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  • 1
    ISSN: 1573-7691
    Keywords: Eigenvalues ; asymmetric matrices ; generalized eigenproblem ; finite element method ; free surface flow
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Stability of steady, two-dimensional, slide coating flow of Newtonian liquid to small, two-dimensional disturbances is analyzed by means of Galerkin's method and finite element basis functions. The resulting sequence of computational problems consists of large, sparse, asymmetric generalized eigenproblemsJx=λ Mx in whichJ andM depend on system parameters andM is singular. These are solved for the leading modes—eigenvalues of algebraically largest real part, and their eigenvectors—by a flexible method assembled from the iterative Arnoldi algorithm with Schur-Wielandt deflation developed by Saad for the asymmetric eigenproblem; initialization that takes advantage of continuation and can incorporate rational acceleration; complex or real shift of eigenvalue, as appropriate; and—a key ingredient-approximately exponential preconditioning by rational transformation suitable to the singular behavior. The results include leading modes of complicated structure, examples of mode overtaking, turning points beyond which the steady flows do not exist, and Hopf points that mark onset of deleterious, spontaneous oscillations of the flow.
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  • 2
    ISSN: 0741-0581
    Keywords: Freeze fractures ; Vesicles ; Liquid crystal ; Life and Medical Sciences ; Cell & Developmental Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Natural Sciences in General
    Notes: A computer-aided graphics approach to correlating transmission electron microscope images of freeze-fractured and thin-sectioned samples is outlined. Any three-dimensional model of the imaged structure can be mathematically sectioned to provide a two-dimensional representation of the model in the “fracture” plane. The method is used to demonstrate that the structure of lamellar liquid crystalline liposomes is based on a family of Dupin cyclides; closed, parallel surfaces with a conjugate ellipse and hyperbola as curvature defects.
    Additional Material: 8 Ill.
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  • 3
    ISSN: 0741-0581
    Keywords: Cryo-electron microscopy ; Cryofixation ; Vitreous ice ; Plunge-cooling ; Life and Medical Sciences ; Cell & Developmental Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Natural Sciences in General
    Notes: The controlled environment vitrification system (CEVS) permits cryofixation of hydrated biological and colloidal dispersions and aggregates from a temperature- and saturation-controlled environment. Otherwise, specimens prepared in an uncontrolled laboratory atmosphere are subject to evaporation and heat transfer, which may introduce artifacts caused by concentration, pH, ionic strength, and temperature changes. Moreover, it is difficult to fix and examine the microstructure of systems at temperatures other than ambient (e.g., biological systems at in vivo conditions and colloidal systems above room temperature). A system has been developed that ensures that a liquid or partially liquid specimen is maintained in its original state while it is being prepared before vitrification and, once prepared, is vitrified with little alteration of its microstructure. A controlled environment is provided within a chamber where temperature and chemical activity of volatile components can be controlled while the specimen is being prepared. The specimen grid is mounted on a plunger, and a synchronous shutter is opened almost simultaneously with the release of the plunger, so that the specimen is propelled abruptly through the shutter opening into a cryogenic bath. We describe the system and its use and illustrate the value of the technique with TEM micrographs of surfactant microstructures in which specimen preparation artifacts were avoided. We also discuss applications to other instruments like SEM, to other techniques like freeze-fracture, and to novel “on the grid” experiments that make it possible to freeze successive instants of dynamic processes such as membrane fusion, chemical reactions, and phase transitions.
    Additional Material: 19 Ill.
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  • 4
    ISSN: 1435-1528
    Keywords: Key words Cationic surfactant rheology–counterion/surfactant ratio–surfactant drag reduction–cationic surfactant microstructure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Rheology, drag reduction and cryo-TEM experiments were performed on Arquad 16–50/NaSal and Ethoquad O/12/NaSal surfactant systems at different counterion-to-surfactant ratios and at constant low surfactant concentrations, 5 mM, appropriate for drag reduction. The molar ratio of counterion-to-surface was varied from 0.6 to 2.5. All the surfactant systems described here are viscoelastic and drag reducing. The viscoelasticity and drag reducing effectiveness increase with increase in counterion/surfactant ratio. Network are present in the solutions with high ratio, and they are viscoelastic. However, shear is needed to induce network formation for solutions at low ratio. Cryo-TEM images confirm the existence of thread-like micelles which form entanglement networks, and show that the micellar network becomes denser with increasing counterion/surfactant ratio in one surfactant series. Both increase in the counterion/surfactant ratio and increase in the shear rate result in shorter relaxation times. For some of these systems, abrupt increase in viscosity is observed at certain shear rates which are time effects affecting microstructure rearrangements rather than formation of shear induced structures.
