Linear and nonlinear thermal instability of Newtonian and non-Newtonian fluid saturated porous media

The present work aims to investigate the influence of different aspects, such as non-standard steady solutions, complex fluid rheologies and non-standard porous-channel geometries, on the stability of a Darcy-Bénard system. In order to do so, both linear and nonlinear stability theories are considered. A linear analysis focuses on studying the dynamics of the single disturbance wave present in the system, while its nonlinear counterpart takes into consideration the interactions among the single modes. The scope of the stability analysis is to obtain information regarding the transition from an equilibrium solution to another one, and also information regarding the transition nature and the emergent solution after the transition. The disturbance governing equations are solved analytically, whenever possible, and numerical by considering different approaches. Among other important results, it is found that a cylinder cross-section does not affect the thermal instability threshold, but just the linear pattern selection for dilatant and pseudoplastic fluid saturated porous media. A new rheological model is proposed as a solution for singular issues involving the power-law model. Also, a generalised class of one parameter basic solutions is proposed as an alternative description of the isoflux Darcy--Bénard problem. Its stability is investigated.

Determination Of Tetrakis(hydroxymethyl)phosphonium Sulfate In Commercial Formulations And Cooling Water By Capillary Electrophoresis With Contactless Conductivity Detection.

A novel capillary electrophoresis method using capacitively coupled contactless conductivity detection is proposed for the determination of the biocide tetrakis(hydroxymethyl)phosphonium sulfate. The feasibility of the electrophoretic separation of this biocide was attributed to the formation of an anionic complex between the biocide and borate ions in the background electrolyte. Evidence of this complex formation was provided by (11) B NMR spectroscopy. A linear relationship (R(2) = 0.9990) between the peak area of the complex and the biocide concentration (50-900 μmol/L) was found. The limit of detection and limit of quantification were 15.0 and 50.1 μmol/L, respectively. The proposed method was applied to the determination of tetrakis(hydroxymethyl)phosphonium sulfate in commercial formulations, and the results were in good agreement with those obtained by the standard iodometric titration method. The method was also evaluated for the analysis of tap water and cooling water samples treated with the biocide. The results of the recovery tests at three concentration levels (300, 400, and 600 μmol/L) varied from 75 to 99%, with a relative standard deviation no higher than 9%.

GLOBAL WELL-POSEDNESS AND NON-LINEAR STABILITY OF PERIODIC TRAVELING WAVES FOR A SCHRODINGER-BENJAMIN-ONO SYSTEM

The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow (namely, a Schrodinger-Benjamin-Ono system) for low-regularity initial data in both periodic and continuous cases; secondly, a family of new periodic traveling waves for the Schrodinger-Benjamin-Ono system is given: by fixing a minimal period we obtain, via the implicit function theorem, a smooth branch of periodic solutions bifurcating a Jacobian elliptic function called dnoidal, and, moreover, we prove that all these periodic traveling waves are nonlinearly stable by perturbations with the same wavelength.

Ionic mobility of the solvated proton and acid-base titration in a four-compartment capillary electrophoresis system

Although H(+) and OH(-) are the most common ions in aqueous media, they are not usually observable in capillary electrophoresis (CE) experiments, because of the extensive use of buffer solutions as the background electrolyte. In the present work, we introduce CE equipment designed to allow the determination of such ions in a similar fashion as any other ion. Basically, it consists of a four-compartment piece of equipment for electrolysis-separated experiments (D. P. de Jesus et at, Anal. Chem., 2005, 77, 607). In such a system, the ends of the capillary are placed in two reservoirs, which are connected to two other reservoirs through electrolyte-filled tubes. The electrodes of the high-voltage power source are positioned in these reservoirs. Thus, the electrolysis products are kept away from the inputs of the capillary. The detection was provided by two capacitively coupled contactless conductivity detectors (CD), each one positioned about 11 cm from the end of the capillary. Two applications were demonstrated: titration-like procedures for nanolitre samples and mobility measurements. Strong and weak acids (pK(a) < 5), pure or mixtures, could be titrated. The analytical curve is linear from 50 mu M up to 10 mM of total dissociable hydrogen (r = 0.99899 for n =10) in 10-nL samples. By including D(2)O in the running electrolyte, we could demonstrate how to measure the mixed proton/deuteron mobility. When H(2)O/D(2)O (9 : 1 v/v) was used as the solvent, the mobility was 289.6 +/- 0.5 x 10(-5) cm(2) V(-1) s(-1). Due to the fast conversion of the species, this value is related to the overall behaviour of all isotopologues and isotopomers of the Zundel and Eigen structures, as well as the Stokesian mobility of proton and deuteron. The effect of neutral (o-phenanthroline) and negatively charged (chloroacetate) bases and aprotic solvent (DMSO) over the H(+) mobility was also demonstrated.

