Mass Transfer Coefficients in Mixer-Settlers

Mass transfer coefficients have been determined for transfer into a highly viscous phase in a stirred tank involving high Schmidt numbers. The results have been used to compute mass transfer coefficients in the extraction of free fatty acids from oils using alcohol and show good agreement with experimental results

Asymptotic behaviour and boundedness of linear systems with time varying coefficients

Motivated by developments in spacecraft dynamics, the asymptotic behaviour and boundedness of solution of a special class of time varying systems in which each term appears as the sum of a constant and a time varying part, are analysed in this paper. It is not possible to apply standard textbook results to such systems, which are originally in second order. Some of the existing results are reformulated. Four theorems which explore the relations between the asymptotic behaviour/boundedness of the constant coefficient system, obtained by equating the time varying terms to zero, to the corresponding behaviour of the time varying system, are developed. The results show the behaviour of the two systems to be intimately related, provided the solutions of the constant coefficient system approach zero are bounded for large values of time, and the time varying terms are suitably restrained. Two problems are tackled using these theorems.

Mode-dependent dispersion in Raman line shapes: Observation and implications from ultrafast Raman loss spectroscopy

Ultrafast Raman loss spectroscopy (URLS) enables one to obtain the vibrational structural information of molecular systems including fluorescent materials. URLS, a nonlinear process analog to stimulated Raman gain, involves a narrow bandwidth picosecond Raman pump pulse anda femtosecond broadband white light continuum. Under nonresonant condition, the Raman response appears as a negative (loss) signal, whereas, on resonance with the electronic transition the line shape changes from a negative to a positive through a dispersive form. The intensities observed and thus, the Franck-Condon activity (coordinate dependent), are sensitive to the wavelength of the white light corresponding to a particular Raman frequency with respect to the Raman pump pulse wavelength, i.e., there is a mode-dependent response in URLS. (C) 2010 American Institute of Physics.

Fractional quantum Hall edge: Effect of nonlinear dispersion and edge roton

According to Wen's theory, a universal behavior of the fractional quantum Hall edge is expected at sufficiently low energies, where the dispersion of the elementary edge excitation is linear. A microscopic calculation shows that the actual dispersion is indeed linear at low energies, but deviates from linearity beyond certain energy, and also exhibits an "edge roton minimum." We determine the edge exponent from a microscopic approach, and find that the nonlinearity of the dispersion makes a surprisingly small correction to the edge exponent even at energies higher than the roton energy. We explain this insensitivity as arising from the fact that the energy at maximum spectral weight continues to show an almost linear behavior up to fairly high energies. We also study, in an effective-field theory, how interactions modify the exponent for a reconstructed edge with multiple edge modes. Relevance to experiment is discussed.

Dispersion of Zirconia in the Presence of Dolapix PC75

The effect of Dolapix PC75 on the electrokinetic and rheological behavior of nano zirconia particles is presented here. The effect of pH, concentration of dispersant, and solids loading on zeta-potential and rheological behavior was studied. Upon interaction with the dispersant, the iso-electric point of zirconia changed and the surface became more negative with increasing concentration of dispersant, suggesting a strong interaction. Maximum charge was obtained in the presence of about 200ppm of Dolapix. Rheological tests at pH 7 showed that the zirconia suspension is viscous at high solids loading and addition of the dispersant decreased the viscosity substantially especially at high solids loading (50wt%). Sedimentation tests confirmed that Dolapix PC75 is a good dispersant for zirconia particles at pH values of 7 and above.

Investigation of the effect of nonlocal scale on ultrasonic wave dispersion characteristics of a monolayer graphene

In this article, an ultrasonic wave propagation in graphene sheet is studied using nonlocal elasticity theory incorporating small scale effects. The graphene sheet is modeled as an isotropic plate of one-atom thick. For this model, the nonlocal governing differential equations of motion are derived from the minimization of the total potential energy of the entire system. An ultrasonic type of wave propagation model is also derived for the graphene sheet. The nonlocal scale parameter introduces certain band gap region in in-plane and flexural wave modes where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite or wave speed tends to zero. The frequency at which this phenomenon occurs is called the escape frequency. The explicit expressions for cutoff frequencies and escape frequencies are derived. The escape frequencies are mainly introduced because of the nonlocal elasticity. Obviously these frequencies are function of nonlocal scaling parameter. It has also been obtained that these frequencies are independent of y-directional wavenumber. It means that for any type of nanostructure, the escape frequencies are purely a function of nonlocal scaling parameter only. It is also independent of the geometry of the structure. It has been found that the cutoff frequencies are function of nonlocal scaling parameter (e(0)a) and the y-directional wavenumber (k(y)). For a given nanostructure, nonlocal small scale coefficient can be obtained by matching the results from molecular dynamics (MD) simulations and the nonlocal elasticity calculations. At that value of the nonlocal scale coefficient, the waves will propagate in the nanostructure at that cut-off frequency. In the present paper, different values of e(o)a are used. One can get the exact e(0)a for a given graphene sheet by matching the MD simulation results of graphene with the results presented in this paper. (C) 2010 Elsevier B.V. All rights reserved.

