A physically based correlation for the effects of power law rheology and inclination on slug bubble rise velocity

A study has been made of the motion of long bubbles in inclined pipes containing viscous Newtonian and non-Newtonian liquids. A semi-theoretical expression for the rise velocity of air bubbles in water is derived on the hypothesis that the dominant factor is the momentum exchange of the bubble underflow, i.e. the bubble nose shape. The correlation calls on empirical inputs from established literature on bubble rise speeds at high Reynolds number. The effects of increasing Newtonian viscosity are analysed with reference to the momentum exchange and it is shown how viscosity reduces the inclination dependence of the bubble Froude number. Results from an experimental survey in seven different non-Newtonian liquids in three different diameter pipes are presented. These data are correlated so as to decouple the effects of surface tension and viscosity. An empirical relation is proposed for the effective shear rate in the fluid travelling around the bubble nose. Our correlation is compared to literature data from a broad range of Reynolds numbers with excellent agreement except at shallow angles.     

Ultrasonic wave and moduli changes in a curing epoxy resin

During the cure cycle, thermosetting polymeric resins change in physical character from a viscous liquid to a gel and finally to a hardened solid. Ultrasonic-wave-propagation techniques can be used to monitor both the extent of cure and the development of solid-phase moduli. This paper outlines such a program and presents results for a room-temperature, amine-cured epoxy system. Signal attenuation and wave-speed data are given as a function of cure time for 1.0 MHz longitudinal and shear waves. The behavior observed is first interpreted in terms of linear-viscoelastic wave-propagation theory. Then using the wave speeds, apparent elastic moduli are calculated as a function of cure time. Finally, relations are developed which suggest a mapping between the moduli and a normalized reaction-extent variable. Implicit in these relations is that the moduli themselves can serve or be viewed as reaction-extent variables.     

A method of determining complex moduli of viscoelastic materials

A method is introduced whereby the complex moduli of viscoelastic materials may be determined in a relatively simple and accurate manner by means of calibration of the measuring system using a specimen of known properties. The appropriate data-reduction equations are presented and use of the method is demonstrated for determination of complex moduli for bovine bones over a four-octave frequency range.     

Dilatational plastic constitutive equations and their application to ductile fracture analysis of axisymmetric specimens

In many ductile materials voids nucleate and grow under large strain and triaxial stress, which yield volumetric plastic expansion. A constitutive equation is presented, which accounts for this plastic dilatancy. The plastic moduli involved in this equation can be calibrated by using necking tests of axisymmetric bars, void model analysis and computer simulation. To verify the rationality of such a constitutive equation and adjust the values of plastic moduli, the constitutive equation with its moduli to be determined is applied to analyse the ductile fracture behaviour of axisymmetric bars.     

Canonical moduli and general solution of equations of a two-dimensional static problem of anisotropic elasticity

Equations of a two-dimensional static problem of anisotropic elasticity are brought to a simple form with the use of orthogonal and affine transformations of coordinates and corresponding transformations of mechanical quantities. It is proved that an arbitrary matrix of elasticity moduli containing six independent components can be always converted by a congruent transformation to a matrix with two independent components, which are called the canonical moduli. Depending on the relations between the canonical moduli, the determinant of the matrix of operators of equations in displacements is presented as a product of various quadratic terms. A general presentation of the solution of equations in displacements in the form of a linear combination of the first derivatives of two quasi-harmonic functions satisfying two independent equations is given. A symmetry operator (i.e., a formula of production of new solutions) is found to correspond to each presentation. In a three-dimensional case, the matrix of elasticity moduli with 21 independent components is congruent to a matrix with 12 independent canonical moduli.     

On the quasistatic effective elastic moduli for elastic waves in three-dimensional phononic crystals

Effective elastic moduli for 3D solid–solid phononic crystals of arbitrary anisotropy and oblique lattice structure are formulated analytically using the plane-wave expansion (PWE) method and the recently proposed monodromy-matrix (MM) method. The latter approach employs Fourier series in two dimensions with direct numerical integration along the third direction. As a result, the MM method converges much quicker to the exact moduli in comparison with the PWE as the number of Fourier coefficients increases. The MM method yields a more explicit formula than previous results, enabling a closed-form upper bound on the effective Christoffel tensor. The MM approach significantly improves the efficiency and accuracy of evaluating effective wave speeds for high-contrast composites and for configurations of closely spaced inclusions, as demonstrated by three-dimensional examples.     

Experimental and theoretical aspects of the two-roll mill problem

Experiments are described in which two cylinders of the same radii-rotate with identical speeds in a bath of Newtonian or non-Newtonian liquid. The torque on one of the cylinders is measured as a function of rotational speed for various values of the cylinder separation and the flow patterns are observed by a dye-injection technique.The observed experimental results for a Newtonian liquid correlate well with the theoretical predictions but a similar correlation in the case of elastic liquids is made difficult by the strongly three-dimensional nature of the flow in this case and the difficulty in estimating the amount of liquid passing through the rollers. The possibility of flow reversal effects due to the high Trouton ratios in the case of the elastic liquids is investigated both experimentally and theoretically.     

The deformation and fracture of balloons

Inflation of balloons provides a straightforward way of achieving large biaxial deformations. Previous studies have shown that when a balloon bursts, crack propagation occurs at very high speed – much higher than would be expected from the low strain modulus and elastic wave velocity of the rubber. The present paper is concerned with studies of the deformation and fracture of cylindrical balloons. On inflation, the deformations of such a balloon pass through an unstable region but subsequently increase monotonically with pressure. In this relatively high pressure region, the ratio of the longitudinal and circumferential extension ratios is broadly in accord with expectations from high-strain elasticity theory when the ratio of the corresponding stresses is taken into account. On bursting, crack speeds up to around 300 m/s in this region. It is shown that these speeds are in accord with large increase in incremental moduli for the highly-strained rubber. Marked changes in crack tip profile observed at very high crack speeds are consistent with control of the rate of growth by inertia rather than by the viscoelastic properties of the rubber (as is believed to be the case at lower speeds). Consistent with this, various elastomers having different glass transition temperatures show similar crack growth behaviour in the very high speed region.     

The effect of additives on the speed of the crystallization front of xylitol with various degrees of supercooling

Some liquids can be kept in a supercooled or supersaturated metastable state for substantially long periods. Such liquids can be applied as long-term heat storage where the latent heat can be released when needed. As xylitol possesses a relatively high value of latent heat and as it can be easily supercooled, it has promising properties for this application. However, the speed of the crystallization of xylitol is low, leading to a low release rate of latent heat.Several additives have been experimentally tested for the purpose of accelerating the crystallization speed. The effect of the additives on the latent heat, on the melting temperatures, and on the long-term durability of the supercooled state was also measured.The highest speeds of the crystallization front, at a temperature of 22 °C, were achieved with methanol as an additive leading to speeds 33 times higher in vertical experiments and in 170 times higher in horizontal ones than with pure xylitol. The improved speed of the crystallization front is mostly caused by the methanol flow currents generated as a result of the separation of methanol during crystallization, and to a lesser extent, as a result of the increase in the speed of the growth of the crystals.     

最大地面风速的预测研究

为了解决航天发射场极值风速的预测问题,本文提出了用于极值风速预测的一种新方法－－相关系数法,并利用此方法对三种典型的概率分布进行了对比研究,在对比过程中,检验了三组极值风速,假设每组检验样本内的极值风速数据是统计独立的,于是极值风速就可以描述为随机过程,研究表明最适于描述极值风速的概率分布是reverse Weibull分布,与peak-over-threshold法所得出的结论具有良好的一致性。