Capillary electrophoresis method for plasmatic determination of imatinib mesylate in chronic myeloid leukemia patients

Imatinib (IMAT) is a tyrosine kinase inhibitor that has been used for the treatment of chronic myeloid leukemia (CML). Despite the efficacy of IMAT therapy, some cases of treatment resistance have been described in CML. Developing a plasma method is important since there are several studies that provided a higher correlation between IMAT plasma concentration and response to treatment. Therefore, in this investigation we validated a method by CE as an alternative, new, simple and fast electrophoretic method for IMAT determination in human plasma. The analysis was performed using a fused silica capillary (50 mm id x 46.5 cm total length, 38.0 cm effective length); 50 mmol/L sodium phosphate buffer, pH 2.5, as BGE; hydrodynamic injection time of 20 s (50 mbar); voltage of 30 kV; capillary temperature of 35 degrees C and detection at 200 nm. Plasma samples pre-treatment involved liquid-liquid extraction with methyl-tert-butyl ether as the extracting solvent. The method was linear from 0.125 to 5.00 mg/mL. The LOQ was 0.125 mg/mL. Mean absolute recovery of IMAT was 67%. The method showed to be precise and accurate with RSD and relative error values lower than 15%. Furthermore, the application of the method was performed in the analysis of plasma samples from CML patients undergoing treatment with IMAT.

Modulational Instability in Periodic Quadratic Nonlinear Materials

We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never completely removes the instability. The low-frequency part of the gain spectrum is accurately predicted by an averaged theory and disappears for certain gratings. The high-frequency part is related to the inherent gain of the homogeneous non-phase-matched material and is a consistent spectral feature.

Theoretical and numerical analyses of convective instability in porous media with upward throughflow

Exact analytical solutions have been obtained for a hydrothermal system consisting of a horizontal porous layer with upward throughflow. The boundary conditions considered are constant temperature, constant pressure at the top, and constant vertical temperature gradient, constant Darcy velocity at the bottom of the layer. After deriving the exact analytical solutions, we examine the stability of the solutions using linear stability theory and the Galerkin method. It has been found that the exact solutions for such a hydrothermal system become unstable when the Rayleigh number of the system is equal to or greater than the corresponding critical Rayleigh number. For small and moderate Peclet numbers (Pe less than or equal to 6), an increase in upward throughflow destabilizes the convective flow in the horizontal layer. To confirm these findings, the finite element method with the progressive asymptotic approach procedure is used to compute the convective cells in such a hydrothermal system. Copyright (C) 1999 John Wiley & Sons, Ltd.

Determination of fluoxetine and norfluoxetine enantiomers in human plasma by polypyrrole-coated capillary in-tube solid-phase microextraction coupled with liquid chromatography-fluorescence detection

A sensitive, selective, and reproducible in-tube polypyrrole-coated capillary (PPY) solid-phase microextraction and liquid chromatographic method for fluoxetine and norfluoxetine enantiomers analysis in plasma samples has been developed, validated, and further applied to the analysis of plasma samples from elderly patients undergoing therapy with antidepressants. Important factors in the optimization of in-tube SPME efficiency are discussed, including the sample draw/eject volume, draw/eject cycle number, draw/eject flow-rate, sample pH, and influence of plasma proteins. Separation of the analytes was achieved with a Chiralcel OD-R column and a mobile phase consisting of potassium hexafluorophosphate 7.5 mM and sodium phosphate 0.25 M solution, pH 3.0, and acetonitrile (75:25, v/v) in the isocratic mode, at a flow rate of 1.0 mL/min. Detection was carried out by fluorescence absorbance at Ex/Em 230/290 nm. The multifunctional porous surface structure of the PPY-coated film provided high precision and accuracy for enantiomers. Compared with other commercial capillaries, PPY-coated capillary showed better extraction efficiency for all the analytes. The quantification limits of the proposed method were 10 ng/mL for R- and S-fluoxetine, and 15 ng/mL for R- and S-norfluoxetine, with a coefficient of variation lower than 13%. The response of the method for enantiomers is linear over a dynamic range, from the limit of quantification to 700ng/mL, with correlation coefficients higher than 0.9940. The in-tube SPME/LC method can therefore be successfully used to analyze plasma samples from ageing patients undergoing therapy with fluoxetine. (C) 2009 Elsevier B.V. All rights reserved.

