Page 318 - Process Modelling and Simulation With Finite Element Methods

Modeling of Multi-Phase Flow Using the Level Set Method 305

experience any gravitational force. This is the bare effect of the acoustic
levitation, without consideration of capillary-gravity waves induced on the free
surface by acoustic interactions. But, lower drop is rising in a column due to
buoyancy. The above mentioned changes can be incorporated by changing Fy
term in sub-domain settings Menu as follows:

Subdomain Mode
Select Incompressible N-S from Multiphysics Menu
Select the Coefficient tab
Set Fy = sigma*kappa*smdelta*phiy + ro*gy*(tanh(-(y-yc))>O)

Apply/OK
The new constant used yc is set to 2, i.e. y co-ordinate of the center of upper
bubble. The force term used in this way applies no gravity to upper drop whereas
lower drop experiences gravitational force equal to pg.
Numerical results are shown in Figure 8.3 in terms of contour plot of
level set function at @=O and surface plot of velocity field. The two drops
initially separated by a distance equal to two times their diameter approach
quite faster than the previous simulation where both the drops were rising.
Eventually, two drops coalesce quickly and evolution of the interface of two
drops after the coalescence event has been brought out through this simulation.
Cusp formation is observed at time t=2 sec. The coalesced drop regains its
original shape as it rises in a column. The different shapes of two drops before
collision can be attributed to the fact that pressure is continuously decreasing
along the length of the column and hence radii of curvature would increase
according to the Young-Laplace equation. This can be validated by changing the
configuration so that pressure change is uniform as described in the following
section.

Curvature Analysis
The procedure outlined for the curvature analysis of the coalescence of two
drops under gravity is followed for the coalescence of acoustically suspended
drops. The fem structure is exported to the MATLAB workspace after the
simulation is over and MATLAB model m-file ana1ysis.m is run to study the
standard deviation and mean of Id as shown in the Figure 8.5.
Both the first and second moments of Id show a sharp peak at the time of
the coalescence, attributed to the rupture of the interface.