PHYSICAL MATHEMATICS SEMINAR
TITLE: MATHEMATICAL MODELS OF VISCOUS SINTERING
SPEAKER: DARREN CROWDY
Imperial College
London & Massachusetts Institute of Technology
ABSTRACT:
Viscous sintering is an industrial manufacturing process (e.g for metals, glasses, ceramics)
in which an initial compact of touching particles (typically, a few microns in diameter) is
heated to a high enough temperature that the particles become mobile and coalesce due to
surface energy (and other) effects. The compact densifies as the inter-particulate pores close up.
Mesoscale modeling of this process relies on insights into the microscale behavior of the system.
This talk will survey recent advances in the mathematical modeling of such systems. A general
class of free boundary problems consisting of very viscous (Stokes) flow driven by surface tension
will be considered and shown, in the planar case, to have useful analytical properties. This leads to
a wide range of exact mathematical solutions as well as simple models relevant to describing both
early-stage and late-stage viscous sintering. The work has also led to a surprising ``generalized
Stokes paradox'' which highlights some unexpected, and physically counter-intuitive, limitations of
the mathematical model when the interaction of multiple pores (or bubbles) in Stokes flow is involved.
TUESDAY, MAY 6, 2003
2:30 pm
Building 2, Room 338
Refreshments will be served at 3:30 PM in Room 2-349
Massachusetts Institute of Technology
Department of Mathematics
Cambridge, MA 02139