David Leppinen

Capillary pinch-off in inviscid fluids

The axisymmetric pinch-off of an inviscid drop of density ρ1 immersed in an ambient inviscid fluid of density ρ2 is examined over a range of the density ratio D=ρ2/ρ1. For moderate values of D, time-dependent simulations based on a boundary-integral representation show that inviscid pinch-off is asymptotically self-similar with both radial and axial length scales decreasing like τ2/3 and velocities increasing like τ−1/3, where τ is the time to pinch-off. The similarity form is independent of initial conditions for a given value of D. The similarity equations are solved directly using a modified Newton’s method and continuation on D to obtain a branch of similarity solutions for 0⩽D⩽11.8. All solutions have a double-cone interfacial shape with one of the cones folding back over the other in such a way that its internal angle is greater than 90°. Bernoulli suction due to a rapid internal jet from the narrow cone into the folded-back cone plays a significant role near pinching. The similarity solutions are l...

Cavitation and bubble dynamics: the Kelvin impulse and its applications

Cavitation and bubble dynamics have a wide range of practical applications in a range of disciplines, including hydraulic, mechanical and naval engineering, oil exploration, clinical medicine and sonochemistry. However, this paper focuses on how a fundamental concept, the Kelvin impulse, can provide practical insights into engineering and industrial design problems. The pathway is provided through physical insight, idealized experiments and enhancing the accuracy and interpretation of the computation. In 1966, Benjamin and Ellis made a number of important statements relating to the use of the Kelvin impulse in cavitation and bubble dynamics, one of these being ‘One should always reason in terms of the Kelvin impulse, not in terms of the fluid momentum…’. We revisit part of this paper, developing the Kelvin impulse from first principles, using it, not only as a check on advanced computations (for which it was first used!), but also to provide greater physical insights into cavitation bubble dynamics near boundaries (rigid, potential free surface, two-fluid interface, flexible surface and axisymmetric stagnation point flow) and to provide predictions on different types of bubble collapse behaviour, later compared against experiments. The paper concludes with two recent studies involving (i) the direction of the jet formation in a cavitation bubble close to a rigid boundary in the presence of high-intensity ultrasound propagated parallel to the surface and (ii) the study of a ‘paradigm bubble model’ for the collapse of a translating spherical bubble, sometimes leading to a constant velocity high-speed jet, known as the Longuet-Higgins jet.

High Speed Imaging of Cavitation around Dental Ultrasonic Scaler Tips

Cavitation occurs around dental ultrasonic scalers, which are used clinically for removing dental biofilm and calculus. However it is not known if this contributes to the cleaning process. Characterisation of the cavitation around ultrasonic scalers will assist in assessing its contribution and in developing new clinical devices for removing biofilm with cavitation. The aim is to use high speed camera imaging to quantify cavitation patterns around an ultrasonic scaler. A Satelec ultrasonic scaler operating at 29 kHz with three different shaped tips has been studied at medium and high operating power using high speed imaging at 15,000, 90,000 and 250,000 frames per second. The tip displacement has been recorded using scanning laser vibrometry. Cavitation occurs at the free end of the tip and increases with power while the area and width of the cavitation cloud varies for different shaped tips. The cavitation starts at the antinodes, with little or no cavitation at the node. High speed image sequences combined with scanning laser vibrometry show individual microbubbles imploding and bubble clouds lifting and moving away from the ultrasonic scaler tip, with larger tip displacement causing more cavitation.

Pulsating Bubbles Near Boundaries

The highly nonlinear behaviour of vigorously pulsating non-spherical bubbles near rigid and compliant boundaries, free surfaces and fluid-fluid interfaces has a wide application, ranging from problems in hydraulic and naval engineering, turbopumps in rockets, seismic airguns in marine exploration, underwater explosions, surface cleaning, mixing processes at interfaces and sonochemistry through to a diversity of uses in therapeutic medicine and surgery including shockwave lithitropsy, cell ablation in cancers, sonoporation and drug delivery using contrastagent bubbles. In this chapter the generic features of the bubble dynamics are presented through an appreciation of the fundamental physics associated with the phenomenon, the latest analytical and computational developments together with the available knowledge provided by experimentation. The study for incompressible and weakly compressible models is presented with a view to providing a better understanding of cavitation phenomena such that improved engineering and industrial design may be an outcome.