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  • 5
    ISSN: 1435-1528
    Keywords: Key words Extensional viscosity ; extensional flow ; elongational viscosity ; opposed nozzles ; extensional rheometry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Opposed-nozzle devices are widely used to try to measure the extensional viscosity of low-viscosity liquids. A thorough literature survey shows that there are still several unanswered questions on the relationship between the quantity measured in opposed-nozzle devices and the “true” extensional viscosity of the liquids. In addition to extensional stresses, opposed nozzle measurements are influenced by dynamic pressure, shear on the nozzles, and liquid inertia. Therefore the ratio of the apparent extensional viscosity that is measured to the shear viscosity that is independently measured is greater than three even for Newtonian liquids. The effect of inertia on the extensional measurements is analyzed by computer-aided solution of the Navier-Stokes system, and by experiments on low-viscosity Newtonian liquids (1mPas≤η S ≤800mPas). The effect of nozzle separation-to-diameter ratio on the average residence time of the liquid is analyzed under the assumption of simple extensional flow kinematics. The average residence time of the liquid is independent of this ratio unless the radial inflow section of the extensional flow volume is related to the nozzle separation. Experiments indicate that in some cases widening the gap lowers the apparent extensional viscosity that is measured, whereas in other cases the opposite is true. In the light of these theoretical considerations and experimental observations, the use of systematic corrections to extensional viscosity measurements on non-Newtonian liquids is not recommended. Thus opposed nozzle devices should be considered as useful indexers rather than rheometers. Finally, measurements on a series of semi-dilute solutions of high molecular weight poly(ethylene oxide) in water are also reported.
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  • 6
    ISSN: 1435-1528
    Keywords: Iron oxide ; flocculated suspension ; linear viscoelasticity ; percolation ; cryo-scanning electron microscopy ; concentrated colloidal suspension
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Suspensions consisting of particles of colloidal dimensions have been reported to form connected structures. When attractive forces act between particles in suspension they may flocculate and, depending on particle concentration, shear history and other parameters, flocs may build-up in a three-dimensional network which spans the suspension sample. In this paper a floc network model is introduced to interpret the elastic behavior of flocculated suspensions at small deformations. Elastic percolation concepts are used to explain the variation of the elastic modulus with concentration. Data taken from the suspension rheology literature, and new results with suspensions of magnetic γ-Fe2O3 and non-magnetic α-Fe2O3 particles in mineral oil are interpreted with the model proposed. Non-zero elastic modulus appeared at threshold particle concentrations of about 0.7 vol.% and 0.4 vol.% of the magnetic and non-magnetic suspensions, respectively. The difference is attributed to the denser flocs formed by magnetic suspensions. The volume fraction of particles in the flocs was estimated from the threshold particle concentration by transforming this concentration into a critical volume concentration of flocs, and identifying this critical concentration with the theoretical percolation threshold of three-dimensional networks of different coordination numbers. The results obtained indicate that the flocs are low-density structures, in agreement with cryo-scanning electron micrographs. Above the critical concentration the dynamic elastic modulus G′ was found to follow a scaling law of the type G′ ∼ (Φ f -Φ f c ) f , where Φ f is the volume fraction of flocs in suspension, and Φ f c is its threshold value. For magnetic suspensions the exponent f was found to rise from a low value of about 1.0 to a value of 2.26 as particle concentration was increased. For the non-magnetic a similar change in f was observed; f changed from 0.95 to 3.6. Two other flocculated suspension systems taken from the literature showed a similar change in exponent. This suggests the possibility of a change in the mechanism of stress transport in the suspension as concentration increases, i.e., from a floc-floc bond-bending force mechanism to a rigidity percolation mechanism.
