PHYSICAL MATHEMATICS SEMINAR
TITLE: RIPENING OF POROUS MEDIA
SPEAKER: BENNY DAVIDOVITCH
POST-DOCTORAL RESEARCHER
EXXONMOBIL RESEARCH AND ENGINEERING
ABSTRACT:
When solid grains are put in a saturated solution they undergo a coarsening process in the
course of which one big chunk is formed. This general phase-separation phenomenon is
known as "Ostwald ripening". Limiting cases of the ripening process, when the volume
fraction of the solid grains in the liquid is either very small (Lifshitz-Slyozov theory) or
close to 1 (grain growth, foams), are governed by scaling laws and were studied extensively
since the 1950's.
In this talk I will focus on the intermediate case, where the volume fraction of the solid grains
is relatively high (0.3-0.8), and both phases might be connected. This situation is typical for
sedimentary porous media, especially oil and water reservoirs, whose coarsening process
occurs over geological time scales. I will show that in this case the phase space of possible
morphologies contains many unstable equilibrium states that can be considered as hyperbolic .
fixed points of the dynamics. These fixed points are surfaces of constant mean curvature (CMC)
he morphology and the dynamics of the system will be described by characterizing these
configurations using tools from differential geometry and linear stability analysis. If time allows,
I will discuss briefly a preliminary experimental work on the subject.
TUESDAY, FEBRUARY 11, 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