Effect of initial disturbance amplitude in gravity affected jet break-up

The initial disturbance amplitude has an effect on stretching jets that is not observed for capillary jet instability where gravitational acceleration is not significant. For inviscid and viscous fluids, gravity diminishes the effect that the initial amplitude has on jet length and its ability to prevent satellite formation. In stretching jets, not only the dimensionless frequency of the disturbance but also its initial amplitude must be known to properly study their satellite forming nature. Indirect methods of relating the applied disturbance energy to an initial velocity perturbation are not simple when the gravity parameter G is changing. When G A 0, the optimum disturbance frequency Omega(opt) and the initial disturbance amplitude are related, with Omega(opt) proportional to f (G) x In(1 /epsilon(nu)). Results from numerical simulations and experiments are presented here. (c) 2005 Elsevier Ltd. All rights reserved.

Drop formation and breakup of low viscosity elastic fluids: Effects of molecular weight and concentration

The dynamics of drop formation and pinch-off have been investigated for a series of low viscosity elastic fluids possessing similar shear viscosities, but differing substantially in elastic properties. On initial approach to the pinch region, the viscoelastic fluids all exhibit the same global necking behavior that is observed for a Newtonian fluid of equivalent shear viscosity. For these low viscosity dilute polymer solutions, inertial and capillary forces form the dominant balance in this potential flow regime, with the viscous force being negligible. The approach to the pinch point, which corresponds to the point of rupture for a Newtonian fluid, is extremely rapid in such solutions, with the sudden increase in curvature producing very large extension rates at this location. In this region the polymer molecules are significantly extended, causing a localized increase in the elastic stresses, which grow to balance the capillary pressure. This prevents the necked fluid from breaking off, as would occur in the equivalent Newtonian fluid. Alternatively, a cylindrical filament forms in which elastic stresses and capillary pressure balance, and the radius decreases exponentially with time. A (0+1)-dimensional finitely extensible nonlinear elastic dumbbell theory incorporating inertial, capillary, and elastic stresses is able to capture the basic features of the experimental observations. Before the critical "pinch time" t(p), an inertial-capillary balance leads to the expected 2/3-power scaling of the minimum radius with time: R-min similar to(t(p)-t)(2/3). However, the diverging deformation rate results in large molecular deformations and rapid crossover to an elastocapillary balance for times t>t(p). In this region, the filament radius decreases exponentially with time R-min similar to exp[(t(p)-t)/lambda(1)], where lambda(1) is the characteristic time constant of the polymer molecules. Measurements of the relaxation times of polyethylene oxide solutions of varying concentrations and molecular weights obtained from high speed imaging of the rate of change of filament radius are significantly higher than the relaxation times estimated from Rouse-Zimm theory, even though the solutions are within the dilute concentration region as determined using intrinsic viscosity measurements. The effective relaxation times exhibit the expected scaling with molecular weight but with an additional dependence on the concentration of the polymer in solution. This is consistent with the expectation that the polymer molecules are in fact highly extended during the approach to the pinch region (i.e., prior to the elastocapillary filament thinning regime) and subsequently as the filament is formed they are further extended by filament stretching at a constant rate until full extension of the polymer coil is achieved. In this highly extended state, intermolecular interactions become significant, producing relaxation times far above theoretical predictions for dilute polymer solutions under equilibrium conditions. (C) 2006 American Institute of Physics

Capillary jet instability under the influence of gravity

The focus of this paper is on the effect of gravity stretching on disturbed capillary jet instability. Break-up and droplet formation under low flows are simulated using finite difference solution of a one-dimensional approximation of disturbed capillary jet instability chosen from the work by Eggers and Dupont (J. Fluid Mech. 155 (1994) 289). Experiments were conducted using water and aqueous glycerol solutions to compare with simulations. We use a gravity parameter, G, which quantifies gravity stretching by relating flow velocity, orifice size and acceleration and is the reciprocal of the Fronde number. The optimum disturbance frequency Omega(opt) was found to be inversely proportional to G. However, this relationship appears to be complex for the range of G's investigated. At low G, the relationship between Omega(opt) and G appears to be linear but takes on a weakly decaying like trend as G increases. As flows are lowered, the satellite-free regime decreases, although experimental observation found that merging of main and satellite drops sometimes offset this effect to result in monodispersed droplet trains post break-up. Viscosity did not significantly affect the relationship between the disturbance frequency and G, although satellite drops could be seen more clearly close to the upper limit for instability at high G's. It is possible to define regimes of satellite formation under low flows by considering local wavenumbers at the point of instability. (C) 2004 Elsevier Ltd. All rights reserved.

