  A generalized boundary integral method is developed to investigate the
rheology of multiple emulsions with orderly structures up to n layers and up to
mi droplets in the i-th layer in microchannels with various geometries.
Recently, as fine templates to prepare microcapsules for targeted drug
delivery, multiple emulsions with complex structures have been generated
through microfluidics. The deformation and breakup of multiple emulsions are
critical to the transport and release of their inclusion. However, the
numerical investigation of the rheology of multiple emulsions is only limited
to a simple case, i.e., double emulsions with only one core, currently. In this
letter, two-dimensional boundary element method is employed to study the
rheology of multiple emulsions under modest outer flows. Especially, the
hydrodynamics of the engulfed droplets, which might be useful in their
controlled coalescence for chemical reactions and in their controlled release
for drug delivery, is investigated. Although the entire particle has an
equilibrium shape under modest outer flows initially, the slow movement of the
inner droplets might cause the contact of the outer and inner interface, and
eventually induces a breakup of the particle. Thus, appropriate outer flows and
internal structures of multiple emulsions might provide a possibility to
execute the control release through hydrodynamics.
