Cavitation in medicine.

We generally think of bubbles as benign and harmless and yet they can manifest the most remarkable range of physical effects. Some of those effects are the stuff of our everyday experience as in the tinkling of a brook or the sounds of breaking waves at the beach. But even these mundane effects are examples of the ability of bubbles to gather, focus and radiate energy (acoustic energy in the above examples).

Improvement of acoustic theory of ultrasonic waves in dilute bubbly liquids.

The theory of the acoustics of dilute bubbly liquids is reviewed, and the dispersion relation is modified by including the effect of liquid compressibility on the natural frequency of the bubbles. The modified theory is shown to more accurately predict the trend in measured attenuation of ultrasonic waves. The model limitations associated with such high-frequency waves are discussed.

Statistical equilibrium of bubble oscillations in dilute bubbly flows.

The problem of predicting the moments of the distribution of bubble radius in bubbly flows is considered. The particular case where bubble oscillations occur due to a rapid (impulsive or step change) change in pressure is analyzed, and it is mathematically shown that in this case, inviscid bubble oscillations reach a stationary statistical equilibrium, whereby phase cancellations among bubbles with different sizes lead to time-invariant values of the statistics. It is also shown that at statistical equilibrium, moments of the bubble radius may be computed using the period-averaged bubble radius in place of the instantaneous one.

Pressure wave propagation in a shaken granular bed.

Pressure waves in a granular material travel through particle contact points and are primarily transmitted by the "force chains" that carry most of the load in a granular medium. However, these force chains tend to be fragile and ephemeral and can be disrupted by very minor perturbations including the waves themselves. External vibration also disrupts the force chains and therefore also changes the wave propagation characteristics.

Pressure wave propagation in a granular bed.

The transmission of pressure waves in granular materials is complicated by the heterogeneity and nonlinearity inherent in these systems. Such waves are propagated through particle contacts primarily along the "force chains" which carry most of the load in granular materials. These fragile and ephemeral chains coupled with irregular particle packing lead to the observed heterogeneity.

Lumped parameter model for computing the minimum pressure during mechanical heart valve closure.

The cavitation inception threshold of mechanical heart valves has been shown to be highly variable. This is in part due to the random distribution of the initial and final conditions that characterize leaflet closure. While numerous hypotheses exist explaining the mechanisms of inception, no consistent scaling laws have been developed to describe this phenomenon due to the complex nature of these dynamic conditions.