Complex plasmas are low temperature plasmas containing microparticles in addition to the ions, electrons and neutral particles. Under most laboratory conditions, the microparticles are charged negatively by collecting electrons from the plasma. They then interact with each other via a screened Coulomb potential, forming, for instance, a crystalline phase  When the microparticles are illuminated with a laser sheet, their positions can be recorded with a conventional camera. This allows tracing the motion of individual microparticles, therefore making possible an investigation on the atomistic level. In this paper, we present complex plasma experiments on bubbles and blobs such as those shown i

A V Ivlev

G E Morfill

H M Thomas

M Rubin-Zuzic

M Schwabe

S Zhdanov

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Bubbles, blobs, and cusps in complex plasmas
M. Schwabe1, M. Rubin-Zuzic1, S. Zhdanov1, A. V. Ivlev1, H. M. Thomas1, G. E. Morfill1
1 Max-Planck-Institut für extraterrestrische Physik, Garching, Germany
Complex plasmas are low temperature plasmas containing microparticles in addition to the
ions, electrons and neutral particles. Under most laboratory conditions, the microparticles are
charged negatively by collecting electrons from the plasma. They then interact with each other
via a screened Coulomb potential, forming, for instance, a crystalline phase [1].
When the microparticles are illuminated with a laser sheet, their positions can be recorded
with a conventional camera. This allows tracing the motion of individual microparticles, there-
fore making possible an investigation on the atomistic level.
In this paper, we present complex plasma experiments on bubbles and blobs such as those
shown in Figure 1. Bubbles are small, particle free regions (with a “lid”, see Figure 1) that
appear in the microparticle fluid below the void. The lid typically consists of up to a few layers
of microparticles, which are ejected upwards, and the microparticles are pushed towards the
upper part of the cloud. Blobs are microparticle droplets which are compressed into nearly
Figure 1: Bubble (lower left) and blob (right) in a complex plasma composed of 6.8µm MF
particles (Argon at a pressure of 18Pa, temperature difference between upper and lower part of
the chamber 64.5K). Field of view: 23×19mm2.
37th EPS Conference on Plasma Physics O5.319
spherical shape when a group of microparticles is pushed into the void. Sometimes, the cloud
beneath the void forms tips–cusps–pointing upwards.
The experiments were performed in the PK-3 Plus chamber. This radio-frequency (RF) plasma
reactor consists of two parallel electrodes of 6cm diameter with a distance of 3cm [2]. As buffer
gas, usually Argon or Neon at pressures in the range of (10 to 100)Pa is used. Monodisperse
melamine-formaldehyde particles of various sizes in the range of (3 to 7)µm are inserted into
the plasma and illuminated with laser light spread into a plane. Their motion is recorded with a
camera at a frame rate of up to 1000fps.
As is typical for RF discharges, the microparticles in PK-3 Plus are normally levitated by the
strong electric fields in the plasma sheath near the lower electrode. However, it is desirable to
perform experiments in the bulk of the discharge, away from the anisotropies and strong fields
imposed by the sheaths. The best method to achieve this is to perform experiments in micro-
gravity, for instance on the International Space Station [2]. Under those conditions, a central,
particle free region is formed–the void. It is caused by the drag force of the ions streaming from
the center of the discharge to the sides of the plasma vessel.
Another way to eliminate the influence of gravity is to compensate it by an equally strong
force. This can, for instance, be done by applying a strong temperature gradient between the
upper and lower base plate of the vacuum chamber. This induces a thermophoretic force on the
microparticles, lifting them into the plasma bulk.
This way, it is possible to adjust the temperature gradient such that particles are levitated in
Figure 2: The beginning stage of the instability, recorded with
6.81µm size MF particles in Argon gas at a pressure of 18Pa
and a temperature difference between the top and bottom of
the chamber of 64K. The field of view is 29×18mm2.
the center of the discharge. Un-
der those conditions, phenom-
ena typical for microgravity
can be observed; specifically a
central void is formed.
Usually, when the tempera-
ture difference is large enough
to compensate for gravity, the
void boundary is smooth and
well defined. In contrast, under
certain conditions, an instabil-
ity and the subsequent forma-
tion of bubbles and blobs can
be triggered. The first sign of
37th EPS Conference on Plasma Physics O5.319
the instability is that the void boundary begins to show indentations, as is shown in Figure 2.
Then, microparticles start to move through the void, and bubbles and droplets appear [3, 4].
