Rapid mixing of liquids is important for most microfluidic applications. However, mixing is slow in conventional micromixers, because, in the absence of turbulence, mixing here occurs by molecular diffusion. Recent experiments show that mixing can be enhanced by generating transient flow resulting in chaotic advection. While these are planar microchannels, here we show that three-dimensional or...

We study the mixing properties of the single-site Markov chain known as the Glauber dynam-ics for sampling k-colorings of a sparse random graph G(n, d/n) for constant d. The best knownrapid mixing results for general graphs are in terms of the maximum degree ∆ of the input graphG and hold when k > 11∆/6 for all G. Improved results hold when k > α∆ for graphs withgirth ≥ 5 and ∆ ...

In this thesis we study the mixing time of systematic scan Markov chains on finite spin systems. A systematic scan Markov chain is a Markov chain which updates the sites in a deterministic order and this type of Markov chain is often seen as intuitively appealing in terms of implementation to scientists conducting experimental work. Until recently systematic scan Markov chains have largely resi...

Magnetically functionalized PDMS-based micropillar arrays have been successfully designed, fabricated and implanted for controllable microfluidic mixing. The arrangement of PDMS micropillar arrays inside the microchannel can be flexibly controlled by an external magnetic field. As a consequence, the flow fields inside the microchannel can be regulated at will via magnetic activation convenientl...

Homogeneous and rapid mixing in microfluidic devices is difficult to accomplish, owing to the low Reynolds number associated with most flows in microfluidic channels. Here, an efficient electroosmotic micromixer based on a carefully designed lateral structure is demonstrated. The electroosmotic flow in this mixer with an asymmetrical structure induces enhanced disturbance in the micro channel, ...