A perturbation solution for long wavelength thermoacoustic propagation in dispersions

AbstractIn thermoacoustic scattering the scattered field consists of a propagating acoustic wave together with a non-propagational “thermal” wave of much shorter wavelength. Although the scattered field may be obtained from a Rayleigh expansion, in cases where the particle radius is small compared with the acoustic wave length, these solutions are ill-conditioned. For this reason asymptotic or perturbation solutions are sought. In many situations the radius of the scatter is comparable to the length of the thermal wave. By exploiting the non-propagational character of the thermal field we obtain an asymptotic solution for long acoustic waves that is valid over a wide range of thermal wavelengths, on both sides of the thermal resonance condition. We show that this solution gives excellent agreement with both the full solution of the coupled Helmholtz equations and experimental measurements. This treatment provides a bridge between perturbation theory approximations in the long wavelength limit and high frequency solutions to the thermal field employing the geometric theory of diffraction

Ultrasonic study of the gelation of gelatin: phase diagram, hysteresis and kinetics

We map the ultrasonic (8 MHz) speed and attenuation of edible-grade gelatin in water, exploring the key dependencies on temperature, concentration and time. The ultrasonic signatures of the sol-gel transition, confirmed by rheological measurements, and incomplete gel formation at low concentrations, enable a phase diagram of the system to be constructed. Sensitivity is also demonstrated to the kinetics of gel formation and melting, and associated hysteresis effects upon cyclic temperature sweeps. Furthermore, simple acoustic models of the sol and gel state enable estimation of the speed of sound and compressibility of gelatin. Our results demonstrate the potential of ultrasonic measurements to characterise the structure and visco-elasticity of gelatin hydrogels.Comment: 15 pages, 8 figure

Development of a discrete element model with moving realistic geometry to simulate particle motion in a Mi-Pro granulator

This paper presents the implementation of a methodology incorporating a 3D CAD geometry into a 3D Discrete Element Method (DEM) code; discussing some of the issues which were experienced. The 3D CAD model was discretised into a finite element mesh and the finite wall method was employed for contact detection between the elements and the spherical particles. The geometry was based on a lab scale Mi-Pro granulator. Simulations were performed to represent dry particle motion in this piece of equipment. The model was validated by high speed photography of the particle motion at the surface of the Mi-Pro�s clear bowl walls. The results indicated that the particle motion was dominated by the high speed impeller and that a roping regime exists. The results from this work give a greater insight into the particle motion and can be used to understand the complex interactions which occur within this equipment