The authors examine the problem of diffusion over a fluctuating barrier in limit where fluctuations are extremely fast compared with all other timescales problem. In white noise limit, decay probability from metastable state is exponential characteristic timescale exhibiting Arrhenius behaviour. For small but finite correlation times for part potential, effective increases time. Implications liquids above glass transition discussed.

Many microfluidic systems-including chemical reaction, sample analysis, separation, chemotaxis, and drug development injection-require control precision of solute transport. Although concentration levels are easily specified at injection, pressure-driven transport through channels is known to spread the initial distribution, resulting in reduced concentrations downstream. Here we document an unexpected phenomenon: The channel's cross-sectional aspect ratio alone can shape profile along...

We experimentally explore the motion of falling spheres in strongly stratified fluids which fluid transitions from low density at top to high bottom and document an internal splash sphere may reverse its direction (from falling, rising, again) as it penetrates a region strong transition. present measurements sphere’s velocity exhibit nonmonotonic profiles connecting maximum minimum terminal velocities, matching earlier [J. Fluid Mech. 381, 175 (1999)], but further new levitation phenomenon....

A sphere exhibits a prolonged residence time when settling through stable stratification of miscible fluids due to the deformation fluid-density field. Using Green's function formulation, first-principles numerically assisted theoretical model for sphere–fluid coupled dynamics at low Reynolds number is derived. Predictions model, which uses no adjustable parameters, are compared with data from an experimental investigation spheres varying sizes and densities in stratified corn syrup. The...

The behavior of settling particles in stratified fluid is important a variety applications, from environmental to medical. We document phenomenon which sphere, when crossing density transitions, slows down substantially comparison its speed the bottom denser layer, due entrainment buoyant fluid. present results an experimental study effects interface on flight times as well theoretical model derived first principles low Reynolds number regimes for miscible fluids. Our work provides new...

The influence of ambient fluid stratification on buoyant miscible jets and plumes is studied theoretically experimentally. Given a fixed set jet/plume parameters, an sandwiched between top bottom homogeneous densities, theoretical criterion identified to show how step-like density profiles constitute the most effective mixers within broad class stable transitions. This assessed both analytically experimentally, respectively by establishing rigorous priori estimates generalized...

Avellaneda and one of the authors ([1], [3]) have recently established that an upper bound for enhanced diffusivity in large scale, long time advection‐diffusion with periodic steady incompressible velocity fields has form where Pe is Peclet number reciprocal Prandtl number. In this paper, flow maximal minimal diffusion are studied. Maximal requires some directions tensor also lower . For diffusion, effect field to boost by a negligible amount bounded fixed constant times bare regardless...

In 1953 G.I. Taylor showed theoretically and experimentally that a passive tracer diffusing in the presence of laminar pipe flow would experience an enhanced diffusion longitudinal direction beyond bare molecular diffusivity, κ, amount 2 U 192κ , where is radius maximum fluid velocity.This behavior predicted to arise after transient timescaleκ diffusive timescale for cross pipe.Typically, κ very small, so provided fairly long time has passed, this large boost.Before timescale, evolution...

We present an experimental study of single porous spheres settling in a near two-layer ambient density fluid. Data are compared with first-principle model based on diffusive processes. The correctly predicts accelerations the sphere but does not capture retention time at transition quantitatively. Entrainment lighter fluid through shell encapsulating is included this empirically. With parametrization, which exhibits power law dependence Reynolds numbers, times accurately captured....

Abstract We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in dimensions background flow over periodic, multiply connected fluid domain that includes stationary obstacles variable bottom topography. One approach is formulated terms of velocity potential while other evolves vortex sheet strength. Both methods employ layer potentials form periodized Cauchy integrals to compute normal surface, are compatible...

We study the role geometry plays in emergence of asymmetries diffusing passive scalars advected by pressure-driven flows ducts and pipes different aspect ratios. uncover nonintuitive, multi-time-scale behavior gauged a new statistic, which we term "geometric skewness" S^{G}, measures instantaneously forming at short times due to flow geometry. This signature distinguishes elliptical any ratio, for S^{G}=0, from rectangular whose S^{G} is generically nonzero, and, interestingly, shows that...

Abstract An extremely broad and important class of phenomena in nature involves the settling aggregation matter under gravitation fluid systems. Here, we observe model mathematically an unexpected fundamental mechanism by which particles suspended within stratification may self-assemble form large aggregates without adhesion. This phenomenon arises through a complex interplay involving solute diffusion, impermeable boundaries, aggregate geometry, produces toroidal flows. We show that these...

Recently, one of the authors, studying a model for turbulent diffusion involving large-scale velocity field rapidly fluctuating in time, rigorously demonstrated intermittency diffusing scalar by exhibiting broader than Gaussian tails PDF. Here, we explore this further with exact formulas within context general initial data possessing both mean and component. Several new phenomena due to presence nonzero are documented here. We will establish that limiting long time PDF has tails, as well...

We present three-dimensional direct numerical simulations of a vortex ring settling in sharply stratified miscible ambient fluids for near two-layer configurations, and comparisons these with the results from laboratory experiments. The core fluid rings has density higher than both top bottom layers fluid, is fully layers. This setup ensures rich parameter space that we partially explore this study. In particular, critical (bifurcation) phenomenon identified distinguishes long-time behavior...

We explore the problem of a moving free surface in water-saturated porous medium that has either homogeneous or periodically heterogeneous permeability field. identify scaling relations and derive similarity solutions for homogeneous, constant coefficient case both Cartesian an axisymmetric, radial coordinate system. utilize these scalings to half-height slumping time scales as rough guide field groundwater cleanup strategies involving injected brines. averaged using homogenization...

We present experimental observations and quantified theoretical predictions of the nanoscale hydrodynamics induced by nanorod precession emulating primary cilia motion in developing embryos. observe phenomena including micron size particles which exhibit epicyclic orbits with coherent fluctuations distinguishable from comparable amplitude thermal noise. Quantifying mixing transport physics such motions on small scales is critical to understanding fundamental biological processes as...

Abstract A vertically moving boundary in a stratified fluid can create and maintain horizontal density gradient, or vertical layering of density, through the mechanism viscous entrainment. Experiments to study evolution stability axisymmetric flows with layered are performed by towing narrow fibre upwards stably fluid. The forms closed loop thus its effective length is infinite. layer denser entrained thickness measured implementing tracking analysis dyed images. Thickness values up 70 times...