(235e) Multi-Length Interfacial Dynamics in Microchannels Via Spectral Boundary Element Algorithms

The dynamics of multi-phase soft particle, such as droplets, capsules
and erythrocytes, in confined solid geometries under Stokes flow
conditions is a problem of great technological and fundamental interest
since it is encountered in a broad range of industrial, biomedical and
physiological processes. The last few decades, interfacial dynamics in
Stokes flow via the solution of boundary integral equations has developed
considerably.  The main benefits of this approach are the reduction of
the problem dimensionality by one and the great parallel scalability.
Thus, considerable progress has been made for the study of droplets and
bubbles in viscous flows, as well as membrane-like interfaces such as
those in artificial capsules and erythrocytes, in microfluidic channels
and the microcirculation.

In this talk we will present our efforts to study efficiently a family
of particularly challenging interfacial problems; namely, the case of
multi-length interfacial dynamics in Stokes flow.  In many interfacial
processes, multiple length scales appear and affect the interfacial
dynamics. Common examples constitute the drop coalescence process
(which, beyond the drop size, also includes the small gap between
the interfaces), droplets/cells in close proximity to solid surfaces
(as in microfluidic channels, porous media, and the microcirculation)
as well as the appearance of tips and necks during large interfacial
deformation in strong flows.

Currently the study of multi-length interfacial dynamics in three
dimensions constitutes a computational challenge owing to the requirement
of extreme numerical accuracy for the accurate determination of the
dynamics between the regular (particle-size) scale and the small length
scale present in these problems.  To overcome this difficulty, we have
developed a series of efficient and highly-accurate interfacial algorithms
based on our Spectral Boundary Element implementation for Stokes flow.
As applications for multi-length interfacial systems, we will present
our investigation of large deformation of soft particles, involving
pointed tips and tails in micro-channels.  We will also present our
investigation of die particles, which can be orders of magnitude smaller
than the channel size.