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Applied Math Seminar – Shibin Dai, University of Alabama

January 18 @ 11:00 am - 12:00 pm

Title: Mean field models for thin film droplet coarsening

Abstract: A thin liquid film coating a solid substrate is unstable and the late stage morphology is essentially quasiequilibrium droplets connected by an ultra thin film. Droplets exchange mass and coarsening occurs — the total number of droplets N(t) decreases while the average size of droplets increases. It is predicted that N(t) obeys a power law $N(t) \sim ct^{-2/5}$ in the 1D case. For the physically realistic case when the underlying substrate is two dimensional, it is predicted that the average volume of droplets V follows a temporal power-logarithmic law: $V^{4/3}lnV \sim ct.$ We will discuss some mean field models for both the 1D and 2D cases, and prove that the coarsening rates can not exceed the above mentioned power laws. If time permits, we will discuss a rigorous derivation of the 2D mean field model.

Details

Date:
January 18
Time:
11:00 am - 12:00 pm
Event Categories:
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Organizer

Wei Zhu
Phone:
205-348-1987