It is difficult to mix solutions in microchannels. Under typical operating conditions, flows in these channels are laminar-the spontaneous fluctuations of velocity that tend to homogenize fluids in turbulent flows are absent, and molecular diffusion across the channels is slow. We present a passive method for mixing streams of steady pressure-driven flows in microchannels at low Reynolds number. Using this method, the length of the channel required for mixing grows only logarithmically with the Péclet number, and hydrodynamic dispersion along the channel is reduced relative to that in a simple, smooth channel. This method uses bas-relief structures on the floor of the channel that are easily fabricated with commonly used methods of planar lithography.

Microfluidic devices for manipulating fluids are widespread and finding uses in many scientific and industrial contexts. Their design often requires unusual geometries and the interplay of multiple physical effects such as pressure gradients, electrokinetics, and capillarity. These circumstances lead to interesting variants of well-studied fluid dynamical problems and some new fluid responses. We provide an overview of flows in microdevices with focus on electrokinetics, mixing and dispersion, and multiphase flows. We highlight topics important for the description of the fluid dynamics: driving forces, geometry, and the chemical characteristics of surfaces. 1.1. Manipulating Microflows Microfluidic flows are readily manipulated using many kinds of external fields (pressure, electric, magnetic, capillary, and so on). As dimensions shrink, the MICROFLUIDICS 383 TABLE 1 Forces and external fields with which to manipulate flows in microfluidic configurations. It is also possible to use external means to manipulate particles embedded in flows, as in electrophoresis or the use of magnetic forces (e.g., Zabow et al. 2002) Driving force Subcategorization Remarks; representative references Pressure gradient ∇ p Familiar case as in pipe flow Capillary effects Surface tension, γ Capillary pressure difference Thermal (e.g., Sammarco & Burns 1999) Electrical (electrocapillarity) (e.g., Pollack et al. 2000; Prins et al. 2001) Surface tension gradients, ∇γ Typically involve thin films Chemical (e.g., Gallardo et al. 1999) Thermal (e.g., Kataoka & Troian 1999) Electrical Optical Photoresponsive materials Electric fields E DC electro-osmosis Uniform velocity field AC electro-osmosis Rectified flows Dielectrophoresis Response ∝∇E 2 Magnetic field/ Magnetohydrodynamic (e.g., Bau et al. 2001) Lorentz forces stirring Rotation Centrifugal forces (e.g., R.D. Johnson et al. 2001) Sound Acoustic streaming

Microvascular networks support metabolic activity and define microenvironmental conditions within tissues in health and pathology. Recapitulation of functional microvascular structures in vitro could provide a platform for the study of complex vascular phenomena, including angiogenesis and thrombosis. We have engineered living microvascular networks in three-dimensional tissue scaffolds and demonstrated their biofunctionality in vitro. We describe the lithographic technique used to form endothelialized microfluidic vessels within a native collagen matrix; we characterize the morphology, mass transfer processes, and long-term stability of the endothelium; we elucidate the angiogenic activities of the endothelia and differential interactions with perivascular cells seeded in the collagen bulk; and we demonstrate the nonthrombotic nature of the vascular endothelium and its transition to a prothrombotic state during an inflammatory response. The success of these microvascular networks in recapitulating these phenomena points to the broad potential of this platform for the study of cardiovascular biology and pathophysiology.tissue engineering | regenerative medicine | microfluidics | cancer | blood T he microvasculature is an extensive organ that mediates the interaction between blood and tissues. It defines the biological and physical characteristics of the microenvironment within tissues and plays a role in the initiation and progression of many pathologies, including cancer (1) and cardiovascular diseases (2, 3). Conventional planar cultures fail to recreate the in vivo physiology of the microvasculature with respect to three-dimensional (3D) geometry (lumens and axial branching points), and interactions of endothelium with perivascular cells, extracellular tissue and blood flow (4). Studies of the microvasculature in vivo allow only limited control of physical, chemical, and biological parameters influencing the microvasculature and present challenges with respect to observation (5). In vitro cultures that produce tubular vessels within 3D matrices will aid in elucidation of the roles of the microvasculature in health and disease. Important progress has been made toward this goal: Biologically derived or synthetic materials have been used to generate macrovessel tubes (6) and endothelialized microtubes (7); cellular self-assembly has been used to generate random microvasculature (8); microfabrication has been used to define complex geometries in hydrogels at the micro-scale (9); and distributions of cells and biochemical factors within 3D scaffolds (10). Of particular note, the group of Tien has pioneered the use of collagen to template the growth of vascular endothelium (7, 11) and demonstrated appropriate permeability (7), response to cyclic AMP (12), and differential properties as a function of the luminal shear stress and composition of the medium (13). Nonetheless, prior methodologies have been unable to produce endothelialized networks that can undergo substantial remodeling via angiogenesis; elucidate the ...

Most methods to culture cells in three dimensions depend on a cell-seedable biomaterial to define the global structure of the culture and the microenvironment of the cells. Efforts to tailor these scaffolds have focused on the chemical and mechanical properties of the biomaterial itself. Here, we present a strategy to control the distributions of soluble chemicals within the scaffold with convective mass transfer via microfluidic networks embedded directly within the cell-seeded biomaterial. Our presentation of this strategy includes: a lithographic technique to build functional microfluidic structures within a calcium alginate hydrogel seeded with cells; characterization of this process with respect to microstructural fidelity and cell viability; characterization of convective and diffusive mass transfer of small and large solutes within this microfluidic scaffold; and demonstration of temporal and spatial control of the distribution of non-reactive solutes and reactive solutes (that is, metabolites) within the bulk of the scaffold. This approach to control the chemical environment on a micrometre scale within a macroscopic scaffold could aid in engineering complex tissues.

Plant scientists believe that transpiration-the motion of water from the soil, through a vascular plant, and into the air-occurs by a passive, wicking mechanism. This mechanism is described by the cohesion-tension theory: loss of water by evaporation reduces the pressure of the liquid water within the leaf relative to atmospheric pressure; this reduced pressure pulls liquid water out of the soil and up the xylem to maintain hydration. Strikingly, the absolute pressure of the water within the xylem is often negative, such that the liquid is under tension and is thermodynamically metastable with respect to the vapour phase. Qualitatively, this mechanism is the same as that which drives fluid through the synthetic wicks that are key elements in technologies for heat transfer, fuel cells and portable chemical systems. Quantitatively, the differences in pressure generated in plants to drive flow can be more than a hundredfold larger than those generated in synthetic wicks. Here we present the design and operation of a microfluidic system formed in a synthetic hydrogel. This synthetic 'tree' captures the main attributes of transpiration in plants: transduction of subsaturation in the vapour phase of water into negative pressures in the liquid phase, stabilization and flow of liquid water at large negative pressures (-1.0 MPa or lower), continuous heat transfer with the evaporation of liquid water at negative pressure, and continuous extraction of liquid water from subsaturated sources. This development opens the opportunity for technological uses of water under tension and for new experimental studies of the liquid state of water.