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We theoretically investigate the effect of random fluctuations on the motion of elongated microswimmers near hydrodynamic transport barriers in externally-driven fluid flows. Focusing on the two-dimensional hyperbolic flow, we consider the effects of translational and rotational diffusion as well as tumbling, i.e. sudden jumps in the swimmer orientation. Regardless of whether diffusion or tumbling are the primary source of fluctuations, we find that noise significantly increases the probability that a swimmer crosses one-way barriers in the flow, which block the swimmer from returning to its initial position. We employ an asymptotic method for calculating the probability density of noisy swimmer trajectories in a given fluid flow, which produces solutions to the time-dependent Fokker-Planck equation in the weak-noise limit. This procedure mirrors the semiclassical approximation in quantum mechanics and similarly involves calculating the least-action paths of a Hamiltonian system derived from the swimmers Fokker-Planck equation. Using the semiclassical technique, we compute (i) the steady-state orientation distribution of swimmers with rotational diffusion and tumbling and (ii) the probability that a diffusive swimmer crosses a one-way barrier. The semiclassical results compare favorably with Monte Carlo calculations.
Phoresis, the drift of particles induced by scalar gradients in a flow, can result in an effective compressibility, bringing together or repelling particles from each other. Here, we ask whether this effect can affect the transport of particles in a
We use momentum transfer arguments to predict the friction factor $f$ in two-dimensional turbulent soap-film flows with rough boundaries (an analogue of three-dimensional pipe flow) as a function of Reynolds number Re and roughness $r$, considering s
We study the spreading of viruses, such as SARS-CoV-2, by airborne aerosols, via a new first-passage-time problem for Lagrangian tracers that are advected by a turbulent flow: By direct numerical simulations of the three-dimensional (3D) incompressib
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We develop a framework to study the role of variability in transport across a streamline of a reference flow. Two complementary schemes are presented: a graphical approach for individual cases, and an analytical approach for general properties. The s