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Mesoscopic stability and sedimentation waves in settling periodic arrays
1Institut für Theoretische Physik A, RWTH Aachen Templergraben 55, 52056 Aachen, Germany. ufelder@physik.rwth-aachen.de
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 20, 2003
Summary
The stability of particle arrays in fluid was studied. Body-centered and face-centered cubic arrays show macroscopic stability under gravity, allowing for particle motion and wave propagation.
Area of Science:
- Fluid dynamics
- Materials science
- Physics
Background:
- Particle sedimentation in viscous fluids is crucial for understanding material deposition and suspension behavior.
- The arrangement of particles significantly influences the stability of settling systems.
Purpose of the Study:
- To investigate the stability of periodic particle arrays settling in a viscous fluid under gravity.
- To determine which crystal structures exhibit stability during sedimentation.
Main Methods:
- Utilized the point sedimentation model to analyze particle behavior.
- Examined simple cubic, body-centered cubic, and face-centered cubic arrays.
- Investigated stability concerning gravity direction and wave vector properties.
Main Results:
- Simple cubic arrays are unstable.
- Body-centered and face-centered cubic arrays demonstrate macroscopic stability when gravity aligns with crystal axes.
- Instability is suppressed in finite systems with periodic boundary conditions below a critical size.
Conclusions:
- Mesoscopically stable particle arrays can exhibit stable behavior in finite systems.
- Sedimentation waves can propagate through these stable finite systems.
- Particle arrangement is a key factor in gravitational sedimentation stability.