Bubble Collision Simulations in Milliseconds | Two Minute Papers #231


Dear Fellow Scholars, this is Two Minute Papers
with Károly Zsolnai-Fehér.
This paper is about simulating on a computer
what happens when bubbles collide.
Prepare for lots of beautiful footage.
This is typically done by simulating the Navier-Stokes
equations that describe the evolution of the
velocity and pressure within a piece of fluid
over time.
However, because the world around us is a
continuum, we cannot compute these quantities
in an infinite number of points.
So, we have to subdivide the 3D space into
a grid, and compute them only in these gridpoints.
The finer the grid, the more details appear
in our simulations.
If we try to simulate what happens when these
bubbles collide, we would need to create a
grid that can capture these details.
This is an issue, because the thickness of
a bubble film is in the order of 10-800 nanometers,
and this would require a hopelessly fine high-resolution
grid.
By the way, measuring the thickness of bubbles
is a science of its own, there is a fantastic
reddit discussion on it, I put a link to it
in the video description, make sure to check
it out.
So, these overly fine grids take too long
to compute, so what do we do?
Well, first, we need to focus on how to directly
compute how the shape of soap bubbles evolves
over time.
Fortunately, from Belgian physicist Joseph
Plateau we know that they seek to reduce their
surface area, but, retain their volume over
time.
One of the many beautiful phenomena in nature.
So, this shall be the first step – we simulate
forces that create the appropriate shape changes
and proceed into an intermediate state.
However, by pushing the film inwards, its
volume has decreased, therefore this intermediate
state is not how it should look in nature.
This is to be remedied now where we apply
a volume correction step.
In the validation section, it is shown that
the results follow to Plateau’s laws quite
closely.
Also, you know well that my favorite kind
of validation is when we let reality be our
judge, and in this work, the results have
been compared to a real-life experimental
setup and proved to be very close to it.
Take a little time to absorb this.
We can write a computer program that reproduces
what would happen in reality and result in
lots of beautiful video footage.
Loving it!
And, the best part is that the first surface
evolution step is done through an effective
implementation of the hyperbolic mean curvature
flow, which means that the entirety of the
process is typically 3 to 20 times faster
than the state of the art while being more
robust in handling splitting and merging scenarios.
The computation times are now in the order
of milliseconds instead of seconds.
The earlier work in this comparison was also
showcased in Two Minute Papers, if I see it
correctly, it was in episode number 18.
Holy mother of papers, how far we have come
since.
I’ve put a link to it in the video description.
The paper is beautifully written, and there
are plenty of goodies therein, for instance,
an issue with non-manifold junctions is addressed,
so make sure to have a look.
The source code of this project is also available.
Thanks for watching and for your generous
support, and I’ll see you next time!

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