A semi-schematic model for the center of mass dynamics in supercooled molecular liquids

We introduce a semi-schematic mode-coupling model to describe the slow dynamics in molecular liquids, retaining explicitly only the description of the center of mass degrees of freedom. Angular degrees of freedom are condensed in a q-vector independent coupling parameter. We compare the time and q-dependence of the density fluctuation correlators with numerical data from a 250 ns long molecular dynamics simulation. Notwithstanding the choice of a network-forming liquid as a model for comparing theory and simulation, the model describes the main static and dynamic features of the relaxation in a broad q-vector range.Comment: Revtex, 2 figure

Effect of turbulence on the drag and lift of a particle

A direct numerical simulation ~DNS! is used to study the effect of a freestream isotropic turbulent flow on the drag and lift forces on a spherical particle. The particle diameter is about 1.5???10 times the Kolmogorov scale, the particle Reynolds number is about 60???600, and the freestream turbulence intensity is about 10%???25%. The isotropic turbulent field considered here is stationary, i.e., frozen in time. It is shown that the freestream turbulence does not have a substantial and systematic effect on the time-averaged mean drag. The standard drag correlation based on the instantaneous or mean relative velocity results in a reasonably accurate prediction of the mean drag obtained from the DNS. However, the accuracy of prediction of the instantaneous drag decreases with increasing particle size. For the smaller particles, the low frequency oscillations in the DNS drag are well captured by the standard drag, but for the larger particles significant differences exist even for the low frequency components. Inclusion of the added-mass and history forces, computed based on the fluid velocity at the center of the particle, does not improve the prediction. Different estimates of the fluid velocity seen by the particle are examined. It is shown that the mean drag is insensitive to the fluid velocity measured at the particle center, or obtained by averaging over a fluid volume of the order of the particle size. The fluctuations diminish as the size of the averaging volume increases. The effect of increasing freestream turbulence intensity for the same particle size is studied. Fluctuations in the drag and lift forces are shown to scale with the mean drag and freestream intensity. The standard drag without the added-mass and history forces provides the best approximation to the DNS result.published or submitted for publicationis peer reviewe

Wall effect for high Reynolds number motion of spheres in shear thinning fluids

This article does not have an abstract

Estimation of zero-shear viscosity of polymer solutions from falling sphere data

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The influence of fluid elasticity on wall effects for creeping sphere motion in cylindrical tubes

Experimental results are presented of wall effect for the slow motion of spheres in elastic, constant-viscosity liquids. The results are correlated in terms of diameter ratio for d/D < 0.3, and Weissenberg number We < 5. Weissenberg number is defined as We = 2θVm/d, with θ the Maxwellian relaxation time (θ = N1/2τγ). The wall effect is found to be adequately described by Newtonian expressions for small Weissenberg number, We < 0.01. For larger values of the Weissenberg number, We > 0.2, virtually no wall effect is discernible; the small effect observed is correlated by the wall factor expression The wall effect observed is ascribed to the influence of fluid elasticity alone, since all the fluids used were elastic to a greater or lesser extent, but showed no shear thinning. f=1-0.17d/D

Wall effect for the fall of spheres in cylindrical tubes at high Reynolds number

New experimental results on the wall effect for sphere motion in cylindrical tubes are presented and discussed for the conditions d/D ≤ 0.9 and Re<SUB>m</SUB> ≤ 20000. Extensive comparisons with previous studies have been carried out to evaluate their predictability and to demonstrate the utility of the present results. The wall factor, defined as the ratio of settling velocity in an unbounded medium to that measured in a cylindrical tube, is found to depend on sphere-to-tube diameter ratio and on sphere Reynolds number. However, for small values of the Reynolds number (Re ≤ 0.5), as well for large values (Re ≥ 1000), the Reynolds number dependence of the wall factor disappears; in these regions, only the dependence on diameter ratio remains

Creeping motion of spheres through shear-thinning elastic fluids described by the Carreau viscosity equation

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Effect of turbulence on the drag and lift of a particle

A direct numerical simulation (DNS) is used to study the effect of a freestream isotropic turbulent flow on the drag and lift forces on a spherical particle. The particle diameter is about 1.5 to 10 times the Kolmogorov scale, the particle Reynolds number is about 60 to 600, and the freestream turbulence intensity is about 10 to 25%. It is shown that the freestream turbulence does not have a substantial and systematic effect on the time-averaged mean drag. The standard drag correlation based on the instantaneous or mean slip velocity results in a reasonably accurate prediction of the mean drag obtained from the DNS. However, the accuracy of prediction of the instantaneous drag decreases with increasing particle size. For the smaller particles, the low frequency oscillations in the DNS drag are well captured by the standard drag, but for the larger particles significant differences exist even for the low frequency components. Inclusion of the added-mass and history forces, computed based on the fluid velocity at the center of the particle, does not improve the prediction. Different estimates of the fluid velocity seen by the particle are examined. It is shown that the mean drag is insensitive to the fluid velocity measured at the particle center, or obtained by averaging over a fluid volume of the order of the particle size. The fluctuations diminish as the size of the averaging volume increases. The effect of increasing freestream turbulence intensity for the same particle size is studied. Fluctuations in the drag and lift forces are shown to scale with the mean drag and freestream intensity. The standard drag without the added-mass and history forces provides the best approximation to the DNS result.published or submitted for publicationis peer reviewe

Creeping motion of spheres through Ellis model fluids

Experimental results for creeping motion of spheres through Ellis model fluids are compared with the theory of Hopke and Slattery. For 58 data points in the required range of 1. Although the maximum deviation between this correlation and the data reaches nearly 36%, the average deviation is less than 10%. The correlation covers a wide range of Ellis model parameters, and approaches the Newtonian case