Approximate multipole coefficients of RF ion traps as functions of aperture size

In this study we present approximate analytical expressions for estimating the variation in multipole expansion coefficients as a function of the size of the apertures in the electrodes in axially symmetric (3D) and two-dimensional (2D) ion trap ion traps. Following the approach adopted in our earlier studies which focused on the role of apertures to fields within the traps, here too, the analytical expression we develop is a sum of two terms, A(n,noAperiure), the multipole expansion coefficient for a trap with no apertures and A(n,dueToAperture), the multipole expansion coefficient contributed by the aperture. A(n,noAperture) has been obtained numerically and A(n,dueToAperture) is obtained from the n th derivative of the potential within the trap. The expressions derived have been tested on two 3D geometries and two 2D geometries. These include the quadrupole ion trap (QIT) and the cylindrical ion trap (CIT) for 3D geometries and the linear ion trap (LIT) and the rectilinear ion trap (RIT) for the 2D geometries. Multipole expansion coefficients A(2) to A(12), estimated by our analytical expressions, were compared with the values obtained numerically (using the boundary element method) for aperture sizes varying up to 50% of the trap dimension. In all the plots presented, it is observed that our analytical expression for the variation of multipole expansion coefficients versus aperture size closely follows the trend of the numerical evaluations for the range of aperture sizes considered. The maximum relative percentage errors, which provide an estimate of the deviation of our values from those obtained numerically for each multipole expansion coefficient, are seen to be largely in the range of 10-15%. The leading multipole expansion coefficient, A(2), however, is seen to be estimated very well by our expressions, with most values being within 1% of the numerically determined values, with larger deviations seen for the QIT and the LIT for large aperture sizes. (C) 2010 Elsevier B.V. All rights reserved.

Dispersion of resistivity anomalies in critical binary liquid systems

The critical resistivity in the binary liquid systems n-C7H16 + CH3OH and CS2 + CH3NO2 is measured from 10 Hz to 100 kHz. There is no noticeable effect of the frequency on the resistivity singularities. Thus any contribution from dielectric dispersion is not appreciable.

A sufficient criterion for Rayleigh-Taylor instability of incompressible viscous three-layer flow

Using normal mode analysis Rayleigh-Taylor instability is investigated for three-layer viscous stratified incompressible steady flow, when the top 3rd and bottom 1st layers extend up to infinity, the middle layer has a small thickness δ. The wave Reynolds number in the middle layer is assumed to be sufficiently small. A dispersion relation (a seventh degree polynomial in wave frequency ω) valid up to the order of the maximal value of all possible Kj (j less-than-or-equals, slant 0, K is the wave number) in each coefficient of the polynomial is obtained. A sufficient condition for instability is found out for the first time, pursuing a medium wavelength analysis. It depends on ratios (α and β) of the coefficients of viscosity, the thickness of the middle layer δ, surface tension ratio T and wave number K. This is a new analytical criterion for Rayleigh-Taylor instability of three-layer fluids. It recovers the results of the corresponding problem for two-layer fluids. Among the results obtained, it is observed that taking the coefficients of viscosity of 2nd and 3rd layers same can inhibit the effect of surface tension completely. For large wave number K, the thickness of the middle layer should be correspondingly small to keep the domain of dependence of the threshold wave number Kc constant for fixed α, β and T.

Diffusion coefficients for selected binary liquid systems: cyclohexanes and n-alkyl alcohols

In the present work the integral diffusion coefficients are estimated by using the diaphragm cell technique. The diffusion coefficients are measured at various compositions for two sets binary systems: one of cyclohexane and n-paraffinic alcohols and the other of methylcyclohexane and n-paraffinic alcohols. The alcohols used are seven members of homologous series of n-paraffinic alcohols from ethanol to octanol. The maximum possible error in the experimental diffusion coefficient could be 8% for both the cyclohexane-n-alkyl alcohol system and methylcyclohexane-n-alkyl alcohol system. A correlation for each of the two sets of binary systems is given. The maximum deviation in the correlations was less than 6.5 and 3.5% for cyclohexane-n-alkyl alcohols and methylcyclohexane-n-alkyl alcohols, respectively.

Modulus Spectroscopy and Dielectric Dispersion Studies in Alkali Metal Perchlorates

Alkali metal perchlorates (KClO4, RbClO4, and CsClO4) undergo a structural phase transition from the orthorhombic to the cubic phase at elevated temperatures. A detailed dielectric study of these crystals across the phase transition is carried out at different frequencies. The crystals are found to exhibit pronounced dielectric dispersion in the kHz frequency range. The results support the view that these transitions are of order–disorder type. The dielectric behaviour at temperatures above Tc is discussed in terms of modulus spectroscopy. An estimate of conductivity relaxation times above the phase transition temperatures made from modulus spectroscopy data gives values of 3.1, 12.2 and 17.7 μs for KClO4, RbClO4, and CsClO4, respectively.