This article describes the process of formation of droplets and bubbles in microfluidic T-junction geometries. At low capillary numbers break-up is not dominated by shear stresses: experimental results support the assertion that the dominant contribution to the dynamics of break-up arises from the pressure drop across the emerging droplet or bubble. This pressure drop results from the high resistance to flow of the continuous (carrier) fluid in the thin films that separate the droplet from the walls of the microchannel when the droplet fills almost the entire cross-section of the channel. A simple scaling relation, based on this assertion, predicts the size of droplets and bubbles produced in the T-junctions over a range of rates of flow of the two immiscible phases, the viscosity of the continuous phase, the interfacial tension, and the geometrical dimensions of the device.

This paper derives the difference in pressure between the beginning and the end of a rectangular microchannel through which a flowing liquid (water, with or without surfactant, and mixtures of water and glycerol) carries bubbles that contact all four walls of the channel. It uses an indirect method to derive the pressure in the channel. The pressure drop depends predominantly on the number of bubbles in the channel at both low and high concentrations of surfactant. At intermediate concentrations of surfactant, if the channel contains bubbles (of the same or different lengths), the total, aggregated length of the bubbles in the channel is the dominant contributor to the pressure drop. The difference between these two cases stems from increased flow of liquid through the ''gutters''-the regions of the system bounded by the curved body of the bubble and the corners of the channel-in the presence of intermediate concentrations of surfactant. This paper presents a systematic and quantitative investigation of the influence of surfactants on the flow of fluids in microchannels containing bubbles. It derives the contributions to the overall pressure drop from three regions of the channel: (i) the slugs of liquid between the bubbles (and separated from the bubbles), in which liquid flows as though no bubbles were present; (ii) the gutters along the corners of the microchannels; and (iii) the curved caps at the ends of the bubble.

Droplets of one liquid suspended in a second, immiscible liquid move through a microfluidic device in which a channel splits into two branches that reconnect downstream. The droplets choose a path based on the number of droplets that occupy each branch. The interaction among droplets in the channels results in complex sequences of path selection. The linearity of the flow through the microchannels, however, ensures that the behavior of the system can be reversed. This reversibility makes it possible to encrypt and decrypt signals coded in the intervals between droplets. The encoding/decoding device is a functional microfluidic system that requires droplets to navigate a network in a precise manner without the use of valves, switches, or other means of external control.

We describe the rich dynamic behavior--including period-doubling and period-halving bifurcations, intermittency, and chaos--observed in the breakup of an inviscid fluid in a coflowing, viscous liquid, both confined in a microfabricated flow-focusing geometry. Experimental observations support inertia-dominated dynamics of the interface, and suggest the possible similarity to the dynamics of a topologically inverted counterpart of this system, that is, a dripping faucet.

This paper demonstrates a methodology for micromixing that is sufficiently simple that it can be used in portable microfluidic devices. It illustrates the use of the micromixer by incorporating it into an elementary, portable microfluidic system that includes sample introduction, sample filtration, and valving. This system has the following characteristics: (i) it is powered with a single hand-operated source of vacuum, (ii) it allows samples to be loaded easily by depositing them into prefabricated wells, (iii) the samples are filtered in situ to prevent clogging of the microchannels, (iv) the structure of the channels ensure mixing of the laminar streams by interaction with bubbles of gas introduced into the channels, (v) the device is prepared in a single-step soft-lithographic process, and (vi) the device can be prepared to be resistant to the adsorption of proteins, and can be used with or without surface-active agents.We fabricated the device (Figs. 1a) in a polydimethylsiloxane (PDMS) slab sealed to a PDMS substrate. We chose to use PDMS because it is the most useful material for testing concepts in microfluidics, and because it is easily coupled with

Flows of droplets through networks of microchannels differ significantly from the flow of simple fluids. Our report focuses on the paths of individual droplets through the simplest possible network: a channel that splits into two arms that subsequently recombine. This simple system exhibits complex patterns of flow: both periodic and irregular, depending on the frequency at which the drops are fed into the "loop." A numerical model explains these results and shows regions of regular patterns separated by regions of high complexity. Our results elicit new questions regarding the dynamics of flow of discrete elements of fluids through networks, and point to potential opportunities and difficulties in the design of integrated mini-laboratories operating on droplets.

Understanding spatiotemporal complexity 1-3 is important to many disciplines, from biology 4,5 to finance 6 . However, because it is seldom possible to achieve complete control over the parameters that determine the behaviour of real complex systems, it has been difficult to study such behaviour experimentally. Here we demonstrate a simple microfluidic bubble generator that shows stable oscillatory patterns (both in space and time) of unanticipated complexity and uniquely long repetition periods. At low flow rates, the device produces a regular stream of bubbles of uniform size. As the flow increases, the system shows intricate dynamic behaviour typified by a stable limit cycle of order 29 bubbles per period, which repeats without change over intervals of up to 100 periods and more. As well as providing an example of a well-characterized and experimentally tractable model system with which to study complex, nonlinear dynamics, such behaviour demonstrates that it is possible to observe complex and stable limit cycles without active external control.Even though nonlinear temporal dynamics is well understood 1 , the understanding of systems having complex dynamics in both time and space is still limited 2,3,7 . Spatiotemporal dynamics may underlie phenomena as varied as weather 8 , evolution of geophysical patterns 9 , the movement of stock markets 6 , the flux through metabolic pathways 4 , biomechanical processes 10 and morphogenesis 2,5 . So-called large spatiotemporal systemssystems in which the number of effective degrees of freedom is large-demonstrate the applicability of amplitude and phase equations 2,11 in the characterization of spatiotemporal patterns 2,7 . Small systems-systems with only a few degrees of freedom-are substantially more complicated to study because the boundaries of these systems strongly influence their dynamics and are difficult to treat analytically. Truly tractable experimental demonstrations 12,13 of spatiotemporal dynamics are scarce 11 , and the need for them is correspondingly high 2 . Here we provide an example of such a tractable system that is amenable to rational design and modification.The system comprises coupled microfluidic flow-focusing devices. A single flow-focusing device 14,15 (Fig. 1a) was first implemented in a microfluidic chip by Anna et al. 16 ; the system has three inlet channels-two outer supplying liquid and the centre one supplying gas-that merge at a junction leading to a single outlet channel. In this geometry, the pinch-off process that generates bubbles is regulated 17 by the inflow of liquid into the orifice (at a typical speed u inflow ∼ 0.01−1 m s −1 ); this inflow is slower by two to five orders of magnitude than the relaxation rates (the typical interfacial and bulk relaxation speeds are u interfacial ∼ γ/μ ∼ 100 m s −1 and u sound ∼ 1,000 m s −1 , respectively, where γ is the interfacial tension and μ is the viscosity of the liquid). As a result, the breakup process in the simple flow-focusing device is highly reproducible and leads to the generati...

This work demonstrates that pressure-driven flow in a microfluidic network can solve mazelike problems by exploring all possible solutions in a parallel fashion. Microfluidic networks can be fabricated easily by soft lithography and rapid prototyping. To find the best path between the inlet and the outlet of these networks, the channels are filled with a fluid, and the path of a second, dyed fluid moving under pressuredriven flow is traced from the inlet to the outlet. Varying the viscosities of these fluids allows the behavior of the system to be tailored. For example, filling the channels with immiscible fluids of different viscosities enhances the resolution of paths of different fluidic resistances.