Diffusive dynamics of interacting particles in equilibrium and under hydrodynamic sedimentation

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Doctoral thesis (article-based)
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76, [34]
Dissertations / Laboratory of Physics, Helsinki University of Technology, 115
Diffusive motion of particles plays an important role in many phenomena in surface physics, for example in chemical reactions, surface growth, and spreading. Diffusive motion can be observed in many different systems. In this thesis we study diffusion and dynamics in two fundamentally different kinds of systems: (i) in Brownian surface systems, and (ii) in a non-Brownian system of sedimenting particles with full hydrodynamic interactions. The quantities of central importance are the diffusion coefficients and the related correlation functions. In the sedimentation system we also discuss the behavior of the velocity fluctuations which has attracted a lot of attention recently. First we study the system of spherical Brownian particles on a smooth surface. We find that while the tracer diffusion coefficient is a decreasing function of density, as expected, the collective diffusion coefficient strongly increases with increasing density. This behavior is completely dictated by the isothermal compressibility, since the center of mass mobility is independent of density in this system. Then we consider the influence of a periodic surface potential and the relation of the continuum model to the lattice gas model. It turns out that the lattice gas model approximates well the dynamics of the continuum model except at the limit when coverage approaches unity. Next we present the corresponding results in a system of rodlike molecules. For the rodlike molecules the normalized tracer diffusion coefficient is found to behave exactly as the tracer diffusion coefficient of the single spheres, while the collective diffusion coefficient is strongly enhanced. In the system of sedimenting non-Brownian particles we find that the average sedimentation velocity of spherical particles decreases monotonically as a function of density but deviates from the phenomenological Richardson-Zaki law at the lowest densities. However, the average sedimentation velocity of spheroids displays non-monotonic behavior as a function of density. The maximum at the intermediate densities is attributed to a change in the orientational distribution of the spheroids. Finally, we study velocity fluctuations and diffusion coefficients in a system of sedimenting spherical particles confined between two parallel vertical walls. We find that the velocity fluctuations in the direction parallel to gravity grow linearly with system size, while the velocity fluctuations in the horizontal directions saturate. Also the tracer diffusion coefficient, which is closely related to the velocity fluctuations, demonstrates similar behavior.
surface diffusion, Brownian dynamics, sedimentation, computer simulations
Other note
  • J. M. Lahtinen, T. Hjelt and T. Ala-Nissilä, Diffusive spreading of rodlike molecules on surfaces, Surface Science, 454-456, 598 (2000).
  • J. M. Lahtinen, T. Hjelt, T. Ala-Nissilä, and Z. Chvoj, Diffusion of hard disks and rodlike molecules on surfaces, Physical Review E, 64, 021204 (2001).
  • T. Hjelt, E. Kuusela, J. M. Lahtinen, T. Ala-Nissilä, I. Vattulainen, and S. C. Ying, Memory Effects and Memory Functions in Surface Diffusion, in Collective Diffusion on Surfaces: Correlation Effects and Adatom Interactions, ed. by M. C. Tringides and Z. Chvoj, pp. 47-57, Kluwer (2001).
  • J. M. Lahtinen, M. Mašín, T. Laurila, T. Ala-Nissilä, and Z. Chvoj, Many-particle diffusion in continuum: Influence of a periodic surface potential, Journal of Chemical Physics, 116, 7666 (2002).
  • E. Kuusela, J. M. Lahtinen, and T. Ala-Nissilä, Orientational ordering of spheroids under finite Reynolds number sedimentation, Submitted to Physical Review Letters (2002).
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