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Michael
Schindler

Free-Surface Microflows and Particle Transport

Supervisor: Prof. Dr. Peter Hänggi
[Theoretical physics I]

Date of oral examination:
05/29/2006

125 pages,
english
, OPUS (Online-Publikations-Server) der Universitätsbibliothek Augsburg
In the past decade, the development of so-called 'labs-on-a-chip' has led to an increased interest in microfluidic systems. On typical length scales up to hundred micrometers, water does not behave as we are used to in everyday life. It appears to be viscous like honey, its interface with the surrounding air is stiff and hard such that one could walk on it like a water strider. And, last but not least, all movement is subject to fluctuations, leading to well-known phenomena such as Brownian motion.

The present thesis describes the theoretical aspects of a promising new actuation technique for small amounts of water: Tiny droplets of water are agitated by a 'surface-acoustic wave' (SAW), which is a wave on the surface of a crystalline substrate, illustratively understood as a tiny earthquake. The SAW generates a flow pattern inside the droplets, which can be used to transport small particles in the flow. Strong SAWs are even able to deform the free surface of the fluid and to move the whole droplet.

The thesis is focussed on two aspects of these systems: First, a stable algorithm is presented which allows to calculate internal flows in two dimensions bounded by a free surface. Special emphasis is put on the position and shape of the free surface. Its calculation has to take into account the mutual influence of the flow pattern and the free surface in the parameter regime of large surface tension. As an application of the algorithm, an experimentally observed droplet deformation is considered. The numerical results allow the conclusion that the effective force by the SAW on the fluid gives rise to a large pressure but only to a slow velocity field.

The second part of the thesis describes the accumulation of finite-size particles in free-surface flows. The transport of a particle in a viscous flow comprises a deterministic and a random aspect. Generally, the surrounding flow exerts stress on the particle via its boundary. If the particles are considerably small, additional fluctuations, which are inherent in the fluidic stress, lead to a noticeable Brownian motion. In the theoretical description of small particles in a viscous flow, quite a number of different effects lead to small forces. Some of them annihilate each other, others sum up to noticeable effects. Two such effects are investigated: The accumulation of spherical particles near boundaries, which is caused by the fact that the particle centres cannot touch the boundary of the fluid but stay one particle radius apart. The other effect is an accumulation of particles in flow eddies near the entry point of the SAW into the fluid.

The present thesis describes the theoretical aspects of a promising new actuation technique for small amounts of water: Tiny droplets of water are agitated by a 'surface-acoustic wave' (SAW), which is a wave on the surface of a crystalline substrate, illustratively understood as a tiny earthquake. The SAW generates a flow pattern inside the droplets, which can be used to transport small particles in the flow. Strong SAWs are even able to deform the free surface of the fluid and to move the whole droplet.

The thesis is focussed on two aspects of these systems: First, a stable algorithm is presented which allows to calculate internal flows in two dimensions bounded by a free surface. Special emphasis is put on the position and shape of the free surface. Its calculation has to take into account the mutual influence of the flow pattern and the free surface in the parameter regime of large surface tension. As an application of the algorithm, an experimentally observed droplet deformation is considered. The numerical results allow the conclusion that the effective force by the SAW on the fluid gives rise to a large pressure but only to a slow velocity field.

The second part of the thesis describes the accumulation of finite-size particles in free-surface flows. The transport of a particle in a viscous flow comprises a deterministic and a random aspect. Generally, the surrounding flow exerts stress on the particle via its boundary. If the particles are considerably small, additional fluctuations, which are inherent in the fluidic stress, lead to a noticeable Brownian motion. In the theoretical description of small particles in a viscous flow, quite a number of different effects lead to small forces. Some of them annihilate each other, others sum up to noticeable effects. Two such effects are investigated: The accumulation of spherical particles near boundaries, which is caused by the fact that the particle centres cannot touch the boundary of the fluid but stay one particle radius apart. The other effect is an accumulation of particles in flow eddies near the entry point of the SAW into the fluid.

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