Page 323 - Process Modelling and Simulation With Finite Element Methods
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3 10        Process Modelling and Simulation with Finite Element Methods

         downwards. Hence, the shape of rising drop changes drastically. The lower drop
          almost skids downward traveling drop and changes the contact point between the
          interacting drops. Finally, coalescence takes place at 3.8 seconds.
             Thus,  it  is  found  that  the  contact  point  of  the  interacting  drops  is  very
          significant  in  the  coalescence  phenomenon.  Different  types  of  contacting
          schemes are observed  for different  approaches  considered  in the present  set of
          simulations merely by changing the initial condition.

         8.5  Summary

         The  level  set  method  is  extensively  used  in  the  present  simulations  to  study
         computationally  the  coalescence  of  droplets  in  a  two-phase  system.  FEMLAB
          handles  computationally  intensive  multi-phase  modeling  with  ease  using  its
         multiphysics utility that allows the coupling of different physics into one problem
          as  demonstrated  here  for  the  level-set  method.  In  the  present  simulations,  the
         coalescence  phenomenon  has  been  extensively  studied  using  various
          configurations  for  the  approach  of  drops.  The  curvature  analysis  performed
          captures the rupture of the interface at the time of the coalescence.


          Acknowledgements

          We acknowledge  Per-Olof  Persson  for use  of  his  FEMLAB  code  which  was
          modified  appropriately  to  treat  coalescence.  We  thank  Peter  Norgaard  for
          helpful discussions.

          References

           1.  S. 0. Unverdi  and  G.  Tryggvason,  A  front-tracking  method  for  viscous,
              incompressible, multi-fluid flows, J. Comput. Phys. 100,25 (1992).
           2.  J.  M.  Boulton-Stone  and  Blake,  Gas  bubbles  bursting  at  a  free  surface,
              J. Fluid Mech. 254,437 (1993).
           3.  W. J. Rider  and D. B. Kothe, Reconstructing  volume traclung, J. Comput.
              Phys. 141, 112 (1998).
           4.  N.  Takada,  M.  Misawa,  A.  Tomiyama  and  S.  Fujiwara,  Numerical
              simulation of two- and three-dimensional  two-phase fluid motion by lattice
              Boltzmann method, Comp. Phys. Comm., 129,233 (2000).
           5.  M. Verschueren, F.N. van de Vosse,  and H.E.H. Meijer, “Diffuse interface
              modeling of thermocapillary flow instabilities in a Hele-Shaw cell,” J. Fluid
              Mech.  434:153-166,2001.
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