Microfluidic Lagrangian Trap for Brownian Particles: Three-Dimensional Focusing down to the Nanoscale

Several technologies and biotechnologies employing small-sized particles in microfluidics and nanofluidics rely on the ability of hampering thermal motion for progress. We experimentally demonstrate that nanoparticles suspended in a dilute polymer solution in Poiseuille flow can be trapped in the central region of a microtube, with a trapping efficiency that depends on the squared flow rate. The trap force is caused by the viscoelasticity of the suspending fluid, and can be modulated by selecting liquids with specific rheology. We also propose a simple theoretical argument that supports the experimental evidence, and links the trapping force to a dimensionless parameter comparing viscoelastic normal forces and Brownian forces. The theoretical argument distills into a simple equation, which could be used to downscale flow cytometers, or to design microfluidic devices for counting, coding, or separating nanoparticles.