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SUMMARY:A multi-scale framework to model dry foam dynamics - Sethian\, J (
 University of California\, Berkeley)
DTSTART:20140226T101500Z
DTEND:20140226T110000Z
UID:TALK51105@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-author: Robert I. Saye (Department of Mathematics\, Univers
 ity of California\, Berkeley) \n\nWe describe a mathematical and computati
 onal framework for modeling soap bubble dynamics. We use a scale-separatio
 n approach to split the problem into three distinct phases that cycle over
  and over. During the rearrangement phase\, a cluster of bubbles readjusts
  itself as surface tension in the membranes pushes on air in the pockets a
 ccording to multi-phase incompressible flow\, until a new macroscopic equi
 librium is reached. Once this large-scale equilibrium is reached\, we then
  invoke a drainage stage in which liquid in the lamellae drains into the P
 lateau borders according to thin film equations. Once one of the membranes
  becomes too thin\, the model ruptures the equilibrium by removing that me
 mbrane\, moving the cluster far from equilibrium\, and leading back to the
  rearrangement stage. \n\nThis approach relies on several different comput
 ational methodologies\, including (1) a Voronoi Implicit Interface Method 
 (VIIM) to track the moving interface as a single PDE defined on a fixed me
 sh\; (2) a second order projection method to solve the incompressible Navi
 er-Stokes equations during the macroscopic rearrangement phase\, describin
 g the transport of fluid in the membranes\; (3) a finite element formulati
 on of a set of thin film equations for the fluid in the interfaces themsel
 ves\, defined on the lamellae and Plateau borders\, and linked together th
 rough coupled boundary conditions to describe drainage and (4) a rupture m
 echanism which includes topological rearrangement. We present results from
  a series of computations\, including bubble cascades and thin film interf
 erence from a cluster of collapsing bubbles. \n
LOCATION:Seminar Room 1\, Newton Institute
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