Effective pseudo-potentials of hydrodynamic origin

It is shown that low Reynolds number fluid flows can cause suspended particles to respond as though they were in an equilibrium system with an effective potential. This general result follows naturally from the fact that different methods of moving particles in viscous fluids give rise to very different long-range flows. Two examples are discussed: electrophoretic `levitation' of a heavy charged sphere, for which a hydrodynamic `pseudo-potential' can be written in closed form, and quasi-two dimensional crystals of like-charged colloidal spheres which form near charged walls, whose apparent attraction arises not from a force but from persistent fluid flows.Comment: 10 pages, 3 figures, submitted to J. Fluid Mec

Kinematic irreversibility in surfactant-laden interfaces

The surface shear viscosity of an insoluble surfactant monolayer often depends strongly on its surface pressure. Here, we show that a particle moving within a bounded monolayer breaks the kinematic reversibility of low-Reynolds-number flows. The Lorentz reciprocal theorem allows such irreversibilities to be computed without solving the full nonlinear equations, giving the leading-order contribution of surface-pressure-dependent surface viscosity. In particular, we show that a disk translating or rotating near an interfacial boundary experiences a force in the direction perpendicular to that boundary. In unbounded monolayers, coupled modes of motion can also lead to non-intuitive trajectories, which we illustrate using an interfacial analog of the Magnus effect. This perturbative approach can be extended to more complex geometries, and to 2D suspensions more generally

Induced-charge Electrokinetic Phenomena: Theory and Microfluidic Applications

We give a general, physical description of ``induced-charge electro-osmosis'' (ICEO), the nonlinear electrokinetic slip at a polarizable surface, in the context of some new techniques for microfluidic pumping and mixing. ICEO generalizes ``AC electro-osmosis'' at micro-electrode arrays to various dielectric and conducting structures in weak DC or AC electric fields. The basic effect produces micro-vortices to enhance mixing in microfluidic devices, while various broken symmetries -- controlled potential, irregular shape, non-uniform surface properties, and field gradients -- can be exploited to produce streaming flows. Although we emphasize the qualitative picture of ICEO, we also briefly describe the mathematical theory (for thin double layers and weak fields) and apply it to a metal cylinder with a dielectric coating in a suddenly applied DC field.Comment: 4 pages, 4 figs; revsion with more refs, one new fig, and more emphasis on microfluidic

Slow dynamics of phospholipid monolayers at the air/water interface

Phospholipid monolayers at the air-water interface serve as model systems for various biological interfaces, e.g. lung surfactant layers and outer leaflets of cell membranes. Although the dynamical (viscoelastic) properties of these interfaces may play a key role in stability, dynamics and function, the relatively weak rheological properties of most such monolayers have rendered their study difficult or impossible. A novel technique to measure the dynamical properties of fluid-fluid interfaces have developed accordingly. We microfabricate micron-scale ferromagnetic disks, place them on fluid-fluid interfaces, and use external electromagnets to exert torques upon them. By measuring the rotation that results from a known external torque, we compute the rotational drag, from which we deduce the rheological properties of the interface. Notably, our apparatus enable direct interfacial visualization while the probes are torqued. In this fluid dynamics video, we directly visualize dipalmitoylphosphatidylcholine(DPPC) monolayers at the air-water interface while shearing. At about 9 mN/m, DPPC exhibits a liquid condensed(LC) phase where liquid crystalline domains are compressed each other, and separated by grain boundaries. Under weak oscillatory torque, the grain boundaries slip past each other while larger shear strain forms a yield surface by deforming and fracturing the domains. Shear banding, which is a clear evidence of yield stress, is visualized during steady rotation. Remarkably slow relaxation time was also found due to slow unwinding of the stretched domains.Comment: 1 page, no figures, gallery of fluid motion 200

Induced-Charge Electro-Osmosis

We describe the general phenomenon of `induced-charge electro-osmosis' (ICEO) -- the nonlinear electro-osmotic slip that occurs when an applied field acts on the ionic charge it {\sl induces} around a polarizable surface. Motivated by a simple physical picture, we calculate ICEO flows around conducting cylinders in steady (DC), oscillatory (AC), and suddenly-applied electric fields. This picture, and these systems, represent perhaps the clearest example of nonlinear electrokinetic phenomena. We complement and verify this physically-motivated approach using a matched asymptotic expansion to the electrokinetic equations in the thin double-layer and low potential limits. ICEO slip velocities vary like $u_s \propto E_0^2 L$, where $E_0$ is the field strength and $L$ is a geometric length scale, and are set up on a time scale $\tau_c = \lambda_D L/D$, where $\lambda_D$ is the screening length and $D$ is the ionic diffusion constant. We propose and analyze ICEO microfluidic pumps and mixers that operate without moving parts under low applied potentials. Similar flows around metallic colloids with fixed total charge have been described in the Russian literature (largely unnoticed in the West). ICEO flows around conductors with fixed potential, on the other hand, have no colloidal analog and offer further possibilities for microfluidic applications.Comment: 36 pages, 8 figures, to appear in J. Fluid Mec