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  • 7
    ISSN: 1435-1528
    Keywords: Key words Mixed cationic surfactants ; Turbulent drag reduction ; Rheology ; Apparent extensional viscosity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Experimental studies of the effects of mixtures of cationic surfactants on their drag reduction and rheological behaviors are reported. Cationic alkyl trimethyl quaternary ammonium surfactants with alkyl chain lengths of C12 and C22 were mixed at different molar ratios (total surfactant concentrations were kept at 5 mM with 12.5 mM sodium salicylate (NaSal) as counterion). Drag reduction tests showed that by adding 10% (mol) of C12, the effective drag reduction range expanded to 4–120 °C, compared with 80–130 °C with only the C22 surfactant. Thus mixing cationic surfactants with different alkyl chain lengths is an effective way of tuning the drag reduction temperature range. Cryo-TEM micrographs revealed thread-like micellar networks for surfactant solutions in the drag reducing temperature range, while vesicles were the dominant microstructures at non-drag reducing temperatures. High extensional viscosity was the main rheological feature for all solutions except 50% C12 (mol) solution, which also does not show strong viscoelasticity. It is not clear why this low extensional viscosity solution with relatively weak viscoelasticity is a good drag reducer.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 24 (1981), S. 243-268 
    ISSN: 1572-9613
    Keywords: Fluid microstructures ; thin films ; periodic fluid microstructures ; statistical mechanics of inhomogeneous fluids ; disjoining pressure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The general gradient theory of fluid microstructures is outlined. This theory reduces the determination of fluid microstructures to a boundary value problem. The density and pressure tensor profiles and the tension of planar thin films and layered structures in one-component fluids are investigated. The boundary conditions determining these structures are given a geometric interpretation in the free energy-density diagram. Discussed are the implications of the theory for the validity of Antonov's rule, the duplex film hypothesis, and the asymptotic theory of disjoining pressure and of the origin of a characteristic length scale in spinodal decomposition.
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  • 9
    ISSN: 1573-1634
    Keywords: Capillary dispersion ; hyperdispersion ; fractals ; low saturation ; diffusion equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Recent displacement experiments show ‘anomalously’ rapid spreading of water during imbibition into a prewet porous medium. We explain this phenomenon, calledhyperdispersion, as viscous flow along fractal pore walls in thin films of thicknessh governed by disjoining forces and capillarity. At high capillary pressure, total wetting phase saturation is the sum of thin-film and pendular stucture inventories:S w =S tf +S ps . In many cases, disjoining pressure ∏ is inversely proportional to a powerm of film thicknessh, i.e. ∏ ∞h −m , so thatS tf ∞P c −1/m. The contribution of fractal pendular structures to wetting phase saturation often obeys a power lawS ps ∞P c (3−D), whereD is the Hausdorff or fractal dimension of pore wall roughness. Hence, if wetting phase inventory is primarily pendular structures, and if thin films control the hydraulic resistance of wetting phase, the capillary dispersion coefficient obeysD c ∞S w v , where v=[3−m(4−D) ]/m(3−D). The spreading ishyperdispersive, i.e.D c (S w ) rises as wetting phase saturation approaches zero, ifm〉3/(4−D),hypodispersive, i.e.D c (S 2) falls as wetting phase saturation tends to zero, ifm〈3/(4−D), anddiffusion-like ifm=3/(4−D). Asymptotic analysis of the ‘capillary diffusion’ equation is presented.
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  • 10
    ISSN: 1573-1634
    Keywords: dispersion ; reaction ; perturbation theory ; stochastic modeling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract We carry out a stochastic-perturbation analysis of a one-dimensional convection–dispersion-reaction equation for reversible first-order reactions. The Damköhler number, Da, is distributed randomly from a distribution that has an exponentially decaying correlation function, controlled by a correlation length, ξ. Zeroth- and first-order approximations of the dispersion coefficient, D are computed from moments of the residence-time distribution obtained by solving a one-dimensional network model, in which each unit of the network represents a Darcy-level transport unit, and the solution of the transfer function in zeroth- and first-order approximations of the transport equation. In the zeroth-order approximation, the dispersion coefficient is calculated using the convection–dispersion-reaction equation with constant parameters, that is, perturbation corrections to the local equation are ignored. This zeroth-order dispersion coefficient is a linear function of the variance of the Damköhler number, 〈(ΔDa)2〉. A similar result was reported in a two-dimensional network simulation. The zeroth-order approximation does not give accurate predictions of mixing or spreading of a plume when Damköhler numbers, Da ≪ 1 and its variance, 〈(ΔDa)2〉 〉 0.25 〈Da2〉. On the other hand, the first-order theory leads to a dispersion coefficient that is independent of the reaction parameters and to equations that do accurately predict mixing and spreading for Damköhler numbers and variances in the range √〈(ΔDa)2〉/〈Da〉≤0.3
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