Bubbles navigating through networks of microchannels

This paper describes the behavior of bubbles suspended in a carrier liquid and moving within microfluidic networks of different connectivities. A single-phase continuum fluid, when flowing in a network of channels, partitions itself among all possible paths connecting the inlet and outlet. The flow rates along different paths are determined by the interaction between the fluid and the global structure of the network. That is, the distribution of flows depends on the fluidic resistances of all channels of the network. The movement of bubbles of gas, or droplets of liquid, suspended in a liquid can be quite different from the movement of a single-phase liquid, especially when they have sizes slightly larger than the channels, so that the bubbles (or droplets) contribute to the fluidic resistance of a channel when they are transiting it. This paper examines bubbles in this size range; in the size range examined, the bubbles are discrete and do not divide at junctions. As a consequence, a single bubble traverses only one of the possible paths through the network, and makes a sequence of binary choices ("left" or "right") at each branching intersection it encounters. We designed networks so that, at each junction, a bubble enters the channel into which the volumetric flow rate of the carrier liquid is highest. When there is only a single bubble inside a network at a time, the path taken by the bubble is, counter-intuitively, not necessarily the shortest or the fastest connecting the inlet and outlet. When a small number of bubbles move simultaneously through a network, they interact with one another by modifying fluidic resistances and flows in a time dependent manner; such groups of bubbles show very complex behaviors. When a large number of bubbles (sufficiently large that the volume of the bubbles occupies a significant fraction of the volume of the network) flow simultaneously through a network, however, the collective behavior of bubbles-the fluxes of bubbles through different paths of the network-can resemble the distribution of flows of a single-phase fluid.     

Helical tubulate inclusion compounds of ferrocene and squalene

The inclusion compounds of 2,8-dimethyltricyclo[5.3.1.1^3,9]dodecane-syn-2,syn-8-diol,3, with ferrocene and with squalene have been prepared. The crystal structures of these helical tubulate compounds: (3)₃·(ferrocene)_0.75 [P3₁21,a=b=13.7480(6),c=7.0312(5) Å,Z=1,R=0.038] and (3)₃·(squalene)_0.23 [P3₁21,a=b=13.677(1),c=7.0533(9) Å,Z=1,R=0.042] are described. Supplementary Data relating to this article are deposited with the British Library as supplementary publication No. SUP 82151 (16 pages).     

Dipole,quadrupole, octupole,and dipole–octupole polarizabilities at real and imaginary frequencies for H,HE, and H2 and the dispersion-energy coefficients for interactions between them

We have calculated certain dynamic polarizabilities (for both real and imaginary frequencies) for H, He, and H₂ and the dispersion-energy coefficients for long-range interactions between them. We have done so in a sum-over-states formalism with explicitly electron-correlated wave functions to describe the states. To be precise, we have determined the dipole (α₁), quadrupole (α₂), and octupole (α₃) polarizabilities of H and He for real frequencies (ω) in a range between zero and the first electronic-transition frequency and for imaginary frequencies (iω) on a 32-point Gauss-Legendre grid running from zero to ?ω = 20 E_h, and for H₂, we have found the dipole (α), quadrupole (C), and dipole–octupole (E) polarizability tensors for the same real and imaginary frequencies. The dispersion-energy coefficients, obtained by combining the sum-over-states for-malism for the polarizabilities with analytic integration over ω, gave values of C₆, C₈, and C₁₀ for the atom–atom systems; C, C, C, C, and C for the atom–diatom systems; and C₆, C and C for the H₂? H₂ system. Nearly all the results are considered to be more reliable than those hitherto published and some have been obtained for the first time, e.g., C(iω), E(ω), and E(iω) for H₂ and C, C, and C for the H? H₂ system. © 1993 John Wiley & Sons, Inc.     

BINOL-3,3'-triflone N,N-dimethyl phosphoramidites: through-space 19F,31P spin-spin coupling with a remarkable dependency on temperature and solvent internal pressure

A combined computational and experimental study of the effects of solvent, temperature and stereochemistry on the magnitude of the through-space spin-spin coupling between 31P and 19F nuclei which are six-bonds apart is described. The reaction of 3-trifluoromethylsulfonyl-2,'2-dihydroxy-1,1'-binaphthalene (3-SO2CF3-BINOL) with hexamethylphosphorous triamide (P(NMe2)3) generates a pair of N,N-dimethylphosphoramidites which are diastereomeric due to their differing relative configurations at the stereogenic phosphorous centre and the axially chiral (atropisomeric) BINOL unit. Through-space NMR coupling of the 31P and 19F nuclei of the phosphoramidite and sulfone is detected in one diastereomer only. In the analogous N,N-dimethylphosphoramidite generated from 3,3'-(SO2CF3)2-BINOL only one of the diastereotopic trifluoromethylsulfone moieties couples with the 31P of the phosphoramidite. In both cases, the magnitude of the coupling is strongly modulated (up to 400 %) by solvent and temperature. A detailed DFT analysis of the response of the coupling to the orientation of the CF3 moiety with respect to the P-lone pair facilitates a confident assignment of the stereochemical identity of the pair of diastereomers. The analysis shows that the intriguing effects of environment on the magnitude of the coupling can be rationalised by a complex interplay of solvent internal pressure, molecular volume and thermal access to a wider conformational space. These phenomena suggest the possibility for the design of sensitive molecular probes for local environment that can be addressed via through-space NMR coupling.     

Micropatterning chemical oscillations: waves, autofocusing, and symmetry breaking

Arrays of chemical oscillators are micropatterned by Wet Stamping. The technique is used to demonstrate that chemical waves can be initiated and controlled in oscillatory systems and that such waves can give rise to phenomena not observed in excitable media. Interoscillator coupling and synchronization, kinetic autofocusing, and twist-symmetry breaking are a consequence of the dependence of the oscillation phase on the local concentrations of reagents and on systems' geometry. Conditions under which a generic oscillatory system would exhibit such behaviors are determined.     

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