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.     

Fluoroalkyl and alkyl chains have similar hydrophobicities in binding to the "hydrophobic wall" of carbonic anhydrase

The hydrophobic effect, the free-energetically favorable association of nonpolar solutes in water, makes a dominant contribution to binding of many systems of ligands and proteins. The objective of this study was to examine the hydrophobic effect in biomolecular recognition using two chemically different but structurally similar hydrophobic groups, aliphatic hydrocarbons and aliphatic fluorocarbons, and to determine whether the hydrophobicity of the two groups could be distinguished by thermodynamic and biostructural analysis. This paper uses isothermal titration calorimetry (ITC) to examine the thermodynamics of binding of benzenesulfonamides substituted in the para position with alkyl and fluoroalkyl chains (H(2)NSO(2)C(6)H(4)-CONHCH(2)(CX(2))(n)CX(3), n = 0-4, X = H, F) to human carbonic anhydrase II (HCA II). Both alkyl and fluoroalkyl substituents contribute favorably to the enthalpy and the entropy of binding; these contributions increase as the length of chain of the hydrophobic substituent increases. Crystallography of the protein-ligand complexes indicates that the benzenesulfonamide groups of all ligands examined bind with similar geometry, that the tail groups associate with the hydrophobic wall of HCA II (which is made up of the side chains of residues Phe131, Val135, Pro202, and Leu204), and that the structure of the protein is indistinguishable for all but one of the complexes (the longest member of the fluoroalkyl series). Analysis of the thermodynamics of binding as a function of structure is compatible with the hypothesis that hydrophobic binding of both alkyl and fluoroalkyl chains to hydrophobic surface of carbonic anhydrase is due primarily to the release of nonoptimally hydrogen-bonded water molecules that hydrate the binding cavity (including the hydrophobic wall) of HCA II and to the release of water molecules that surround the hydrophobic chain of the ligands. This study defines the balance of enthalpic and entropic contributions to the hydrophobic effect in this representative system of protein and ligand: hydrophobic interactions, here, seem to comprise approximately equal contributions from enthalpy (plausibly from strengthening networks of hydrogen bonds among molecules of water) and entropy (from release of water from configurationally restricted positions).     

Luminescent ruthenium tripod complexes: properties in solution and on conductive surfaces

Two luminescent ruthenium complexes containing tripod-type end groups linked through a rigid spacer to a phenanthroline derivative, able to confer an axial geometry to the complexes, are described. One of the compounds is functionalized with thioacetate groups in order to link the metal complex to metallic surfaces. The photophysical and electrochemical behavior of the complexes are studied in solution and on conductive substrates and, furthermore, self-assembled monolayers are investigated in a junction using gold and an indium gallium eutectic, as electrodes, and by time-resolved confocal microscopy. The results show that the complexes form very stable and well-ordered monolayers because of the tripod system, which can anchor the complex almost perpendicular to the surfaces.     

Paper-based piezoresistive MEMS sensors

This paper describes the development of MEMS force sensors constructed using paper as the structural material. The working principle on which these paper-based sensors are based is the piezoresistive effect generated by conductive materials patterned on a paper substrate. The device is inexpensive (～$0.04 per device for materials), simple to fabricate, lightweight, and disposable. Paper can be readily folded into three-dimensional structures to increase the stiffness of the sensor while keeping it light in weight. The entire fabrication process can be completed within one hour without expensive cleanroom facilities using simple tools (e.g., a paper cutter and a painting knife). We demonstrated that the paper-based sensor can measure forces with moderate performance (i.e., resolution: 120 μN, measurement range: ±16 mN, and sensitivity: 0.84 mV mN(-1)). We applied this sensor to characterizing the mechanical properties of a soft material. Leveraging the same sensing concept, we also developed a paper-based balance with a measurement range of 15 g, and a resolution of 0.39 g.     

Collineations of projective planes of order 10, part I

No projective plane of order 10 has a collineation group of order 9 which fixes a 12-arc, a set of twelve points no three collinear, as a set. This fact, proved in Part I, is used to prove in Part II that the full collineation group of any projective plane of order 10 has order 1, 3, or 5.     

The strength of weak proximity

This paper studies weak proximity drawings of graphs and demonstrates their advantages over strong proximity drawings in certain cases. Weak proximity drawings are straight line drawings such that if the proximity region of two points p and q representing vertices is devoid of other points representing vertices, then segment (p,q) is allowed, but not forced, to appear in the drawing. This differs from the usual, strong, notion of proximity drawing in which such segments must appear in the drawing.Most previously studied proximity regions are associated with a parameter β, 0β∞. For fixed β, weak β-drawability is at least as expressive as strong β-drawability, as a strong β-drawing is also a weak one. We give examples of graph families and β values where the two notions coincide, and a situation in which it is NP-hard to determine weak β-drawability. On the other hand, we give situations where weak proximity significantly increases the expressive power of β-drawability: we show that every graph has, for all sufficiently small β, a weak β-proximity drawing that is computable in linear time, and we show that every tree has, for every β less than 2, a weak β-drawing that is computable in linear time.