We present a new approach to the design of mixers. This approach relies on a sequence of tailored flows coupled with a new procedure to quantify the local degree of striation, called lamination. Lamination translates to the distance over which the molecular diffusion needs to act to finalise mixing. A novel in situ mixing is achieved by the tailored sequence of flows. This sequence is shown with the property that material lines and lamination grow exponentially, according to processes akin to the well-known baker's map. The degree of mixing (stirring coefficient) likewise shows exponential growth before the saturation of the stirring rate. Such saturation happens when the typical striations' thickness is smaller than the diffusion's length scale. Moreover, without molecular diffusion, the predicted striations' thickness would be smaller than the size of an atom of hydrogen within 40 flow turnover times. In fact, we conclude that about 3 minutes, i.e. 15 turnover times, are sufficient to mix species with very low diffusivities, e.g. suspensions of virus, bacteria, human cells, and DNA.

This article pursues the idea that the degree of striations, called lamination, could be engineered to complement stretching and to design new sequential mixers. It explores lamination and mixing in three new mixing sequences experimentally driven by electromagnetic body forces. To generate these three mixing sequences, Lorentz body forces are dynamically controlled to vary the flow geometry produced by a pair of local jets. The first two sequences are inspired from the "tendril and whorl" and "blinking vortex" flows. The third novel sequence is called the "cat's eyes flip." These three mixing sequences exponentially stretch and laminate material lines representing the interface between two domains to be mixed. Moreover, the mixing coefficient (defined as 1-σ(2)/σ(0)(2) where σ(2)/σ(0)(2) is the rescaled variance) and its rate grow exponentially before saturation. This saturation of the mixing process is related to the departure of the mixing rate from an exponential growth when the striations' thicknesses reach the diffusive length scale of the measurements or species and dyes. Incidentally, in our experiments, for the same energy or forcing input, the cat's eyes flip sequence has higher lamination, stretching, and mixing rates than the tendril and whorl and the blinking vortex sequences. These features show that bakerlike in situ mixers can be conceived by dynamically controlling a pair of local jets and by integrating lamination during stirring stages with persistent geometries. Combined with novel insights provided by the quantification of the lamination, this paper should offer perspectives for the development of new sequential mixers, possibly on all scales.

This article explores the lamination, stretching, and mixing produced by sequences cyclically permuting a cat's eyes flow structure to stir the flow. Such sequences are experimentally driven by electromagnetic forces. Their intensity is kept constant between experiments while the duration of the forcing cycles varies over a decade. Mixing observations show that the mixing processes evolve from a seesaw stirring for short cycles (due to the regular rotation of the principal direction of the cat's eyes flow structures) to a cat's eyes stirring where the seesaw stirring is complemented by the rolling occurring within eddies. The transition from seesaw stirring to cat's eyes stirring is related to the persisting of the cat's eyes flow structure during one turnover time before it is flipped. Reference cases such as steady and random forcing configurations complement this exploration for comparison with the cat's eyes flip sequences. It is shown that cat's eyes flip sequences are efficient and possess baker-like mixing properties with an exponential growth for the length of interfaces and their lamination. The exponential coefficients of the stretching and lamination rates are conserved when varying the duration of the mixing cycles and using the generic cat's eyes flow turnover time as the reference of time to build these exponents. In particular, the stretching coefficients can be assumed as nearly constant when compared to the topological entropy which varies over a decade. This is attributed to the ability of the cat's eyes flip sequences to integrate lamination during the stirring sequences. This integration of the lamination compensates the reduction of flow's unsteadiness when increasing the duration of the mixing cycles so as to conserve a good stirring and mixing performance. Therefore, the lamination, stretching, and mixing of the cat's eyes flip sequences are robust to changes of the cycles’ duration.

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