Concentric liquid reactors for chemical synthesis and separation.

Recent years have witnessed increased interest in systems that are capable of supporting multistep chemical processes without the need for manual handling of intermediates. These systems have been based either on collections of batch reactors1 or on flow-chemistry designs2-4, both of which require considerable engineering effort to set up and control. Here we develop an out-of-equilibrium system in which different reaction zones self-organize into a geometry that can dictate the progress of an entire process sequence. Multiple (routinely around 10, and in some cases more than 20) immiscible or pairwise-immiscible liquids of different densities are placed into a rotating container, in which they experience a centrifugal force that dominates over surface tension. As a result, the liquids organize into concentric layers, with thicknesses as low as 150 micrometres and theoretically reaching tens of micrometres. The layers are robust, yet can be internally mixed by accelerating or decelerating the rotation, and each layer can be individually addressed, enabling the addition, sampling or even withdrawal of entire layers during rotation. These features are combined in proof-of-concept experiments that demonstrate, for example, multistep syntheses of small molecules of medicinal interest, simultaneous acid-base extractions, and selective separations from complex mixtures mediated by chemical shuttles. We propose that 'wall-less' concentric liquid reactors could become a useful addition to the toolbox of process chemistry at small to medium scales and, in a broader context, illustrate the advantages of transplanting material and/or chemical systems from traditional, static settings into a rotating frame of reference.

Stirring-Controlled Synthesis of Ultrastable, Fluorescent Silver Nanoclusters.

This paper describes how macroscopic stirring of a reaction mixture can be used to produce nanostructures exhibiting properties not readily achievable via other protocols. In particular, it is shown that by simply adjusting the stirring rate, a standard glutathione-based method-to date, used to produce only marginally stable fluorescent silver nanoclusters, Ag NCs-can be boosted to yield nanoclusters retaining fluorescence for unprecedented periods of over 2 years. This enhancement derives not simply from increased homogenization of the reaction mixture but mainly from an appropriately timed delivery of oxygen from above the reaction mixture. In effect, oxygen serves as a reagent that dictates size, structure, stability, and functional properties of the growing nanoobjects.

Aerodynamically Levitated Droplets as Small-scale Reactors and Liquid Microprinters.

A thin liquid film spread over the inner surface of a rapidly rotating vial creates an aerodynamic cushion on which one or multiple droplets of various liquids can levitate stably for days or even weeks. These levitating droplets can serve as wall-less ("airware") chemical reactors that can be merged without touching - by remote impulses - to initiate reactions or sequences of reactions at scales down to hundreds of nanomoles. Moreover, under external electric fields, the droplets can act as the world's smallest chemical printers, shedding regular trains of pL or even fL microdrops. In one modality, the levitating droplets operate as completely wirelesss aliquoting/titrating systems delivering pg quantities of reagents into the liquid in the rotating vial; in another modality, they print microdroplet arrays onto target surfaces. The "airware", levitated reactors are inexpensive to set up, remarkably stable to external disturbances and, for printing applications, require operating voltages much lower than in electrospray, electrowetting, or ink jet systems.

Light-Driven, Dynamic Assembly of Micron-To-Centimeter Parts, Micromachines and Microbot Swarms.

This work describes light-driven assembly of dynamic formations and functional particle swarms controlled by appropriately programmed light patterns. The system capitalizes on the use of a fluidic bed whose low thermal conductivity assures that light-generated heat remains "localized" and sets strong convective flows in the immediate vicinity of the particles being irradiated. In this way, even low-power laser light or light from a desktop slide projector can be used to organize dynamic formations of objects spanning four orders of magnitude in size (from microns to centimeters) and over nine orders of magnitude in terms of mass. These dynamic assemblies include open-lattice structures with individual particles performing intricate translational and/or rotational motions, density-gradient particle arrays, nested architectures of mechanical components (e.g., planetary gears), or swarms of light-actuated microbots controlling assembly of other objects.

One-Pot, Three-Phase Recycling of Metals from Li-Ion Batteries in Rotating, Concentric-Liquid Reactors.

