In this thesis, the overdamped dynamics of multiple hydrodynamically interacting colloidal particles is investigated. These particles are described either by bead-spring models or exert their own propulsion, which allows them a self-controlled movement. The partices are called passive or active.
The first part of this work is devoted to the proof of a turbulent flow in sheared systems of elastic dumbbells. Being passive particles, they only move as long as they are driven by an external flow, e. g., a shear flow. In motion, the suspended beads induce a long-range perturbation field, called hydrodynamic interaction, influencing the dynamics of all other beads. In the case of a suspended dumbbell, the particle performs a rotational movement called tumbling, as a result of the interplay of the shear flow, spring force, and hydrodynamic interaction.
In a flow channel, the interaction with the channel walls has to be considered in addition to the particle-particle interaction. A systematic investigation of the motion in dependence of the channel size and the dumbbell elasticity shows a homoclinic bifurcation, where at the critical point a second state of motion, called vacillating breathing, occurs. This condition is characterized by a skew position of the dumbbell against the shear flow in which the hydrodynamic interaction between the two dumbbell beads is balanced by the spring forces, shear flow, and interactions with the wall.
A dimensionless parameter, the Weissenberg number, specifies the ability of the spring forces to equilibrate external stresses generated by the shear flow. Rheological investigations, determining the effective viscosity, as well as the spring contribution via the so-called Kramers-Kirkwood formula reveal a negative contribution to the effective viscosity for soft dumbbells. This result seems unusual, but can be explained by geometrical considerations.
The phenomenon of turbulence is well-known from everyday life caused by inertial effects, e. g., in the atmosphere. Therefore, since the forties of the last century various analysis tools for flows have been developed, which allow to describe turbulent structures within a stochastic methodology. More astonishing has been the observation that by adding elastic particles turbulence occurs in the overdamped regime. Simulations of many suspended, interacting particles also have shown a chaotic behavior. It turns out that the hydrodynamic interaction between the dumbbells are required to induce perturbations of the shear flow and thus to generate a turbulent flow. Here, the occurrence of turbulent characteristics is systematically examined as a function of the number of particles, but also the deformability of the dumbbells, and their length.
The second part of the work is devoted to the collective dynamics of swimming micro-organisms such as bacteria or algae, which have developed effective mechanisms to move in the overdamped regime. The propulsion of these microswimmers generates long-ranged flow fields influencing other swimmers in the surrounding, similar as in the case of dumbbells in the first part. In nature there exist two types of swimmers, namely pushers and pullers, which can be described via the simple model of a force dipole. The collective dynamics of pullers and pushers are fundamentally different from each other, in so far as pushers tend to form clusters of several swimmers, wheras pullers repel each other.
In addition, biological swimmers have developed sensors for the detection of external light sources or chemical gradients and utilized in the process of forage referred to as photo- or chemotaxis. Swimmers tend to move in the direction of high nutrient concentrations or an external light source. However, they have only access to the direction of motion via a stochastic reorientation. Over a longer period of time, their movement corresponds to a biased random-walk and the movement of the micro-swimmer can be described within a diffusion process. Therefore, the distribution of the positions of a higher number of swimmers, which is not bounded by walls denoted as dispersion.
This thesis takes a closer look at the dispersion of this probability distribution of swimmers when they interact hydrodynamically, under the condition of a uniform distribution of the chosen directions of motion. The effect of hydrodynamic interaction is analysed in terms of the diffusion-coefficient depending on the volume-fraction, with reference to a spherical volume of a radius equal to the standard deviation of the distribution. This reference volume accords to the volume occupied by the swimmers. The dispersion differs fundamentally in the case of pushers and pullers. The hydrodynamic interaction ensures an increase of the diffusion coefficient in both cases, but this coefficient remains constant in the case of pushers, whereas for pullers it decreases with decreasing volume fraction. The scaling laws with their exponents being proportional to 1/3 also appear in the case of unequally distributed directions of motion, as considered for the description of photo- or chemotaxis. The scaling seems to be a universal result for hydrodynamically interacting particles.
|School:||Universitaet Bayreuth (Germany)|
|Source:||DAI-C 81/1(E), Dissertation Abstracts International|
|Subjects:||Microbiology, Polymer chemistry|
|Keywords:||Dumbbell suspensions, Vacilating breathing, Hydrodynamics|
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