A first-principle mechanism for particulate aggregation and self-assembly in stratified fluids.

An extremely broad and important class of phenomena in nature involves the settling and aggregation of matter under gravitation in fluid systems. Here, we observe and model mathematically an unexpected fundamental mechanism by which particles suspended within stratification may self-assemble and form large aggregates without adhesion. This phenomenon arises through a complex interplay involving solute diffusion, impermeable boundaries, and aggregate geometry, which produces toroidal flows. We show that these flows yield attractive horizontal forces between particles at the same heights. We observe that many particles demonstrate a collective motion revealing a system which appears to solve jigsaw-like puzzles on its way to organizing into a large-scale disc-like shape, with the effective force increasing as the collective disc radius grows. Control experiments isolate the individual dynamics, which are quantitatively predicted by simulations. Numerical force calculations with two spheres are used to build many-body simulations which capture observed features of self-assembly.

The Diffusion of Passive Tracers in Laminar Shear Flow.

A simple method to experimentally observe and measure the dispersion of a passive tracer in a laminar fluid flow is described. The method consists of first injecting fluorescent dye directly into a pipe filled with distilled water and allowing it to diffuse across the cross-section of the pipe to obtain a uniformly distributed initial condition. Following this period, the laminar flow is activated with a programmable syringe pump to observe the competition of advection and diffusion of the tracer through the pipe. Asymmetries in the tracer distribution are studied and correlations between the pipe cross-section and the shape of the distribution is shown: thin channels (aspect ratio << 1) produce tracers arriving with sharp fronts and tapering tails (front-loaded distributions), while thick channels (aspect ratio ~1) present the opposite behavior (back-loaded distributions). The experimental procedure is applied to capillary tubes of various geometries and is particularly relevant to microfluidic applications by dynamical similarity.

How boundaries shape chemical delivery in microfluidics.

Many microfluidic systems-including chemical reaction, sample analysis, separation, chemotaxis, and drug development and injection-require control and 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 control the shape of the concentration profile along the channel length. Thin channels (aspect ratio << 1) deliver solutes arriving with sharp fronts and tapering tails, whereas thick channels (aspect ratio ~ 1) produce the opposite effect. This occurs for rectangular and elliptical pipes, independent of initial distributions. Thus, it is possible to deliver solute with prescribed distributions, ranging from gradual buildup to sudden delivery, based only on the channel dimensions.

Squaring the Circle: Geometric Skewness and Symmetry Breaking for Passive Scalar Transport in Ducts and Pipes.

We study the role geometry plays in the emergence of asymmetries in diffusing passive scalars advected by pressure-driven flows in ducts and pipes of different aspect ratios. We uncover nonintuitive, multi-time-scale behavior gauged by a new statistic, which we term "geometric skewness" S^{G}, which measures instantaneously forming asymmetries at short times due to flow geometry. This signature distinguishes elliptical pipes of any aspect ratio, for which S^{G}=0, from rectangular ducts whose S^{G} is generically nonzero, and, interestingly, shows that a special duct of aspect ratio ≈0.53335 behaves like a circular pipe as its geometric skewness vanishes. Using a combination of exact solutions, novel short-time asymptotics, and Monte Carlo simulations, we establish the relevant time scales for plateaus and extrema in the evolution of the skewness and kurtosis for our class of geometries. For ducts limiting to channel geometries, we present new exact, single-series formulas for the first four moments on slices used to benchmark Monte Carlo simulations.

Epicyclic orbits in a viscous fluid about a precessing rod: theory and experiments at the micro- and macro-scales.

We present experimental observations and quantified theoretical predictions of the nanoscale hydrodynamics induced by nanorod precession emulating primary cilia motion in developing embryos. We observe phenomena including micron size particles which exhibit epicyclic orbits with coherent fluctuations distinguishable from comparable amplitude thermal noise. Quantifying the mixing and transport physics of such motions on small scales is critical to understanding fundamental biological processes such as extracellular redistribution of nutrients. We present experiments designed to quantify the trajectories of these particles, which are seen to consist of slow orbits about the rod, with secondary epicycles quasicommensurate with the precession rate. A first-principles theory is developed to predict trajectories in such time-varying flows. The theory is further tested using a dynamically similar macroscale experiment to remove thermal noise effects. The excellent agreement between our theory and experiments confirms that the continuum hypothesis applies all the way to the scales of such submicron biological motions.