Imaging and analysis of individual cavitation microbubbles around dental ultrasonic scalers

&NA; Cavitation is a potentially effective and less damaging method of removing biofilm from biomaterial surfaces. The aim of this study is to characterise individual microbubbles around ultrasonic scaler tips using high speed imaging and image processing. This information will provide improved understanding on the disruption of dental biofilm and give insights into how the instruments can be optimised for ultrasonic cleaning. Individual cavitation microbubbles around ultrasonic scalers were analysed using high speed recordings up to a million frames per second with image processing of the bubble movement. The radius and rate of bubble growth together with the collapse was calculated by tracking multiple points on bubbles over time. The tracking method to determine bubble speed demonstrated good inter‐rater reliability (intra class correlation coefficient: 0.993) and can therefore be a useful method to apply in future studies. The bubble speed increased over its oscillation cycle and a maximum of 27 ms−1 was recorded during the collapse phase. The maximum bubble radii ranged from 40 to 80 &mgr;m. Bubble growth was observed when the ultrasonic scaler tip receded from an area and similarly bubble collapse was observed when the tip moved towards an area, corresponding to locations of low pressure around the scaler tip. Previous work shows that this cavitation is involved in biofilm removal. Future experimental work can be based on these findings by using the protocols developed to experimentally analyse cavitation around various clinical instruments and comparing with theoretical calculations. This will help to determine the main cleaning mechanisms of cavitation and how clinical instruments such as ultrasonic scalers can be optimised. HighlightsCavitation bubbles are involved in the removal of bacterial biofilm around dental ultrasonic scalers.The maximum radius of these bubbles ranged from 40 to 80 &mgr;m.Able to track bubbles forming around dental ultrasonic scalers.Image analysis and manual tracking enabled bubble radius and speed to be calculated in their life cycle.

Acoustic bubble dynamics in a microvessel surrounded by elastic material

This paper is concerned with microbubble dynamics in a blood vessel surrounded by elastic tissue subject to ultrasound, which are associated with important applications in medical ultrasonics. Both the blood flow inside the vessel and the tissue flow external to the vessel are modeled using the potential flow theory coupled with the boundary element method. The elasticity of tissue is modeled through the inclusion of a pressure term in the dynamic boundary condition at the interface between the two fluids. Weakly viscous effects are considered using viscous potential flow theory. The numerical model is validated by comparison with the theoretical results of the Rayleigh-Plesset equation for spherical bubbles, the numerical results for acoustic bubbles in an unbounded flow, and the experimental images for a spark generated bubble in a rigid circular cylinder. Numerical analyses are then performed for the bubble oscillation, jet formation and penetration through the bubble, and the deformation of the vessel...

Bubble Behavior Near a Two Fluid Interface

The influence of rigid and free boundaries on the dynamics of bubbles has been researched extensively, both experimentally and theoretically. Experiments by (Benjamin and Ellis 1966) showed that the presence of a solid boundary caused the formation of a liquid jet through the bubble, forming a toroidal bubble. This behavior has been observed in many other experiments since, including (Brujan et al. 2002), (Phillip and Lauterborn 1998), (Tomita and Shima 1986), (Lauterborn and Bolle 1975). Similar behavior is also observed when a bubble collapses near a free surface. In such conditions bubble jetting may be directed away from the surface, with a counter-jet forming out of the free surface. Experiments using spark-generated bubbles by (Blake and Gibson 1981) under free fall conditions and (Chahine and Bovis 1980) in standard gravity showed this counter-jet to be greatly influenced by the standoff distance. Bubbles formed very close to the surface generate severe vertical surface spikes, and those at greater distances create much smaller and smoother deformations to the surface.