An eigenmode analysis of time delays in an acoustically coupled multi-bubble system

The acoustic properties of an inhomogeneous bubbly medium are complex owing to the absorption and re-emission of acoustic energy by the bubbles. This phenomena can be approximated by a globally coupled system of linear oscillators. In previous studies, it has been shown that this simple model can produce results that are in qualitative agreement with experimental data. In order to achieve better quantitative agreement with experimental data, time-delays need to be introduced into the mathematical model. In the present study, the resulting delayed differential equations were solved numerically using a 4th order Runge-Kutta method. The numerical methodology was validated by comparing simplified cases with the solution using analytical methods. The effects of time-delay were assessed by comparing non-timedelayed and time-delayed versions of the mathematical model. Results from numerical simulations were then compared to assess the effects and importance of the inclusion of time-delay in the mathematical model. This study shows that the inclusion of time-delay has a noticeable effect on the lower frequency modes of the model. This effect propagates to the higher frequency modes as the magnitude of the time-delay increases. The results also shows that the time-delay shifts the dominant modes from the lower frequency modes to the higher frequency mode

Sound emission on bubble coalescence: imaging, acoustic and numerical experim

Laboratory and numerical experiments are presented on the emission of sound on bubble coalescence. The aim was to better understand the fluid-dynamical mechanisms leading to sound emission. Bubbles were formed from a needle. Coordinated high-speed video and acoustic measurements demonstrated that the emission of high-amplitude sound coincided with the coalescence of a primary bubble with a smaller secondary. A numerical simulation was performed using a compressible level-set front-capturing code, in which a compressible gas and nearly compressible liquid are modelled by a single set of the Navier-Stokes equations with a generic equation of state for both phases. In the simulations, the spherical primary and secondary bubbles initially at acoustic equilibrium were brought into contact. The numerical calculations predicted the frequency of emitted sound and the bubble coalescence dynamics very well. The results suggest that the equalization of Laplace pressures could be the mechanism leading to sound emission

Symmetric mode resonance of bubbles near a rigid boundary - the nonlinear case with time delay effects

A fundamental understanding of the effect of a surface on the resonance frequency of bubbles will be useful in the future development of diagnostic medical ultrasound equipment, and specifically in the area of targeted contrast agents for the screening and possible treatment of colon cancer. In this work we turn to the wall effects on the nonlinear resonance frequency response of air bubbles in water, following on from an earlier work which considered linear interactions (E. M. B. Payne, S. Illesinghe, A. Ooi, R. Manasseh, J. Acoust Soc. Am. 118, 2841-2849 (2005)). Numerical results for micron-sized bubbles near a rigid boundary are presented, showing the shift in frequency caused by the presence of the boundary and the presence of other bubbles. Time delay effects are also included, showing a damping of the frequency response. Simulations are limited to the special case where all bubbles are in phase (i.e., the symmetric mode), which refers to the case where all bubbles have the same initial conditions and are subjected to the same excitation pressure field. As a result they have identical time histories. An experimental method for measuring the frequency response of a single bubble attached to a surface is also briefly mentioned

Cluster formation restricts dynamic nuclear polarization of xenon in solid mixtures

During dynamic nuclear polarization (DNP) at 1.5 K and 5 T, (129)Xe nuclear magnetic resonance (NMR) spectra of a homogeneous xenon/1-propanol/trityl-radical solid mixture exhibit a single peak, broadened by (1)H neighbors. A second peak appears upon annealing for several hours at 125 K. Its characteristic width and chemical shift indicate the presence of spontaneously formed pure Xe clusters. Microwave irradiation at the appropriate frequencies can bring both peaks to either positive or negative polarization. The peculiar time evolution of (129)Xe polarization in pure Xe clusters during DNP can be modelled as an interplay of spin diffusion and T(1) relaxation. Our simple spherical-cluster model offers a sensitive tool to evaluate major DNP parameters in situ, revealing a severe spin-diffusion bottleneck at the cluster boundaries and a significant sample overheating due to microwave irradiation. Subsequent DNP system modifications designed to reduce the overheating resulted in four-fold increase of (129)Xe polarization, from 5.3% to 21%

