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Using molecular dynamics simulations, we investigate the fate of a nanoparticle deposited on a solid surface as a liquid-liquid interface moves past it, depending on the wetting of the solid by the two liquids and the magnitude of the driving force. Interfacial pinning is observed below a critical value of the driving force. Above the critical driving force for pinning and for large contact angle values we observe stick-slip motion, with intermittent interfacial pinning and particle sliding at the interface. At low contact angles we observe that particle rolling precedes detachment, which indicates the importance of dynamic effects not present in static models. The findings in this work indicate that particle mobilization, and removal efficiencies, originating in dynamic liquid-liquid interfaces can be significantly underestimated by static models.

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.

We performed macroscopic experiments on the motion of a sphere through an array of obstacles that highlight the deterministic nature of the lateral displacements that lead to particle separation in microfluidic systems. The motion of the spheres is irreversible and displays directional locking. The locking directions can be predicted with a single parameter that distinguishes between reversible and irreversible particle-obstacle collisions. These results stress the need to incorporate irreversible interactions to predict the movement of a non-Brownian sphere passing through a periodic array.

The stochastic transport of suspended particles through a periodic pattern of obstacles in microfluidic devices is investigated by means of the Fokker-Planck equation and numerical simulations. Asymmetric arrays of obstacles have been shown to induce the continuous separation of DNA molecules, with particles of different size migrating in different directions within the microdevice (vector separation). We show that the separation of tracer particles only occurs in the presence of a permeating driving force with a nonzero normal component at the surface of the solid obstacles, and arises from differences in the local Peclet number of the particles. On the other hand, finite-size particles also exhibit nonzero, but small, migration angles in the case of nonpermeating fields. Monte Carlo simulations for different driving fields agree with the solutions to the Fokker-Planck equation.

Equilibrium and nonequilibrium aspects of particle adsorption on the walls of fluid-filled nanochannels are examined via molecular dynamics simulations. The force on the particle and the free energy of the system are found to depend on the particle's history (hysteresis), in addition to its radial position and the wetting properties of the fluid, even when the particle moves quasistatically. The hysteresis is associated with changes in the fluid density in the gap between the particle and the wall, which persist over surprisingly long times. The force and free energy exhibit large oscillations with distance when the lattice of the structured nanoparticle is held in register with that of the tube wall, but not if the particle is allowed to rotate freely. Adsorbed particles are trapped in free-energy minima in equilibrium but can desorb if forced along the channel.

The evolution and spatial structure of displacement fronts in fractures with self-affine rough walls are studied by numerical simulations. The fractures are open and the two faces are identical but shifted along their mean plane, either parallel or perpendicular to the flow. An initially flat front advected by the flow is progressively distorted into a self-affine front with a Hurst exponent equal to that of the fracture walls. The lower cutoff of the self-affine regime depends only on the aperture, while the upper cutoff grows with the lateral shift and linearly with the width of the front.

Using molecular dynamics simulations, we study the motion of a closely fitting nanometer-size solid sphere in a fluid-filled cylindrical nanochannel at low Reynolds numbers. At early times, when the particle is close to the middle of the tube, its velocity is in agreement with continuum calculations, despite large thermal fluctuations. At later times, partially wetting fluids exhibit novel adsorption phenomena: the sphere meanders away from the center of the tube and adsorbs onto the wall, and subsequently either sticks to the wall and remains motionless on average, or separates slightly from the tube wall and then either slips parallel to the mean flow or executes an intermittent stick-slip motion.