Slip, swim, mix, pack: Fluid mechanics at the micron scale

This thesis is devoted to fluid behavior at the micrometer length scale and considers four different problems.; We first address the topic of the no-slip boundary condition in Newtonian liquids. After reviewing the field, we present models for apparent slip in three distinct experimental settings: Steady pressure-driven flow over heterogeneous surfaces, unsteady drainage flow over surface-attached bubbles, and flow of passive tracers affected by electrical forces. In all cases, we evaluate the apparent slip lengths and compare them to experimental results. We then propose a new method to probe slip, based on the influence of surface slip on the Brownian motion near a surface of a colloidal particle. We finish by showing that slip has virtually no influence on the non-modal stability of shear flows, despite its strong influence on unstable modes.; The second problem we consider addresses mixing in micro-devices. We show that microchannels which are obtained with a single step of microfabrication (that is, have constant height) are able to generate fully three-dimensional flows, and could therefore be used as single-step passive micro-mixers.; The third problem we present proposes a mechanical model for the motion of the bacterium E. coli near solid boundaries. It has been observed that, near a solid surface, E. coli does not swim in a straight line but in clockwise circles, which we show is a consequence of the hydrodynamic interactions between the free-swimming bacterium and the surface.; The final problem we consider addresses self-assembly of micro-particles. We show that when spherical particles located on a liquid droplet are forced to come together by evaporation of the droplet, the geometrical and mechanical constraints arising during the process lead to unique final clusters. This allows us to propose a methodology to fabricate different clusters.