Eur. Phys. J. Special Topics 228, 5–23 (2019) c  EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature, 2019 https://doi.org/10.1140/epjst/e2019-800142-1 THE E UROPEAN PHYSICAL J OURNAL SPECIAL TOPICS Regular Article Space-time resolution of size-dispersed suspensions in Deterministic Lateral Displacement microfluidic devices Running Deterministic Lateral Displacement under transient conditions to improve separation resolution: a proof of concept Maria Anna Murmura, Alessandra Adrover, and Stefano Cerbelli a Dipartimento di Ingegneria Chimica Materiali Ambiente, Sapienza Universit` a di Roma, Via Eudossiana 18, 00184 Roma, Italy Received 3 September 2018 / Received in final form 17 December 2018 Published online 30 May 2019 Abstract. Deterministic Lateral Displacement (DLD) is a relatively recent microfluidics-assisted technique which allows the size-based sep- aration of a population of micrometric particles suspended in a buffer solution. The core of the device is a shallow channel with rectangu- lar cross-section filled with an array of solid obstacles arranged in a spatially periodic lattice, whose directions are slanted with respect to the channel walls. In practical implementations of DLD, particles are continuously introduced at a localized position of the channel entrance and migrate along different average directions downstream the device according to their size. Thus, at steady state, size-sorted subpopu- lations can be collected at different positions of the channel outlet. Besides, theoretical predictions of recent models of particle transport in these devices suggest that not only the direction of the average particle velocity, but also its magnitude (i.e. the mobility) depends sensitively on particle size. By exploiting this dependence, a novel use of DLD devices is here proposed, where the size-driven separation is realized over time and space by running the process under transient conditions, thus mimicking a classical chromatographic separation. We show how this approach is particularly effective for particles of specific (critical) dimensions, which are known to impair the efficiency of the steady-state separation process. Numerical predictions based on a hard- wall repulsive potential for the particle-obstacle interaction suggest that unprecedented separation performance for near-critical particle size could be obtained in transient conditions within the same channel length used for the time-continuous separation. The case of cylindrical obstacles and spherically shaped particles is considered in detail as an illustrative example. a e-mail: stefano.cerbelli@uniroma1.it