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A new approach to regular and chaotic fluid advection is presented that utilizes the Thurston–Nielsen classification theorem. The prototypical two-dimensional problem of stirring by a finite number of stirrers confined to a disk of fluid is considered. The theory shows that for particular ‘stirring protocols’ a significant increase in complexity of the stirred motion – known as topological chaos – occurs when three or more stirrers are present and are moved about in certain ways. In this sense prior studies of chaotic advection with at most two stirrers, that were, furthermore, usually fixed in place and simply rotated about their axes, have been ‘too simple’. We set out the basic theory without proofs and demonstrate the applicability of several topological concepts to fluid stirring. A key role is played by the representation of a given stirring protocol as a braid in a (2+1)-dimensional space–time made up of the flow plane and a time axis perpendicular to it. A simple experiment in which a viscous liquid is stirred by three stirrers has been conducted and is used to illustrate the theory.

An understanding of chemotaxis at the level of cell-molecule interactions is important because of its relevance in cancer, immunology, and microbiology, just to name a few. This study quantifies the effects of flow on cell migration during chemotaxis in a microfluidic device. The chemotaxis gradient within the device was modeled and compared to experimental results. Chemotaxis experiments were performed using the chemokine CXCL8 under different flow rates with human HL60 promyelocytic leukemia cells expressing a transfected CXCR2 chemokine receptor. Cell trajectories were separated into x and y axis components. When the microchannel flow rates were increased, cell trajectories along the x axis were found to be significantly affected (p < 0.05). Total migration distances were not affected. These results should be considered when using similar microfluidic devices for chemotaxis studies so that flow bias can be minimized. It may be possible to use this effect to estimate the total tractile force exerted by a cell during chemotaxis, which would be particularly valuable for cells whose tractile forces are below the level of detection with standard techniques of traction-force microscopy.

In this study, the dielectrophoretic response of prostate tumor initiating cells (TICs) was investigated in a microfluidic system utilizing contactless dielectrophoresis (cDEP). The dielectrophoretic response of prostate TICs was observed to be distinctively different than that for non-TICs, enabling them to be sorted using cDEP. Culturing the sorted TICs generated spheroids, indicating that they were indeed initiating cells. This study presents the first marker-free TIC separation from non-TICs utilizing their electrical fingerprints through dielectrophoresis.