Separation and collective phenomena of colloidal particles in Brownian ratchets

Abstract

In this thesis, we introduce novel mechanisms for the separation of colloidal particles based on the ratchet effect. It is further demonstrated that hydrodynamic interactions among colloidal particles are able to enhance the ratchet effect and cause interesting collective phenomena. The research has been done by means of theoretical modeling and numerical simulations. The thesis can be divided into three projects.

In the first project, we propose a ratchet-based separation mechanism that results in microfluidic devices with significantly reduced size. For this purpose, we introduce a ratchet model that switches cyclically between two distinct ratchet potentials and a zero-potential state. The applied potentials are chosen such that Brownian particles exhibit reversal of the direction of their mean displacement when relevant parameters such as the on-time of the potentials are varied. This direction reversal offers us new opportunities for the design of microfluidic separation devices. Based on the results of our ratchet model, we propose two new separation mechanisms. Compared to the conventional microfluidic devices, the proposed devices can be made of significantly smaller sizes without sacrificing the resolution of the separation process. In fact, one of our devices can be reduced to a single channel. We study our ratchet model by Brownian dynamics simulations and derive analytical and approximative expressions for the mean displacement. We show that these expressions are valid in relevant regions of the parameter space and that they can be used to predict the occurrence of direction reversal. Furthermore, the separation dynamics in the proposed channel device are investigated by means of Brownian dynamics simulations.

In the second project, we introduce a mechanism that facilitates efficient ratchet-based separation of colloidal particles in pressure-driven flows. Here, the particles are driven through a periodic array of obstacles by a pressure gradient. We propose an obstacle design that breaks the symmetry of fluid flows and therefore fulfills the crucial requirement for ratchet-based particle separation. The proposed mechanism allows a fraction of the flow to penetrate the obstacles, while the immersed particles are sterically excluded. Based on Lattice-Boltzmann simulations of the fluid flow, it is demonstrated that this approach results in highly asymmetrical flow pattern. The key characteristics of the separation process are estimated by means of Brownian ratchet theory and validated with Brownian dynamics simulations. For the efficient simulation of fluid flows we introduce novel boundary conditions for the Lattice-Boltzmann method exploiting the full periodicity of the array.

In the third project, we investigate how hydrodynamic interactions between Brownian particles influence the performance of a fluctuating ratchet. For this purpose, we perform Brownian dynamics simulations of particles that move in a toroidal trap under the influence of a sawtooth potential which fluctuates between two states (on and off). We first consider spatially constant transition rates between the two ratchet states and observe that hydrodynamic interactions significantly increase the mean velocity of the particles but only when they are allowed to change their ratchet states individually. If in addition the transition rate to the off state is localized at the minimum of the ratchet potential, particles form characteristic transient clusters that travel with remarkably high velocities. The clusters form since drifting particles have the ability to push but also pull neighboring particles due to hydrodynamic interactions.