Der Einfluß retardierter hydrodynamischer Wechselwirkungen auf die Bewegung von Kugeln in einer Suspension

This thesis discusses certain aspects of the slow movement of small particles in a fluid. The movement of a suspended particle creates a flowfield which influences the movement of neighbouring particles. An understanding of these hydrodynamic interactions is substantial for the study of the dynamics of suspensions. On the fast time scale of momentum relaxation, on which the correlations of the fluid velocity decay, the retardation of the propagation of the hydrodynamic interactions has to be taken into account. In this work the hydrodynamic interactions are treated on the basis of the linearized Navier-Stokes equations. From the solution of the Navier-Stokes equations the admittance matrix is calculated. The admittance matrix directly relates the velocities of the particles with external forces. The dependence of the admittance matrix on the configuration of the suspended particles contains the information about the hydrodynamic interactions. The effective admittance is introduced as the thermodynamic limit of the multi particle admittance and is the starting point for the investigation of the movement of a sphere in a suspension. A fluctuation-dissipations theorem relates the effective admittance with the velocity autocorrelation function of a particle in a suspension. Using a cluster expansion the effective admittance is calculated to the first order of the density of suspended particles. In this order analytic results for the effective translative and rotative long-time coefficients of the velocity autocorrelation function are calculated. Finally the suspension is regarded macroscopically as an effective medium and the long-time movement of a sphere in an effective medium is compared to the long-time movement of a sphere in a suspension. The translative long-time coefficient of a suspension is exactly reproduced by the macroscopic treatment. For the rotative long-time coefficient the effective picture yields only an approximative value, since local effects remain visible in the suspension in the final phases of the movement of a suspended sphere.

Grantor dc:publisher

Publikationsserver der RWTH Aachen University

Year dc:date

2004

Author dc:creator

• Hermanns, Heinz-Günter

Contributors dc:contributor

• Felderhof, B. Ubbo

• info:eu-repo/classification/ddc/530
• Suspension
• Teilchen
• Kugel
• Streuung
• Bewegungsgleichung
• Hydrodynamisches Modell
• Physik
• hydrodynamic interactions

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

ger

Identifier

https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-123482%22

OAI identifier oai:identifier

oai:publications.rwth-aachen.de:61865