Characterizing the performance of the hydrodynamic trap using a control-based approach

The development of techniques for trapping and precisely manipulating single particles and molecules has catalyzed a revolution in diverse fields ranging from biology to soft condensed matter physics. For example, these techniques have been used for cellular chromosome manipulation (Vorobjev et al. 1993; Harsono et al. 2013), manufacturing 2D and 3D nanostructures (Castelino et al. 2005), nanopatterning (Mcleod and Arnold 2008; Tsai et al. 2012), and for studying non-equilibrium statistical mechanics (Reimann 2002). To this end, a wide variety of techniques have been developed and extensively studied, including those based on optical fields (Ashkin et al. 1986; Grier 2003; Neuman and Block 2004; Righini et al. 2008; Yang et al. 2009; Roxworthy et al. 2012), magnetic fields (Gosse and Croquette 2002; Lee et al. 2004; Mirowski et al. 2005), microvortices (Lutz et al. 2006; Lin et al. 2008; Petit et al. 2012), and electrical fields (Cohen and Moerner 2005, 2006, 2008; Armani et al. 2006; Cummins et al. 2013). Trapping techniques can be broadly classified into passive and active trapping schemes. Passive techniques confine particles by generating a local minimum in a potential energy profile (i.e., a potential well) around the target particle position. This potential energy minimum serves as an attractive point for a particle. For passive traps, feedback control is generally not required to stabilize a trapped particle, because the depth of the potential well can be tuned to mitigate particle fluctuations due to thermal and environmental noise. Passive techniques include optical traps (Grier 2003; Neuman and Block 2004; Chiou et al. 2005; Yang et al. 2009; Dholakia and Čižmár 2011), magnetic traps (Gosse and Croquette 2002; Lee et al. 2004; Mirowski et al. 2005), streaming microvortices or microeddies (Lutz et al. 2006; Lin et al. 2008; Petit et al. 2012), Abstract Hydrodynamic trapping allows for the confinement and manipulation of small objects in free solution, away from solid boundaries and without the need for optical or magnetic fields. In order to achieve robust trapping over long time scales, it is imperative to evaluate trap performance using different control schemes and to understand the effect of system parameters on trap stability. In this work, we investigate the performance of a hydrodynamic trap actuated by varying combinations of proportion-integral-derivative controllers. We further develop a control-based model of the trap, and we characterize trap performance for a wide range of particle Peclet numbers and response times. Overall, an increased understanding of trap performance will facilitate the design of improved controllers to enable robust trapping under variable system parameters.