Proliferation, apoptosis, and survival in high-level microsatellite instability sporadic colorectal cancer

Sporadic colorectal cancer (CRC) characterized by high-level DNA microsatellite instability (MSI-H) has a favorable prognosis. The reason for this MSI-H survival advantage is not known. The aim of this study was to correlate proliferation, apoptosis, and prognosis in CRC stratified by MSI status. The proliferative index (PI) was measured by immunohistochemical staining with the Ki-67 antibody in a selected series of 100 sporadic colorectal cancers classified according to the level of MSI as 31 MSI-H, 29 MSI-Low (MSI-L), and 40 microsatellite stable (MISS). The Ki-67 index was significantly higher in MSI-H cancers (P < 0.0001) in which the PI was 90.1 1.2% (mean +/- SE) compared with 69.5 +/- 3.1 % and 69.5 +/- 2.3 % in MSI-L and MSS subgroups, respectively. There was a positive linear correlation between the apoptotic index (AI) and PI (r = 0.51; P < 0.001), with MSI-H cancers demonstrating an increased AI:PI ratio indicative of a lower index of cell production. A high PI showed a trend toward predicting improved survival within MSI-H cancers (P = 0.09) but did not predict survival in MSI-L or MSS cancers. The Al was not associated with survival in any MSI subgroup. In conclusion, this is the first study to show that sporadic MSI-H cancers are characterized by a higher AL:PI ratio and increased proliferative activity compared with MSI-L and MSS cancers, and that an elevated PI may confer a survival advantage within the MSI-H subset.

The prediction of sharkskin instability observed during film blowing

The characteristics of sharkskin surface instability for linear low density polyethylene are studied as a function of film blowing processing conditions. By means of scanning electron microscopy and surface profilometry, is it found that for the standard industrial die geometry studied, sharkskin only occurs on the inside of the film bubble. Previous work suggests that this instability may be due to critical extensional stress levels at the exit of the die. Isothermal integral viscoelastic simulations of the annular extrusion process are reported, and confirm that the extensional stress at the die exit is large enough to cause local melt rupture. However the extensional stress level at the outer die wall predicts melt rupture of the outside bubble surface also, which contradicts the experimental findings. A significant temperature gradient is expected to exist across the die gap at the exit of the die, due to the external heating of the die and the low conductivity, of the polymer melt. It is shown that a gradient of 20 degreesC is required to cause sharkskin to only appear on the inner bubble surface.

Classical approach to interpretation of the charge-dependence of peptide mobilities obtained by capillary zone electrophoresis

Published mobility measurements obtained by capillary zone electrophoresis of human growth hormone peptides are described reasonably well by the classical theoretical relationships for electrophoretic migration. This conformity between theory and experiment has rendered possible a more critical assessment of a commonly employed empirical relationship between mobility (u), net charge (z) and molecular mass (M) of peptides in capillary electrophoresis. The assumed linear dependence between u and z/M-2/3 is shown to be an approximate description of a shallow curvilinear dependence convex to the abscissa. An improved procedure for the calculation of peptide charge (valence) is also described. (C) 2003 Elsevier B.V. All rights reserved.

