Using numerical simulations, we study the separation of deformable bodies, such as capsules, vesicles, and cells, in deterministic lateral displacement devices, also known as bump arrays. These arrays comprise regular rows of obstacles such as micropillars whose arrangements are shifted between adjacent rows by a fixed amount. We show that, in addition to the zigzag and laterally displaced trajectories that have been observed experimentally, there exists a third type of trajectory which we call dispersive, characterized by seemingly random bumpings off the micropillars. These dispersive trajectories are observed only for large and rigid particles whose diameters are approximately more than half the gap size between micropillars and whose stiffness exceeds approximately 500 MPa. We then map out the regions in phase space, spanned by the row shift, row separation, particle diameter, and particle deformability, in which the different types of trajectories are expected. We also show that, in this phase space, it is possible to transition from zigzag to dispersive trajectories, bypassing lateral displacement. Experimentally, this is undesirable because it limits the ability of the device to sort particles according to size. Finally, we discuss how our numerical simulations may be of use in device prototyping and optimization.

Ciliary movements in protozoa exhibit metachronal wave-like coordination, in which a constant phase difference is maintained between adjacent cilia. It is at present generally thought that metachronal waves require hydrodynamic coupling between adjacent cilia and the extracellular fluid. To test this hypothesis, we aspirated a Paramecium cell using a micropipette which completely sealed the surface of the cell such that no fluid could pass through the micropipette. Thus, the anterior and the posterior regions of the cell were hydrodynamically decoupled. Nevertheless, we still observed that metachronal waves continued to propagate from the anterior to the posterior ends of the cell, suggesting that in addition to hydrodynamic coupling, there are other mechanisms that can also transmit the metachronal waves. Such transmission was also observed in computational modeling where the fluid was fully decoupled between two partitions of a beating ciliary array. We also imposed cyclic stretching on the surface of live Paramecium cells and found that metachronal waves persisted in the presence of cyclic stretching. This demonstrated that, in addition to hydrodynamic coupling, a compliant substrate can also play a critical role in mediating the propagation of metachronal waves.

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