Efficient recycling of spent lithium-ion batteries (LIBs) is essential for making their numerous applications sustainable. Hydrometallurgy-based separation methods are an indispensable part of the recycling process but remain limited by the extraction efficiency and selectivity, and typically require numerous binary liquid-liquid extraction steps in which the capacity of the extracting organic phase or partition coefficient of extracted metals become an overall bottleneck. Herein, rotating reactors are described, in which the aqueous feed, organic extractant, and aqueous acceptor phases are all present in the same rotating vessel and can be vigorously stirred and emulsified without the coalescence of aqueous layers. In this arrangement, the extractant molecules are not equilibrated with the feed and, instead, "shuttle" between the feed/extractant and the extractant/acceptor interfaces multiple times, with each such molecule ultimately transferring approximately ten metal ions. This shuttling allows for using extractant concentrations much lower than in previous designs even for extremely concentrated feeds and, simultaneously, ensures unprecedented speed and selectivity of the one-pot processes. These experimental results are accompanied by theoretical considerations of the selectivity versus speed trends as well as discussion of parameters essential for system upscaling.

Discontinuous transition in a laminar fluid flow: a change of flow topology inside a droplet moving in a micron-size channel.

Even at moderate values of Reynolds number [e.g., Re=O(1)] a curved interface between liquids can induce an abrupt transition between topologically different configurations of laminar flow. Here we show for the first time direct evidence of a sharp transition in the speed of flow of a droplet upon a small increase of the value of the capillary number above a threshold and the associated change of topology of flow. The quantitative results on the dependence of the threshold capillary number on the contrast of viscosities and on the direction of transition cannot be explained by any of the existing theories and call for a new description.

Dynamic memory in a microfluidic system of droplets traveling through a simple network of microchannels.

The flow of droplets through the simplest microfluidic network--a set of two parallel channels with a common inlet and a common outlet--exhibits a rich variety of dynamic behaviors parametrized by the frequency of feeding of droplets into the system and by the asymmetry of the arms of the microfluidic loop. Finite ranges of these two parameters form islands of regular (cyclic) behaviors of a well defined period that can be estimated via simple theoretical arguments. These islands are separated by regions of behaviors that are either irregular or cyclic with a very long periodicity. Interestingly, theoretical arguments and numerical simulations show that within the islands of regular behaviors the state of the system can be degenerate: there can exist a number of distinct sequences of trajectories of droplets, each stable and--in the absence of disturbances--continuing ad infinitum. The system can be switched between these cyclic trajectories with a single stimulus.

Dynamic Assembly of Small Parts in Vortex-Vortex Traps Established within a Rotating Fluid.

Stable, purely fluidic particle traps established by vortex flows induced within a rotating fluid are described. The traps can manipulate various types of small parts, dynamically assembling them into high-symmetry clusters, cages, interlocked architectures, jammed colloidal monoliths, or colloidal formations on gas bubbles. The strength and the shape of the trapping region can be controlled by the strengths of one or both vortices and/or by the system's global angular velocity. The system exhibits a range of interesting dynamical behaviors including a Hopf-bifurcation transition between equilibrium-point trapping and the so-called limit cycle in which the particles are confined to circular orbits. Theoretical considerations indicate that these vortex-vortex traps can be further miniaturized to manipulate objects with sizes down to ≈10 µm.

Whole Teflon valves for handling droplets.

We propose and test a new whole-Teflon gate valve for handling droplets. The valve allows droplet plugs to pass through without disturbing them. This is possible due to the geometric design, the choice of material and lack of any pulses of flow generated by closing or opening the valve. The duct through the valve resembles a simple segment of tubing, without constrictions, change in lumen or side pockets. There are no extra sealing materials with different wettability or chemical resistance. The only material exposed to liquids is FEP Teflon, which is resistant to aggressive chemicals and fully biocompatible. The valve can be integrated into microfluidic systems: we demonstrate a complex system for culturing bacteria in hundreds of microliter droplet chemostats. The valve effectively isolates modules of the system to increase precision of operations on droplets. We verified that the valve allowed millions of droplet plugs to safely pass through, without any cross-contamination with bacteria between the droplets. The valve can be used in automating complex microfluidic systems for experiments in biochemistry, biology and organic chemistry.

Between giant oscillations and uniform distribution of droplets: The role of varying lumen of channels in microfluidic networks.

