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arXiv · 2006.01472

Optimal control of colloidal trajectories in inertial microfluidics using the Saffman effect

Felix Rühle·Christian Schaaf·Holger Stark
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Abstract

In inertial microfluidics colloidal particles in a Poiseuille flow experience the Segr\'e-Silberberg lift force, which drives them to specific positions in the channel cross section. Due to the Saffman effect an external force applied along the microchannel induces a cross-streamline migration to a new equilibrium position. We apply optimal control theory to design the time protocol of the axial control force in order to steer a single particle as precisely as possible from a channel inlet to an outlet at a chosen target position. We discuss the influence of particle radius and channel length and show that optimal steering is cheaper than using a constant control force. Using a single optimized control-force protocol, we demonstrate that even a pulse of particles spread along the channel axis can be steered to a target and that particles of different radii can be separarted most efficiently.

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Felix Rühle, Christian Schaaf, Holger Stark. 2020-06-02. Optimal control of colloidal trajectories in inertial microfluidics using the Saffman effect. https://arxiv.org/abs/2006.01472

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