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.

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.

Theoretical investigation of convective instability in inclined and fluid-saturated three-dimensional fault zones.

The convective instability of pore-fluid flow in inclined and fluid-saturated three-dimensional fault zones has been theoretically investigated in this paper. Due to the consideration of the inclined three-dimensional fault zone with any values of the inclined angle, it is impossible to use the conventional linear stability analysis method for deriving the critical condition (i.e., the critical Rayleigh number) which can be used to investigate the convective instability of the pore-fluid flow in an inclined three-dimensional fault zone system. To overcome this mathematical difficulty, a combination of the variable separation method and the integration elimination method has been used to derive the characteristic equation, which depends on the Rayleigh number and the inclined angle of the inclined three-dimensional fault zone. Using this characteristic equation, the critical Rayleigh number of the system can be numerically found as a function of the inclined angle of the three-dimensional fault zone. For a vertically oriented three-dimensional fault zone system, the critical Rayleigh number of the system can be explicitly derived from the characteristic equation. Comparison of the resulting critical Rayleigh number of the system with that previously derived in a vertically oriented three-dimensional fault zone has demonstrated that the characteristic equation of the Rayleigh number is correct and useful for investigating the convective instability of pore-fluid flow in the inclined three-dimensional fault zone system. The related numerical results from this investigation have indicated that: (1) the convective pore-fluid flow may take place in the inclined three-dimensional fault zone; (2) if the height of the fault zone is used as the characteristic length of the system, a decrease in the inclined angle of the inclined fault zone stabilizes the three-dimensional fundamental convective flow in the inclined three-dimensional fault zone system; (3) if the thickness of the stratum is used as the characteristic length of the system, a decrease in the inclined angle of the inclined fault zone destabilizes the three-dimensional fundamental convective flow in the inclined three-dimensional fault zone system; and that (4) the shape of the inclined three-dimensional fault zone may affect the convective instability of pore-fluid flow in the system. (C) 2004 Published by Elsevier B.V.

A scheme for efficient quantum computation wtih linear optics

Quantum computers promise to increase greatly the efficiency of solving problems such as factoring large integers, combinatorial optimization and quantum physics simulation. One of the greatest challenges now is to implement the basic quantum-computational elements in a physical system and to demonstrate that they can be reliably and scalably controlled. One of the earliest proposals for quantum computation is based on implementing a quantum bit with two optical modes containing one photon. The proposal is appealing because of the ease with which photon interference can be observed. Until now, it suffered from the requirement for non-linear couplings between optical modes containing few photons. Here we show that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photo-detectors. Our methods exploit feedback from photo-detectors and are robust against errors from photon loss and detector inefficiency. The basic elements are accessible to experimental investigation with current technology.

Asset Price Instability and Policy Responses: The Legacy of Liberalisation

The debate about the dynamics and potential policy responses to asset inflation has intensified in recent years. Some analysts, notably Borio and Lowe, have called for 'subtle' changes to existing monetary targeting frameworks to try to deal with the problems of asset inflation and have attempted to developed indicators of financial vulnerability to aid this process. In contrast, this paper argues that the uncertainties involved in understanding financial market developments and their potential impact on the real economy are likely to remain too high to embolden policy makers. The political and institutional risks associated with policy errors are also significant. The fundamental premise that a liberalised financial system is based on 'efficient' market allocation cannot be overlooked. The corollary is that any serious attempt to stabilize financial market outcomes must involve at least a partial reversal of deregulation.

Molecular cocrystals of carboxylic acids. XXVII - An investigation into the use of triphenylphosphine oxide cocrystals for non-linear optics: the crystal structure of the adduct of triphenylphosphine oxide with N-methylpyrrole-2-carboxylic acid

Four adducts of triphenylphosphine oxide with aromatic carboxylic acids have been synthesized and tested for second-order non-linear optical properties. These were with N-methylpyrrole-2-carboxylic acid (I), indole-2-carboxylic acid (2), 3-dimethylaminobenzoic acid (3), and thiophen-2-carboxylic acid (4). Compound (1) produced clear, colourless crystals (space group P2(1)2(1)2(1) With a 9.892(1), b 14.033(1), c 15.305(1) Angstrom, Z 4) which allowed the structure to be determined by X-ray diffraction.