The simplest microfluidic network (a loop) comprises two parallel channels with a common inlet and a common outlet. Recent studies that assumed a constant cross section of the channels along their length have shown that the sequence of droplets entering the left (L) or right (R) arm of the loop can present either a uniform distribution of choices (e.g., RLRLRL...) or long sequences of repeated choices (RRR...LLL), with all the intermediate permutations being dynamically equivalent and virtually equally probable to be observed. We use experiments and computer simulations to show that even small variation of the cross section along channels completely shifts the dynamics either into the strong preference for highly grouped patterns (RRR...LLL) that generate system-size oscillations in flow or just the opposite-to patterns that distribute the droplets homogeneously between the arms of the loop. We also show the importance of noise in the process of self-organization of the spatiotemporal patterns of droplets. Our results provide guidelines for rational design of systems that reproducibly produce either grouped or homogeneous sequences of droplets flowing in microfluidic networks.

Minimization of the Renyi entropy production in the stationary states of the Brownian process with matched death and birth rates.

We analyze the Fleming-Viot process. The system is confined in a box, whose boundaries act as a sink of Brownian particles. The death rate at the boundaries is matched by the branching (birth) rate in the system and thus the number of particles is kept constant. We show that such a process is described by the Renyi entropy whose production is minimized in the stationary state. The entropy production in this process is a monotonically decreasing function of time irrespective of the initial conditions. The first Laplacian eigenvalue is shown to be equal to the Renyi entropy production in the stationary state. As an example we simulate the process in a two-dimensional box.

Iterative operations on microdroplets and continuous monitoring of processes within them; determination of solubility diagrams of proteins.

We demonstrate a technique for controlling the content of multiple microdroplets in time. We use this system to rapidly and quantiatively determine the solubility diagrams of two model proteins (lysozyme and ribonuclease A).

Effects of unsteadiness of the rates of flow on the dynamics of formation of droplets in microfluidic systems.

Oscillations of the input rates of flow have a significant impact on the dynamics of formation of droplets in microfluidic systems and on the quality of generated emulsions.

Transport of resistance through a long microfluidic channel.

We introduce a continuous analytical model of propagation of resistance in pressure-driven flow of two-phase fluid in a single channel. This model can be used to predict and interpret experimental results in droplet microfluidics where the hydrodynamic resistance of a capillary comprises a constant part, specific to the channel and the viscosity of the continuous fluid, and a variable part, related to the presence and distribution of droplets. The continuous model is a convenient generalization of the discrete models as demonstrated via comparisons with discrete simulations and with experiments.

Accurate genetic switch in Escherichia coli: novel mechanism of regulation by co-repressor.

Understanding a biological module involves recognition of its structure and the dynamics of its principal components. In this report we present an analysis of the dynamics of the repression module within the regulation of the trp operon in Escherichia coli. We combine biochemical data for reaction rate constants for the trp repressor binding to trp operator and in vivo data of a number of tryptophan repressors (TrpRs) that bind to the operator. The model of repression presented in this report greatly differs from previous mathematical models. One, two or three TrpRs can bind to the operator and repress the transcription. Moreover, reaction rates for detachment of TrpRs from the operator strongly depend on tryptophan (Trp) concentration, since Trp can also bind to the repressor-operator complex and stabilize it. From the mathematical modeling and analysis of reaction rates and equilibrium constants emerges a high-quality, accurate and effective module of trp repression. This genetic switch responds accurately to fast consumption of Trp from the interior of a cell. It switches with minimal dispersion when the concentration of Trp drops below a thousand molecules per cell.

Pattern formation in nonextensive thermodynamics: selection criterion based on the Renyi entropy production.

We analyze a system of two different types of Brownian particles confined in a cubic box with periodic boundary conditions. Particles of different types annihilate when they come into close contact. The annihilation rate is matched by the birth rate, thus the total number of each kind of particles is conserved. When in a stationary state, the system is divided by an interface into two subregions, each occupied by one type of particles. All possible stationary states correspond to the Laplacian eigenfunctions. We show that the system evolves towards those stationary distributions of particles which minimize the Renyi entropy production. In all cases, the Renyi entropy production decreases monotonically during the evolution despite the fact that the topology and geometry of the interface exhibit abrupt and violent changes.