The instability can be triggered by either increasing the temperature gradient, the pressure or
the particle number density, or by lowering the discharge voltage. It can be stopped by the
inverse actions.
The velocity of the microparticles moving through the void upwards decreases with rising
pressure [3]. This result excludes normal Rayleigh-Bénard convection as the cause of the parti-
cle movement, as this convection becomes stronger with pressure.
A mechanism that occurs in refined gases is thermal creep. It is present if a temperature
gradient is maintained along a surface that is immersed in the gas. This effect induces a gas flow
along the surface in the direction of the temperature gradient [5]. In our system, it can cause a
convection of the whole gas; upwards in the center and downwards along the vertical glass walls.
In order to visualize this gas flow, the plasma was turned off while a temperature difference of
50K was maintained between the upper and lower part of the chamber. We observed a flow of
microparticles to the sides of the chamber and even a reverse of direction close to the side walls,
indicating the gas convection.
The influence of this upwards movement of neutral gas in the central part of the plasma vessel
is also visible in the paths traced by the microparticles in the void. As mentioned above, they
are accelerated upwards inside the void. Also, the streamlines of microparticles inside blobs
show distinct vortices. An example is shown in Figure 3, where the streamlines are visualized
Figure 3: Streamlines traced by particles
inside a blob [4].
using the method of line integral convolution [6].
The particles move upwards on the edges of the
blob and downwards in the center.
This movement reminds of that of water
molecules inside small drops in an air stream–
drops with diameters as small as nanometers, as
the number of particles in our blobs is only 103
to 104. The dimensionless number relevant for the
scaling of multiphase flows is the Weber number
W =
ρv2l
σ
, (1)
where ρ is the fluid density, v its velocity, l the
characteristic length, and σ the surface tension.
The Weber number gives the ratio of inertia forces
37th EPS Conference on Plasma Physics O5.319
to surface tension forces. Estimating it in our case results in W ∼ 100, which is well within the
typical range of the break-up of water drops.
The origin of the instability can be described theoretically by considering that the void bound-
ary is normally stabilized by the drag force of the ions streaming from the discharge center to the
walls. When the discharge power is lowered, the ion flux becomes very weak. The acceleration
of the microparticles upwards into the void may then lead to the development of a Rayleigh-
Taylor instability. In our case, this occurs in comparatively thin membranes in the particle fluid
beneath the void. Therefore, the dispersion relation applicable to the “deep-water regime” can
be used to describe the instability [3]
ω2 + iγEpω =−g̃k+(σ/ρ)k3, (2)
where ω denotes the frequency, γEp the coefficient of the drag force exerted on the micropar-
ticles when they move through the gas, g̃ the acceleration caused by the destabilizing forces,
k the wave number, σ the surface tension, and ρ the mass density of the microparticle cloud.
By measuring the growth rate of the instability, the surface tension can be estimated as σ ∼
10−10 Nm−1. In comparison, we estimated the surface tension by considering the break-up of a
bubble and measuring the mass transported during the time needed for the break-up. The result
agrees with that obtained from the dispersion relation by order of magnitude, demonstrating
that the Rayleigh-Taylor model is feasible.
In conclusion, we present an investigation of microparticle bubbles and blobs in complex
plasmas under the influence of gas convection induced by a temperature gradient. The bubbles
and blobs can be considered as models for nanometer-sized water drops, and the instability
mechanism can be described in terms of the Rayleigh-Taylor instability, demonstrating that this
hydrodynamic mechanism is still applicable even in systems with few particles.
References
[1] H. Thomas, G. E. Morfill et al. Phys. Rev. Lett. 73, 652 (1994)
[2] H. M. Thomas, G. E. Morfill et al. New J. Phys. 10, 033036 (2008)
[3] M. Schwabe, M. Rubin-Zuzic et al. Phys. Rev. Lett. 102, 255005 (2009)
[4] M. Schwabe. Ph.D. thesis, Ludwig-Maximilians-Universität (2009)
[5] E. H. Kennard. Kinetic Theory of Gases. McGraw-Hill Book Company, New York (1938)
[6] B. Cabral and L. C. Leedom. In Proceedings of the 20th annual conference on Computer
graphics and interactive techniques (1993)
37th EPS Conference on Plasma Physics O5.319


Bubbles, blobs, and cusps in complex plasmas

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Bubbles, blobs, and cusps in complex plasmas

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