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 ͑nanoliters͒ 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. CONTENTS

The past decade has seen researchers develop and apply novel technologies for biomolecular detection, at times approaching hard limits imposed by physics and chemistry. In nearly all sensors, the transport of target molecules to the sensor can play as critical a role as the chemical reaction itself in governing binding kinetics, and ultimately performance. Yet rarely does an analysis of the interplay between diffusion, convection and reaction motivate experimental design or interpretation. Here we develop a physically intuitive and practical understanding of analyte transport for researchers who develop and employ biosensors based on surface capture. We explore the qualitatively distinct behaviors that result, develop rules of thumb to quickly determine how a given system will behave, and derive order-of-magnitude estimates for fundamental quantities of interest, such as fluxes, collection rates and equilibration times. We pay particular attention to collection limits for micro- and nanoscale sensors, and highlight unexplained discrepancies between reported values and theoretical limits.

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 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 ∝ E 2 0 L, where E 0 is the field strength and L is a geometric length scale, and are set up on a time scale τ c = λ D L/D, where λ 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.

In microrheology, the local and bulk mechanical properties of a complex fluid are extracted from the motion of probe particles embedded within it. In passive microrheology, particles are forced by thermal fluctuations and probe linear viscoelasticity, whereas active microrheology involves forcing probes externally and can be extended out of equilibrium to the nonlinear regime. Here we review the development, present state, and future directions of this field. We organize our review around the generalized Stokes-Einstein relation (GSER), which plays a central role in the interpretation of microrheology. By discussing the Stokes and Einstein components of the GSER individually, we identify the key assumptions that underpin each, and the consequences that occur when they are violated. We conclude with a discussion of two techniques—multiple particle-tracking and nonlinear microrheology—that have arisen to handle systems in which the GSER breaks down.

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.The advent of microfluidic technology raises the fundamental question of how to pump and mix fluids at micron scales, where pressure-driven flows and inertial instabilities are suppressed by viscosity [1,2]. The most popular non-mechanical pumping strategy is based on electro-osmosis -the effective slip, u , at a liquidelectrolyte/solid interface due to tangential electric field, E . The Helmholtz-Smoluchowski formula,gives the slip in terms of the permittivity, ε, and viscosity, η, of the liquid and the zeta potential, ζ, across the diffuse part of the (thin) interfacial double layer [3]. The usual case of constant (possibly non-uniform [4]) ζ, however, has some drawbacks related to linearity, u ∝ E : (i) the flow is somewhat weak, e.g. u = 70µm/s in aqueous solution with E = 100 V/cm and ζ = 10 mV and (ii) AC fields, which reduce undesirable Faradaic reactions, produce zero time-averaged flow. These drawbacks do not apply to AC electro-osmosis, recently discovered by Ramos et al. [5] and Ajdari [6]. Nonlinear electro-osmotic slip is produced at microelectrodes as an AC field acts on induced double-layer charge prior to complete screening. In spite of extensive work, however, this promising effect remains limited to quasi-planar pairs [7] or arrays [8] of electrodes at a single AC frequency, ω c = τ −1 c , where τ c = λ D L/D is the "RC time" of an equivalent circuit of bulk resistors of size L (the electrode spacing) and double-layer capacitors of thickness, λ D , the Debye screening length, and D is an ionic diffusivity.How general is this phenomenon? Nonlinear electroosmotic flows have also been observed at dielectric impurities on electrodes with AC forcing [9] and, more suggestively, at dielectric (non-electrode) micro-channel corners in DC fields [10]. Although it is largely unknown (and uncited) in the West, similar flows have also been studied in the Russian literature on polarizable colloids [11], including the effect of such flows on dielectrophoresis [12]. The unifying principle in these diverse effects is that an applied field acts on its own induced diffuse charge, so we suggest the term, "induced-charge electro-osmosis" (ICEO), to describe it.In this Letter, w...