Joseph Yerushalmi

Breakup of a laminar capillary jet of a viscoelastic fluid

The stability of non-Newtonian jets was investigated. A linearized stability analysis shows that a liquid column of a viscoelastic fluid exhibits more rapid growth of axisymmetric wave disturbances than a Newtonian fluid of the same zero shear viscosity. This result is independent of the form of constitutive equation chosen. Experiments in weakly elastic fluids confirm this expectation, whereas data on fluids with more pronounced elastic properties indicate that non-linear phenomena are dominating. The disturbances appear as a series of droplets connected by random lengths of threads, which thin with distance and eventually lead to jet breakup. Even in dilute viscoelastic solutions, jet breakup does not occur by the growth of clearly defined waves.

The stability of steady shear flows of some viscoelastic fluids

Abstract The stability of steady shear flows of some viscoelastic fluids relative to small perturbations in the initial data is examined. It is shown that all values of the steady shear rate where the flow curve exhibits a zero or negative slope the flow is unstable. This conclusion is corroborated by existing experimental data and bears upon the phenomenon of melt fracture.

Instability of Jets of Non‐Newtonian Fluids

The instability of jets of some non‐Newtonian fluids under the influence of externally controlled disturbances was studied. Dispersion curves were generated over a range of frequencies. Jets of a 0.1% solution of Carbopol in water, a viscoinelastic fluid, showed a breakup pattern similar to that of jets of water. The dispersion curve matched a viscosity intermediate to the zero shear viscosity of the solution and the viscosity that corresponds to the average shear rate in the tube. Subject to external disturbances, jets of Separan solutions showed a remarkably ordered and regular pattern. On jets of 0.1% Separan, sinusoidal wave formation was absent and a ligament‐droplet configuration formed from the outset. On the less elastic 0.05% Separan jets, there is an initial region in which sinusoidal waves grow exponentially; the growth is later arrested and a ligament‐droplet configuration results. In the initial region the growth rates are about equal to the growth rates that a jet of a Newtonian fluid of the...

The Extent of Correlations in a Stochastic Coalescence Process

Abstract A stochastic model of coalescence is set up and solved for the probabilities of all possible histories of particle growth. The full stochastic model is compared with the so-called kinetic model to which it reduces in the absence of correlations. A primary objective is the assessment of the extent of correlations in poorly mixed systems or in systems of small populations. The study shows that insofar as the total number of particles is concerned, regardless of their size distribution, the results from the kinetic equations match the true stochastic averages even for very small initial populations. But, when size distributors are considered, then, in systems of small population or in large systems that are poorly mixed, the results of the kinetic equations may differ substantially from the stochastic means in the long-term tail; apart from the tail, the distributions from the full stochastic and kinetic models match quite well.

Agglomeration of Ash in Fluidized Beds Gasifying Coal: The Godel Phenomenon

In a bed of anthracite or bituminous coke fluidized by air at 10 to 15 meters per second at 1200� to 1400�C, molten ash forms beads on the surface of a coke particle, some exuding from its interior. The beads merge and detach them-selves to grow further as loose fluidized ash agglomerates of low carbon content.

The response of viscoelastic materials to small deformations

The main features of the theory of linear viscoelasticity are reviewed. The time-dependent behavior of any viscoelastic material can be described in terms of a complex viscosity η (s) which must possess a certain specific analytic character, considered as a function of the complex variable s. It is shown that the complex viscosity representing the dynamic response of viscoelastic fluids to oscillatory motion superimposed upon steady shear can not be evaluated in terms of a spectrum of relaxation times and can not be compared on such basis to the complex viscosity measured in the vicinity of equilibrium. Any non-linear theory of viscoelasticity should be compatible with the linear theory. This criterion is discussed; it is shown that a non-linear constitutive equation of the Rivlin—Ericksen type involving only a finite number of derivatives of the strain rate should not be regarded as a proper constitutive equation.