Climbing two hills is faster than one: collective barrier-crossing by colloids driven through a microchannel

Ohm's law is one of the most central transport rules stating that the total resistance of sequential single resistances is additive. While this rule is most commonly applied to electronic circuits, it also applies to other transport phenomena such as the flow of colloids or nanoparticles through channels containing multiple obstacles, as long as these obstacles are sufficiently far apart. Here we explore the breakdown of Ohm's law for fluids of repulsive colloids driven over two energetic barriers in a microchannel, using real-space microscopy experiments, particle-resolved simulations, and dynamical density functional theory. If the barrier separation is comparable to the particle correlation length, the resistance is highly non-additive, such that the resistance added by the second barrier can be significantly higher or lower than that of the first. Surprisingly, in some cases the second barrier can even add a {\it negative} resistance, such that two identical barriers are easier to cross than a single one. We explain this counterintuitive observation in terms of the structuring of particles trapped between the barriers.