Applied Maths Seminar: Phillips -- Impulsively Generated Drops

William Phillips 
Mathematics, Swinburne University of Technology 

This talk is concerned with the evolution of an unbounded inviscid fluid-fluid interface
subject to an axisymmetric impulse in pressure and how inertial, interfacial and
gravitational forces affect that evolution.  The construct was motivated by the
occurrence of lung hemorrhage resulting from ultrasonic imaging and pursues the notion
that bursts of ultrasound act to expel droplets that puncture the soft air-filled sacs
in the lung plural surface allowing them to fill with blood.  The evolution of the free
surface is described by a boundary integral formulation which is integrated forward in
time numerically.  As the interface evolves, it is seen, depending upon the levels of
gravity and surface tension, to form either axisymmetric surface jets, waves or
droplets.  Moreover the droplets may be spherical, inverted tear-shaped or pancake
like.  Also of interest is the finite time singularity which occurs when the drop
pinches off; this is seen to be of the power law type with an exponent of 2/3.