Separation of nanoparticles by flow past a patterned substrate.

Motivated by the problem of efficiently separating nanoparticles of different character held in solution, we investigate trajectory deflection and particle trapping in flows of nanoparticle suspensions past patterned surfaces. We consider rigid atomistic particles suspended in a viscous liquid solvent and driven by a pressure gradient through a channel, one side of which has a pattern of alternating stripes which attract or repel the particles. We first consider van der Waals forces alone, where the wall interaction is obtained by summing over semi-infinite slabs of material having a Lennard-Jones interaction with or without an attractive term, yielding a force field with nontrivial three-dimensional spatial variation. This wall interaction can either trap particles on the attractive stripes or deflect the trajectories of mobile particles away from the direction of mean flow. Using molecular dynamics simulations we determine the motion of particles of different sizes in this potential, and observe distinct but modest deflections of several degrees from the direction of the imposed fluid flow. The effects of electrostatic interactions are considered by decorating the particles and walls with opposite charges, resulting in significantly more trapping and larger deflection angles. We use Langevin simulations to treat the motion of larger particles in the van der Waals case, and again observe particle trapping and deflection, although the numerical details of the results differ from the molecular dynamics simulations. In the Langevin case we are furthermore able to obtain bounds on the deflection angle from an analysis of the associated Fokker-Planck equation. We conclude that patterned surfaces deflect particle trajectories to a degree depending on their size, and may be used as a vector chromatography separation technique.