Stochastic and deterministic vector chromatography of suspended particles in one-dimensional periodic potentials

We present a comprehensive description of vector chromatography (VC) that includes deterministic and stochastic transport in one-dimensional periodic free-energy landscapes, with both energetic and entropic contributions, and identifies the parameters governing the deflection angle. We also investigate the dependence of the deflection angle on the shape of the free-energy landscape by varying the width of the linear transitions in an otherwise dichotomous potential. Finally, we present experimental results obtained in a microfluidic system in which gravity drives the suspended particles and, in combination with a bottom surface patterned with shallow rectangular grooves, creates a periodic landscape of (potential) energy barriers. The experiments validate the model and demonstrate that a simple, passive microdevice can lead to VC of colloidal particles based on both size and density. More generally, other fields, e.g., electric, dielectrophoretic, or magnetic, can play or enhance the role of gravity, potentially leading to a versatile technique.