A review of drainage and spontaneous rupture in free standing thin films with tangentially immobile interfaces

A review of spontaneous rupture in thin films with tangentially immobile interfaces is presented that emphasizes the theoretical developments of film drainage and corrugation growth through the linearization of lubrication theory in a cylindrical geometry. Spontaneous rupture occurs when corrugations from adjacent interfaces become unstable and grow to a critical thickness. A corrugated interface is composed of a number of waveforms and each waveform becomes unstable at a unique transition thickness. The onset of instability occurs at the maximum transition thickness, and it is shown that only upper and lower bounds of this thickness can be predicted from linear stability analysis. The upper bound is equivalent to the Freakel criterion and is obtained from the zeroth order approximation of the H-3 term in the evolution equation. This criterion is determined solely by the film radius, interfacial tension and Hamaker constant. The lower bound is obtained from the first order approximation of the H-3 term in the evolution equation and is dependent on the film thinning velocity A semi-empirical equation, referred to as the MTR equation, is obtained by combining the drainage theory of Manev et al. [J. Dispersion Sci. Technol., 18 (1997) 769] and the experimental measurements of Radoev et al. [J. Colloid Interface Sci. 95 (1983) 254] and is shown to provide accurate predictions of film thinning velocity near the critical thickness of rupture. The MTR equation permits the prediction of the lower bound of the maximum transition thickness based entirely on film radius, Plateau border radius, interfacial tension, temperature and Hamaker constant. The MTR equation extrapolates to Reynolds equation under conditions when the Plateau border pressure is small, which provides a lower bound for the maximum transition thickness that is equivalent to the criterion of Gumerman and Homsy [Chem. Eng. Commun. 2 (1975) 27]. The relative accuracy of either bound is thought to be dependent on the amplitude of the hydrodynamic corrugations, and a semiempirical correlation is also obtained that permits the amplitude to be calculated as a function of the upper and lower bound of the maximum transition thickness. The relationship between the evolving theoretical developments is demonstrated by three film thickness master curves, which reduce to simple analytical expressions under limiting conditions when the drainage pressure drop is controlled by either the Plateau border capillary pressure or the van der Waals disjoining pressure. The master curves simplify solution of the various theoretical predictions enormously over the entire range of the linear approximation. Finally, it is shown that when the Frenkel criterion is used to assess film stability, recent studies reach conclusions that are contrary to the relevance of spontaneous rupture as a cell-opening mechanism in foams. (C) 2003 Elsevier Science B.V. All rights reserved.

Capillary bridging and long-range attractive forces in a mean-field approach

When a mixture is confined, one of the phases can condense out. This condensate, which is otherwise metastable in the bulk, is stabilized by the presence of surfaces. In a sphere-plane geometry, routinely used in atomic force microscope and surface force apparatus, it, can form a bridge connecting the surfaces. The pressure drop in the bridge gives rise to additional long-range attractive forces between them. By minimizing the free energy of a binary mixture we obtain the force-distance curves as well as the structural phase diagram of the configuration with the bridge. Numerical results predict a discontinuous transition between the states with and without the bridge and linear force-distance curves with hysteresis. We also show that similar phenomenon can be observed in a number of different systems, e.g., liquid crystals and polymer mixtures. (C). 2004 American Institute of Physics.

Demixing instability in coil-rod blends undergoing polycondensation reactions

The authors extend their earlier work on the stability of a reacting binary polymer blend with respect to demixing [D. J. Read, Macromolecules 31, 899 (1998); P. I. C. Teixeira , Macromolecules 33, 387 (2000)] to the case where one of the polymers is rod-like and may order nematically. As before, the authors combine the random phase approximation for the free energy with a Markov chain model for the chemistry to obtain the spinodal as a function of the relevant degrees of reaction. These are then calculated by assuming a simple second-order chemical kinetics. Results are presented, for linear systems, which illustrate the effects of varying the proportion of coils and rods, their relative sizes, and the strength of the nematic interaction between the rods. (c) 2007 American Institute of Physics.

Nonlinear Saffman-Taylor instability

We show, both theoretically and experimentally, that the interface between two viscous fluids in a Hele-Shaw cell can be nonlinearly unstable before the Saffman-Taylor linear instability point is reached. We identify the family of exact elastica solutions [Nye et al., Eur. J. Phys. 5, 73 (1984)] as the unstable branch of the corresponding subcritical bifurcation which ends up at a topological singularity defined by interface pinchoff. We devise an experimental procedure to prepare arbitrary initial conditions in a Hele-Shaw cell. This is used to test the proposed bifurcation scenario and quantitatively asses its practical relevance.