  A variety of numerical methods exist for the study of deformable particles in
dense suspensions. None of the standard tools, however, currently include
volume-changing objects such as oscillating microbubbles in three-dimensional
periodic domains. In the first part of this work, we develop a novel method to
include such entities based on the boundary integral method. We show that the
well-known boundary integral equation must be amended with two additional terms
containing the volume flux through the bubble surface. We rigorously prove the
existence and uniqueness of the solution. Our proof contains as a subset the
simpler boundary integral equation without volume-changing objects (such as red
blood cell or capsule suspensions) which is widely used but for which a formal
proof in periodic domains has not been published to date.
  In the second part, we apply our method to study microbubbles for targeted
drug delivery. The ideal drug delivery agent should stay away from the
biochemically active vessel walls during circulation. However, upon reaching
its target it should attain a near-wall position for efficient drug uptake.
Though seemingly contradictory, we show that lipid-coated microbubbles in
conjunction with a localized ultrasound pulse possess precisely these two
properties. This ultrasound-triggered margination is due to hydrodynamic
interactions between the red blood cells and the oscillating lipid-coated
microbubbles which alternate between a soft and a stiff state. We find that the
effect is very robust, existing even if the duration in the stiff state is more
than three times lower than the opposing time in the soft state.
