the determination of free volatile amines after solid-phase microextraction

Summary Gas-liquid chromatographic capillary columns coated with 14% diphenyldimethylpolysiloxane, base-deactivated 5% diphenyldimethylpolysiloxane, or poly(ethylene glycol), and deactivated porous polymer for capillary gas-solid chromatography were evaluated for analysis of low-molecular-weight (C₁−C₉) amines. Solid-phase microextraction with a polydimethylsiloxane fiber was used for headspace sampling and for introduction of the sample into the gas chromatograph. As expected, basic of aliphatic gaseous or volatile aliphatic amines (carbon number: C₁−C₄). A thick (e. g. 3 μm) film of 5% diphenyldimethylpolysiloxane enabled determination of analytes in a wider molecular-weight range (C₃−C₉) with acceptable efficiency and resolution.