Passive acoustic bubble sizing in sparged systems

Passive acoustic bubble sizing was investigated in both controlled tests and in a stirred, sparged tank typical of the biotechnology or minerals processing industries. Acoustic techniques have promise for industrial systems where other bubble analysis methods are impractical. Acoustic signals were studied for bubbles precisely formed at higher airflow rates. Acoustic pulses varied with bubble production rate as well as with bubble size. A technique of windowing pulses is proposed. Two alternative versions of this windowing technique were applied to a stirred, sparged tank, giving good agreement. It was shown that, in some cases, it may also be possible to acoustically estimate the spatial distribution of void fraction

Waves attractors in rotating fluids: a paradigm for ill-posed Cauchy problems

In the limit of low viscosity, we show that the amplitude of the modes of oscillation of a rotating fluid, namely inertial modes, concentrate along an attractor formed by a periodic orbit of characteristics of the underlying hyperbolic Poincar\'e equation. The dynamics of characteristics is used to elaborate a scenario for the asymptotic behaviour of the eigenmodes and eigenspectrum in the physically relevant r\'egime of very low viscosities which are out of reach numerically. This problem offers a canonical ill-posed Cauchy problem which has applications in other fields.Comment: 4 pages, 5 fi

Building sustainable market linkages through innovations platforms for technology adoption: Case studies from Uganda, Kenya and Tanzania.

Finding and sustaining markets for Orange-fleshed sweetpotatoes is a challenge in many parts of East Africa. Farmers face numerous difficulties in identifying credible business partners, while traders and other market chain actors are frustrated by inconsistencies in supply. In the Dissemination of New Agricultural Technology in Africa (DONATA) OFSP project, Innovation Platforms for Technology Adoption (IPTAs) in Ethiopia, Kenya, Rwanda, Tanzania and Uganda have brought together relevant value chain stakeholders to develop institutional mechanisms which have supported the up-scaling of OFSP technologies (e.g. new varieties, agronomic practices, and post-harvest activities) and marketing strategies. This paper presents key strides attained in accessing equitable markets by IPTAs in three DONATA project countries. While some IPTAs have segmented the market and differentiated the producer groups along product lines, others have supported various chain actors to strengthen their businesses thus increasing throughput to the markets. Hence in the former case, groups are classified along major OFSP products marketed (vines, roots and processed products), while in the latter, specialized actors take on these functions. Successes include firm contracts for supply of OFSP flour to supermarkets in Kenya, supply of roots to urban markets in Uganda, and sale of vines to individuals and organizations in Tanzania. The major challenges include aligning production to demand for consistent supply, poor market infrastructure and low consumer awareness of the benefits of OFSP. Future prospects lie with newly established relations with big buyers and also working closely with other initiatives to consolidate gains achieved to date

An analysis of observed daily maximum wind gusts in the UK

The greatest attention to the UK wind climatology has focused upon mean windspeeds, despite a knowledge of gust speeds being essential to a variety of users. This paper goes some way to redressing this imbalance by analysing observed daily maximum gust speeds from a 43-station network over the period 1980–2005. Complementing these data are dynamically downscaled reanalysis data, generated using the PRECIS Regional Climate Modelling system, for the period 1959–2001. Inter-annual variations in both the observed and downscaled reanalysis gust speeds are presented, with a statistically significant (at the 95% confidence interval) 5% increase across the network in daily maximum gust speeds between 1959 and the early 1990s, followed by an apparent decrease. The benefit of incorporating dynamically downscaled reanalysis data is revealed by the fact that the decrease in gust speeds since 1993 may be placed in the context of a very slight increase displayed over the longer 1959–2001 period. Furthermore, the severity of individual windstorm events is considered, with high profile recent events placed into the context of the long term record. A daily cycle is identified from the station observations in the timing of the daily maximum gust speeds, with an afternoon peak occurring between 12:00–15:00, exhibiting spatial and intra-annual variations