John R. Blake's research while affiliated with University of Birmingham and other places

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.

In hydraulic and naval engineering, cavitation is often associated with intense vortical structures. In this paper, we discuss developments associated with solid spheres and bubbles near a tip-vortex and a ring vortex. The first part of the paper reviews the mathematical and numerical development of vortex filament methods and representation of solid spheres and bubbles. Equations of motion are based on the Biot–Savart law and the Kelvin impulse. The classic studies of the motion of a sphere towards and parallel to the vortex axis is extended to consider bubble motion in the presence of a line vortex. The second study is concerned with bubble–vortex ring interaction for both small and large bubble examples. The multipole approach used in this paper compares favourably with the numerical experimental studies of Chahine (1995), ‘Bubble interactions with vortices’, in Fluid Vortices, Kluwer Academic Press, for the prediction of bubble shapes.

In this paper we examine the dynamics of an initially stable bubble due to ultrasonic forcing by an acoustic wave. A tissue layer is modelled as a density interface acted upon by surface tension to mimic membrane effects. The effect of a rigid backing to the thin tissue layer is investigated. We are interested in ultrasound contrast agent type bubbles which have immediate biomedical applications such as the delivery of drugs and the instigation of sonoporation. We use the axisymmetric boundary integral technique detailed in Curtiss et al. (J. Comput. Phys., 2013, submitted) to model the interaction between a single bubble and the tissue layer. We have identified a new peeling mechanism whereby the re-expansion of a toroidal bubble can peel away tissue from a rigid backing. We explore the problem over a large range of parameters including tissue layer depth, interfacial tension and ultrasonic forcing.

Fluid mechanics plays a vital role in early vertebrate embryo development, an example being the establishment of left-right asymmetry. Following the dorsal-ventral and anterior-posterior axes, the left-right axis is the last to be established; in several species it has been shown that an important process involved with this is the production of a left-right asymmetric flow driven by 'whirling' cilia. It has previously been established in experimental and mathematical models of the mouse ventral node that the combination of a consistent rotational direction and posterior tilt creates left-right asymmetric flow. The zebrafish organising structure, Kupffer's vesicle, has a more complex internal arrangement of cilia than the mouse ventral node; experimental studies show the flow exhibits an anticlockwise rotational motion when viewing the embryo from the dorsal roof, looking in the ventral direction. Reports of the arrangement and configuration of cilia suggest two possible mechanisms for the generation of this flow from existing axis information: (1) posterior tilt combined with increased cilia density on the dorsal roof, and (2) dorsal tilt of 'equatorial' cilia. We develop a mathematical model of symmetry breaking cilia-driven flow in Kupffer's vesicle using the regularized Stokeslet boundary element method. Computations of the flow produced by tilted whirling cilia in an enclosed domain suggest that a possible mechanism capable of producing the flow field with qualitative and quantitative features closest to those observed experimentally is a combination of posteriorly tilted roof and floor cilia, and dorsally tilted equatorial cilia.

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.

Cilia and flagella are actively bending slender organelles, performing functions such as motility, feeding and embryonic symmetry breaking. We review the mechanics of viscous-dominated microscale flow, including time-reversal symmetry, drag anisotropy of slender bodies, and wall effects. We focus on the fundamental force singularity, higher-order multipoles, and the method of images, providing physical insight and forming a basis for computational approaches. Two biological problems are then considered in more detail: 1) left-right symmetry breaking flow in the node, a microscopic structure in developing vertebrate embryos, and 2) motility of microswimmers through non-Newtonian fluids. Our model of the embryonic node reveals how particle transport associated with morphogenesis is modulated by the gradual emergence of cilium posterior tilt. Our model of swimming makes use of force distributions within a body-conforming finite-element framework, allowing the solution of nonlinear inertialess Carreau flow. We find that a three-sphere model swimmer and a model sperm are similarly affected by shear-thinning; in both cases swimming due to a prescribed beat is enhanced by shear-thinning, with optimal Deborah number around 0.8. The sperm exhibits an almost perfect linear relationship between velocity and the logarithm of the ratio of zero to infinite shear viscosity, with shear-thickening hindering cell progress.

Laser-generated cavitation bubbles in a thin liquid layer lead to the formation of fast liquid jets at both the free surface to the liquid layer and as an opposing jet within the collapsing bubble. This paper studies this phenomenom from both an analytical perspecitive, using the Kelvin impulse, and through computational techniques based on the boundary integral method. Output includes bubble and jet shapes and the percentage of the impulse and energy in the jet of the collapsing bubble. Calculations indicate that in excess of 30% of the liquid energy and 60% of the impulse can be found in the jet in the examples considered in this paper.

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.

This paper investigates the behaviour of a non-spherical cavitation bubble in an acoustic standing wave. The study has important applications to sonochemistry and in understanding features of therapeutic ultrasound in the megahertz range, extending our understanding of bubble behaviour in the highly nonlinear regime where jet and toroidal bubble formation may be important. The theory developed herein represents a further development of the material presented in Part 1 of this paper (Wang & Blake, J. Fluid Mech. vol. 659, 2010, pp. 191–224) to a standing wave, including repeated topological changes from a singly to a multiply connected bubble. The fluid mechanics is assumed to be compressible potential flow. Matched asymptotic expansions for an inner and outer flow are performed to second order in terms of a small parameter, the bubble-wall Mach number, leading to weakly compressible flow formulation of the problem. The method allows the development of a computational model for non-spherical bubbles by using a modified boundary-integral method. The computations show that the bubble remains approximately of a spherical shape when the acoustic pressure is small or is initiated at the node or antinode of the acoustic pressure field. When initiated between the node and antinode at higher acoustic pressures, the bubble loses its spherical shape at the end of the collapse phase after only a few oscillations. A high-speed liquid bubble jet forms and is directed towards the node, impacting the opposite bubble surface and penetrating through the bubble to form a toroidal bubble. The bubble first rebounds in a toroidal form but re-combines to a singly connected bubble, expanding continuously and gradually returning to a near spherical shape. These processes are repeated in the next oscillation.