Microfluidics: Fluid physics at the nanoliter scale

Microfabricated integrated circuits revolutionized computation by vastly reducing the space, labor, and time required for calculations. Microfluidic systems hold similar promise for the large-scale automation of chemistry and biology, suggesting the possibility of numerous experiments performed rapidly and in parallel, while consuming little reagent. While it is too early to tell whether such a vision will be realized, significant progress has been achieved, and various applications of significant scientific and practical interest have been developed. Here a review of the physics of small volumes (nanoliters) of fluids is presented, as parametrized by a series of dimensionless numbers expressing the relative importance of various physical phenomena. Specifically, this review explores the Reynolds number Re, addressing inertial effects; the Péclet number Pe, which concerns convective and diffusive transport; the capillary number Ca expressing the importance of interfacial tension; the Deborah, Weissenberg, and elasticity numbers De, Wi, and El, describing elastic effects due to deformable microstructural elements like polymers; the Grashof and Rayleigh numbers Gr and Ra, describing density-driven flows; and the Knudsen number, describing the importance of noncontinuum molecular effects. Furthermore, the long-range nature of viscous flows and the small device dimensions inherent in microfluidics mean that the influence of boundaries is typically significant. A variety of strategies have been developed to manipulate fluids by exploiting boundary effects; among these are electrokinetic effects, acoustic streaming, and fluid-structure interactions. The goal is to describe the physics behind the rich variety of fluid phenomena occurring on the nanoliter scale using simple scaling arguments, with the hopes of developing an intuitive sense for this occasionally counterintuitive world

Schematic Models for Active Nonlinear Microrheology

We analyze the nonlinear active microrheology of dense colloidal suspensions using a schematic model of mode-coupling theory. The model describes the strongly nonlinear behavior of the microscopic friction coefficient as a function of applied external force in terms of a delocalization transition. To probe this regime, we have performed Brownian dynamics simulations of a system of quasi-hard spheres. We also analyze experimental data on hard-sphere-like colloidal suspensions [Habdas et al., Europhys. Lett., 2004, 67, 477]. The behavior at very large forces is addressed specifically

A highly oriented cubic phase formed by lipids under shear

We demonstrate the formation of a macroscopically oriented inverse bicontinuous cubic (QII) lipid phase from a sponge (L3) phase by controlled hydration during shear flow. The L3 phase was the monoolein/ butanediol/water system; the addition of water reduces the butanediol concentration, inducing the formation of a diamond (QIID) cubic phase, which is oriented by the shear flow. The phenomenon was reproduced in both capillary and Couette geometries, indicating that this represents a robust general route for the production of highly aligned bulkQII samples, with applications in nanomaterial templating and protein research

Steady advection-diffusion around finite absorbers in two-dimensional potential flows

We perform an exhaustive study of the simplest, nontrivial problem in advection-diffusion -- a finite absorber of arbitrary cross section in a steady two-dimensional potential flow of concentrated fluid. This classical problem has been studied extensively in the theory of solidification from a flowing melt, and it also arises in Advection-Diffusion-Limited Aggregation. In both cases, the fundamental object is the flux to a circular disk, obtained by conformal mapping from more complicated shapes. We construct the first accurate numerical solution using an efficient new method, which involves mapping to the interior of the disk and using a spectral method in polar coordinates. Our method also combines exact asymptotics and an adaptive mesh to handle boundary layers. Starting from a well-known integral equation in streamline coordinates, we also derive new, high-order asymptotic expansions for high and low P\'eclet numbers (\Pe). Remarkably, the `high' \Pe expansion remains accurate even for such low \Pe as $10^{-3}$. The two expansions overlap well near \Pe = 0.1, allowing the construction of an analytical connection formula that is uniformly accurate for all \Pe and angles on the disk with a maximum relative error of 1.75%. We also obtain an analytical formula for the Nusselt number ($\Nu$) as a function of the P\'eclet number with a maximum relative error of 0.53% for all possible geometries. Because our finite-plate problem can be conformally mapped to other geometries, the general problem of two-dimensional advection-diffusion past an arbitrary finite absorber in a potential flow can be considered effectively solved.Comment: 29 pages, 12 figs (mostly in color