The history force on a small particle in a linearly stratified fluid

The hydrodynamic force experienced by a small spherical particle undergoing an arbitrary time-dependent motion in a weakly density-stratified fluid is investigated theoretically. The study is carried out under the Oberbeck–Boussinesq approximation and in the limit of small Reynolds and small Péclet numbers. The force acting on the particle is obtained by using matched-asymptotic expansions. In this approach, the small parameter is given by $a/\ell $, where $a$ is the particle radius and $\ell $ is the stratification length, as defined by Ardekani & Stocker (Phys. Rev. Lett., vol. 105, 2010, article 084502), which depends on the Brunt–Väisälä frequency, on the fluid kinematic viscosity and on the thermal or the concentration diffusivity (depending on the case considered). The matching procedure used here, which is based on series expansions of generalized functions, slightly differs from that generally used in similar problems. In addition to the classical Stokes drag, it is found that the particle experiences a memory force given by two convolution products, one of which involves, as usual, the particle acceleration and the other one, the particle velocity. Owing to the stratification, the transient behaviour of this memory force, in response to an abrupt motion, consists of an initial fast decrease followed by a damped oscillation with an angular frequency corresponding to the Brunt–Väisälä frequency. The perturbation force eventually tends to a constant which provides us with correction terms that should be added to the Stokes drag to accurately predict the settling time of a particle in a diffusive stratified fluid.

Non-Metallic Inclusions Control for High Strength Anti-HIC X65 Tube Steel

The hot metal fed converter in Panzhihua Steel Company is characterized by high sulfur content of 0.085% and high phosphorus content of 0.133%. Under this condition, some technologies like control of sulfur and T[O] content, ladle slag optimization, calcium treatment and protective casting were used in practice, and the desired result of T[O] as low as 0.0014% and sulfur content of 0.0023%was achieved, which met the cleanness requirements by anti-HIC X65 tube steel. With the help of inclusion control technology, grade of inclusions in as-cast steel was less than 0.5. In addition, total amount of inclusions was only 0.0044% which dispersed in slab in form of small spherical particle.

Simulation of a Layered Resonator for a Microfluidic Ultrasonic Separator

This paper focuses on the simulation of a layered resonator for a microfluidic ultrasonic separator with a special emphasis on analysing the stored energy-frequency product in the microfluid chamber. Since the acoustic force acting on a small spherical particle in a standing wave in the cavity of an ultrasonic separator is proportional to the product of the energy density in the standing wave and the driving frequency, the energy-frequency product can be used as a prediction of the separation performance in an ultrasonic separator. The electro-acoustic characteristics of the resonator under different conditions are also investigated. In particular, the influence of the reflector thickness on the stored energy-frequency product of the layered resonator is examined. Furthermore, the acoustic pressure distribution in the fluid chamber of the ultrasonic separator is investigated in detail. Predicted results from simulations compare well with experimental measurements and show that the model can be used to predict the electro-acoustic characteristics and the separation performance.

LASER-INDUCED OPTICAL-EMISSION STUDIES OF NIOBIUM CLUSTERS

The laser-induced optical emission of niobium clusters generated via the standard laser-vaporization technique is studied in the wavelength range from 350 to 750 nm. Particles with a radius of approximately 4 nm were heated by pulsed Nd:YAG laser operating at the fourth harmonic at 266 nm. The emission spectra are recorded as a function of delay time after the excitation and show a broad structureless continuum similar to blackbody radiation. Using the emissivity of a small spherical particle given by the Mie theory together with Planck’s law the experimental spectra can be reproduced quite well by varying the temperature of the particle. Thus temperatures can be deduced from the spectra. Increasing delay time leads to decreasing temperature of the particles which can be attributed to radiation cooling.