Search results for "VISCOSITY"

Unsteady Separation for High Reynolds Numbers Navier-Stokes Solutions

2010

In this paper we compute the numerical solutions of Navier-Stokes equations in the case of the two dimensional disk impulsively started in a uniform back- ground flow. We shall solve the Navier-Stokes equations (for different Reynolds numbers ranging from 1.5 · 10^3 up to 10^5 ) with a fully spectral numerical scheme. We shall give a description of unsteady separation process in terms of large and small scale interactions acting over the flow. The beginning of these interactions will be linked to the topological change of the streamwise pressure gradient on the disk. Moreover we shall see how these stages of separation are related to the complex singularities of the solution. Infact the ana…

1993

In a new theoretical approach the separation of a pair of chain molecules (measured thermodynamically by the second osmotic virial coefficient A2) is treated as a two-step process: In the first step the molecules are detached from each other by the addition of solvent—keeping their dimensions constant—and in the second step the now isolated coils are allowed to relax into their equilibrium dimensions. For the description of the second step, in which only segments belonging to one molecule take part, an intra-molecular interaction parameter is introduced on the basis of the intrinsic viscosity. The present two-parameter approach yields A2 = A + σ M−(1−a) for the dependence of A2 on the molec…

A Viscosity Equation for Minimizers of a Class of Very Degenerate Elliptic Functionals

2013

We consider the functional $$J(v) = \int_\varOmega\bigl[f\bigl(|\nabla v|\bigr) - v\bigr] dx, $$ where Ω is a bounded domain and f:[0,+∞)→ℝ is a convex function vanishing for s∈[0,σ], with σ>0. We prove that a minimizer u of J satisfies an equation of the form $$\min\bigl(F\bigl(\nabla u, D^2 u\bigr), |\nabla u|-\sigma\bigr)=0 $$ in the viscosity sense.

Darstellung, eigenschaften und umsetzungen von polyvinylsulfofluoriden

1960

Vinylsulfofluorid wurde mit Azo-bis-isobutyronitril polymerisiert. Es wurden Polymerisationsgrade bis 390 erreicht. Die Molekulargewichte wurden durch Viskositatsmessungen an den durch Verseifung der Polyvinylsulfofluoride gewonnenen Natriumsalzen der Polyvinylsulfonsaure ermittelt. Die Polyvinylsulfofluoride wurden mit Ammoniak, aliphatischen und aromatischen Aminen umgesetzt. Dabei wurden Umsatze bis zu 80 Mol% erreicht. Vinylsulfofluoride was polymerized with azo-bis-isobutyronitrile. The degree of polymerisation was up to 390. The molecular-weights were determined by measuring the viscosity of the sodium-salts of polyvinylsulfonic acids obtained by saponification of polyvinylsulfofluori…

Testing of a constitutive equation with free volume dependent relaxation spectrum

1979

A model of non-linear viscoelasticity with relaxation times dependent upon free volume is here proposed. The free volume is related to the isotropic part of the stress tensor by means of a simple differential equation. The model predictions are compared with a large amount of experimental results taken on polymeric melts or concentrated solutions and reported in the literature. The single parameter of the model is determined, within each set of data, by fitting of the viscosity curve. A satisfactory agreement is obtained with data taken under both elongation and shear for which also the relaxation behavior after single and double strain steps is considered.

Apparent and Real Distribution in GPC (Experiments with PMMA Samples)

1971

Abstract Molecular weight distribution curves obtained by GPC are broadened if concentration and flow rate are fixed in the usual range. Therefore, the apparent nonuniformity U app of the samples is larger than the real non-uniformity U = (Mw/Mn) −1. For a number of fractionated and unfractionated samples of polymethyl methacrylate we determined M n and M w by osmotic, light-scattering, and viscosity measurements. Thus, the real value of U can be compared to U app obtained by GPC at different concentrations and flow rates, υ. The excess nonuniformity U exc is evaluated as function of concentration c, polydispersity, molecular weight, and flow rate. For c = 0 and υ = 0, U exc is not far from…

Gelchromatographie mit zwei Detektoren. Ein verfahren zur Korrektur von Gelchromatogrammen

1978

The relationship between the experimental function E(v) for the viscosity and the chromatogram after correction of instrumental spreading, w(v0) can be expressed by the integral equation where v0 is the elution volume under the integral sign and D(v, v0) is a function that describes the shape of the band spreading curve of a monodisperse sample. The relationship between the experimental chromatogram e(v) is given by the Tung equation. If the function D(v, v0) is independent of the molecular weight, then it is possible to solve these equations simultaneously and to calculate the functions w(v0) and D(v, v0). A mathematical method is given.

Viscoelastic properties of concentrated dispersions in water of soy lecithin

2003

Abstract Viscoelastic properties of soy lecithin dispersions at 60, 120, 180 and 240 g l−1 in water have been studied as a function of ionic strength (NaCl concentrations in the range 10−5–10−2 mol l−1) and of preparation method (sonication, freezing–unfreezing). Viscosity measurements of sonicated dispersions in a rotatory viscometer show Newtonian and plastic (Bingham) behavior, whereas the frozen–unfrozen dispersions show a spectacular change in their viscoelastic properties, that is, a non-Newtonian behavior with pseudoplastic characteristics and rheopexy. These properties have been related to electrokinetic characteristics of the segregated vesicles in each case. A decrease in ζ-potent…

Microgels of polyaspartamide and poly(ethylene glycol) derivatives obtained by γ-irradiation

2002

Abstract The copolymer PHG based on α , β -poly( N -2-hydroxyethyl)- dl -aspartamide (PHEA) functionalized with glycidyl methacrylate has been exposed in aqueous solution to a γ -ray source at different irradiation doses (2, 2.5 and 3.5 kGy), alone or in combination with poly(ethylene glycol)dimethacrylate (PEGDMA) or poly(ethylene glycol)diacrylate (PEGDA). The irradiation produces microgel systems that have been characterized by viscosity measurements. Lyophilization of microgels gives rise to samples able to swell instantaneously in water whereas their treatment with acetone produces swellable microparticles that have been characterized.

Extensional flow of HDPE/LDPE blends

1982

Elongational viscosity data, obtained through the converging flow analysis by Cogswell, are presented for two types of HDPE/LDPE blends at various compositions and different temperatures. The results relative to the homopolymer parents compare favourably with literature data obtained also with different and more sophisticated techniques. Those relative to blends show peculiar features for the two cases: when the newtonian viscosity of the LDPE is higher all the blends show a behaviour typical of the LDPE with a maximum in η el /η0 enhanced at small percentage of HDPE; when the newtonian viscosity of the LDPE is similar to that of the HDPE there is only a gradual change in the properties.