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Cloaking, shielding and hydrodynamic dispersion in Hele-Shaw flows

Steffen Hardt
Institute for Nano- and Microfluidics
TU Darmstadt

Hele-Shaw flows, i.e. flows between parallel plates separated by a small gap, offer additional degrees of freedom compared to microchannel flows that are often unidirectional. These degrees of freedom can be utilized to sculpt flows in a predictable and controllable manner. Here we demonstrate the cloaking and shielding of objects in a Hele-Show domain. The term “objects” refers to solid bodies of different shapes arranged between the parallel plates. These objects are obstacles to the flow inside the Hele-Shaw cell. Making use of electroosmosis, the flow around these objects can be sculpted in such a way that cloaking is achieved, which means that far away from an object the streamlines are the same as if the object did not exist. Alternatively, the flow can be tuned to achieve shielding, which means that the hydrodynamic stress at the surface of the object is largely eliminated. We present a theoretical concept for cloaking and shielding as well as its experimental realization. Furthermore, a situation is considered in which a passive tracer is advected with the flow in a Hele-Shaw cell. Analogous to Taylor-Aris dispersion in a microchannel, advective-diffusive transport results in hydrodynamic dispersion. Different from the classical Taylor-Aris case, dispersion not only occurs along one axis, but inside the plane of the Hele-Shaw cell. We present a theoretical model for dispersion in Hele-Shaw flows that connects the local structure of the flow field and the dispersion tensor.