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Prof. Dejan Slepcev (Carnegie Mellon University, Pittsburgh,
USA)
| Speaker: |
Prof. Dejan Slepcev
(Carnegie Mellon University, Pittsburgh, USA)
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| Date: |
Wednesday June 22, 2011
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| Title: |
Crossover
of
the coarsening rates in demixing of binary viscous fluids
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Abstract
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When
a
binary fluid mixture is quenched, two domains of two different
equilibrium volume fractions form. The phases are divided by a
characteristic interfacial layer. The dynamics is driven by the energy
which concentrates along the interfacial layer. The area of the
interfacial layer decreases with time by material transport from
higher-curvature regions to lower-curvature regions. As the time
progresses the configuration coarsens and the length scale, L,
characterizing the interfacial pattern grows.
There are two parallel transport mechanisms. Material can be
transported by diffusion, the relative motion of the two different
species, through the bulk or by convection, the transport by the bulk
flow. It turns out that each transport mechanism becomes dominant
during certain time interval in the demixing process.
We will discuss how which mechanism dominates affects the rate of
coarsening. In particular we will discuss how one can rigorously
establish coarsening rates in form of weak upper bounds: the
coarsening cannot proceed faster than L ≤ t1/3 for diffusion-mediated
and subsequently L ≤ t for convection-mediated transport. These rates
are in agreement with the heuristically expected coarsening rates. This
is based on joint work with Felix Otto and Christian Seis.
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