Simulating the interaction between a falling solid object and a soap film
I. T. Davies
Department of Mathematics, Aberystwyth University, Aberystwyth, Ceredigion SY23 3BZ, UK
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Simulations were conducted in Surface Evolver, Version 2.70.
See http://facstaff.susqu.edu/brakke/evolver/evolver.html, starting
from the structure given in the file superquad_soapfilm_sim.fe.
At each iteration, we dump information about the energy of the
structure, the position and orientation of the super-quadric object,
and the forces exerted on the object by the foam into the given
data files. Information about the relevant parameters for each
data file is given below.
To generate the figures plotted in the paper, we analysed this
data using bespoke Python programs and plotted the result using
the matplotlib library and gnuplot, version 5.0
(http://www.gnuplot.info/). The snapshots from the simulations
are generated directly from Surface Evolver.
Each file includes 20 columns, which represent the following information:
• itnum – Iteration number. Each line in the data files is for a
particular iteration.
• alpha_n1, alpha_n2, alpha_n3 – The angles that the normal vectors
defining the object make with the vertical z-axis.
• net_forcex, net_forcey, net_forcez – The x,y,z components of the
network force exerted on the object by the soap film.
• pre_forcex, pre_forcey, pre_forcez – The x,y,z components of the
pressure force exerted on the object by the foam.
• net_torque_x, net_torque_y, net_torque_z - The x,y,z components
of the network torque exerted on the object by the soap film.
• pre_torque_x, pre_torque_y, pre_torque_z - The x,y,z components
of the pressure torque exerted on the object by the soap film.
We ran many simulations, varying a parameter at a time. The files included
in this dataset are as follows:
(i) sphere_soapfilm_rc_XX.dat give the information from simulations for
a sphere with radius 1 falling through a soap film contained in a tube
with radius XX.
(ii) superquad_lambda_XX_Bo1.dat give the information from simulations
for a super-quadric object with shape parameter \lambda = XX and Bond
number 1 falling through a soap film contained in a cylinder with radius 4.
(iii) stable_orientation_sphere_Bo1.dat, stable_orientation_flat_cube_Bo1.dat¸
stable_orientation_rotated_cube_Bo1.dat stable_orientation_diagonal_cube_Bo1.dat
include the results of dropping a sphere and cubes in the flat, rotated and
diagonal stable orientations (with Bond number 1) through a soap film with radius 4.
(iv) The files “cube_soapfilm_n1_X_n2_Y.dat" (36 files) are for simulations in
which a super-quadric object (with \lambda=10 and Bond number one) falls through
a soap film from different initial orientations. X denotes the multiple of
0.05\pi the cube has been rotated around the x-axis during the initial setup
while Y denotes the multiple of 0.05\pi the cube has been rotated around the
y-axis.
(v) The following files are for super-quadric objects falling from four initial
(x,y) positions from above a soap film, with these x,y coordinates given by
XXXXXXX and YYYYYYY in the file names:
• “sphere_x_XXXXXXX_y_YYYYYYY.dat” – object is a sphere
• “cube_flat_l6_x_XXXXXXX_y_YYYYYYY.dat” – super-quadric object in the flat
orientation (\lambda=6)
• “cube_flat_l10_x_XXXXXXX_y_YYYYYYY.dat” – super-quadric object in the flat
orientation (\lambda=10)
• “cube_diagonal1_x_ XXXXXXX_y_YYYYYYY.dat” – super-quadric object in a
diagonal orientation (with a vertical face closest to the cylinder wall)
and \lambda=10.
• “cube_diagonal2_x_ XXXXXXX_y_YYYYYYY.dat” – super-quadric object in a
diagonal orientation (with two slanted faces closest to the cylinder wall)
and \lambda=10.
• “cube_rotated_x_XXXXXXX_y_YYYYYYY.dat” – super-quadric object in a
rotated orientation with \lambda=10.
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ITD
August 2018