Circulatory bubble dynamics: From physical to biological aspects

Bubbles can form in the body during or after decompression from pressure exposures such as those undergone by scuba divers, astronauts, caisson and tunnel workers. Bubble growth and detachment physics then becomes significant in predicting and controlling the probability of these bubbles causing mechanical problems by blocking vessels, displacing tissues, or inducing an inflammatory cascade if they persist for too long in the body before being dissolved. By contrast to decompression induced bubbles whose site of initial formation and exact composition are debated, there are other instances of bubbles in the bloodstream which are well-defined. Gas emboli unwillingly introduced during surgical procedures and ultrasound microbubbles injected for use as contrast or drug delivery agents are therefore also discussed. After presenting the different ways that bubbles can end up in the human bloodstream, the general mathematical formalism related to the physics of bubble growth and detachment from decompression is reviewed. Bubble behavior in the bloodstream is then discussed, including bubble dissolution in blood, bubble rheology and biological interactions for the different cases of bubble and blood composition considered.     

Star‐branched polystyrenes by nitroxide living free‐radical polymerization

Star‐branched polystyrenes, with polydispersity indices of 1.15–1.56 and 4–644 equal arms, were synthesized by the reaction of 2,2,6,6‐tetramethylpiperidin‐1‐yloxy (TEMPO)‐capped polystyrene (PS‐T) with divinylbenzene (DVB). The characterization of PS‐T and the final star polymers was carried out by size exclusion chromatography, low‐angle laser light scattering, and viscometry. The degree of branching of the star polymers depended on the DVB/PS‐T ratio and the PS‐T molecular weight. An asymmetric (or miktoarm) star homopolymer of the PS_nPS′_n type was made by the reaction of the PS_n symmetric star, which had n TEMPO molecules on its nucleus and consisted of a multifunctional initiator, with extra styrene. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 320–325, 2001     

A conductance study of reducing volume liquid bridges

This work demonstrates how electrical conductance measurements can be employed for the study of liquid bridge behavior when their volume varies with time while their separation distance remains constant. The liquid bridges are edge pinned between two vertical, identical rods (r-bridges) at varying separation distances. Liquid evaporation is used as a means of reducing the bridge volume in a continuous smooth fashion. A zero-order continuation sequence with respect to Bond number and liquid bridge volume is combined with the shooting method for the solution of the Young-Laplace equation to give the liquid bridge shape as a function of its instantaneous volume. A novel, very efficient computational scheme is developed based on singular perturbation expansion for the solution of the Laplace equation in the liquid bridge to compute its electrical conductance that proved faster by orders of magnitude compared to other alternative approaches. The potential for estimating the liquid bridge characteristics or the evaporation rate by matching the experimental and theoretical results is discussed extensively.     

Synthesis of model polycyclohexylene/polyethylene miktoarm star copolymers with three and four arms

The synthesis of well‐defined 3‐ and 4‐miktoarm star copolymers of the A₂B and A₃B types is described, where A is 1,4‐polybutadiene and B is poly(1,3‐cyclohexadiene). The synthetic approach involves the reaction of poly(1,3‐cyclohexadienyl)lithium with an excess of methyltrichlorosilane or tetrachlorosilane followed, after the removal of excess silane, by a small excess of polybutadienyllithium. Characterization was carried out by size exclusion chromatography, low‐angle laser light scattering, laser differential refractometry, and NMR spectroscopy. The complete heterogeneous catalytic hydrogenation of the A₂B and A₃B miktoarm stars, with a calcium carbonate‐supported palladium catalyst, leads to the formation of A₂B and A₃B miktoarm stars with one amorphous polycyclohexylene arm with an extremely high glass‐transition temperature and two or three crystalline polyethylene arms. Differential scanning calorimetry was used to determine the glass‐transition temperature of the amorphous blocks of the starting and hydrogenated stars and the melting temperature of polyethylene. Solid‐state ¹³C NMR spectroscopy was performed to ensure the complete saturation of the polycyclohexadiene and polybutadiene arms. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2575–2582, 2002     

Modeling local flotation frequency in a turbulent flow field

Despite the significance of turbulent fluid motion for enhancing the flotation rate in several industrial processes, there is no unified approach to the modeling of the flotation rate in a turbulent flow field. Appropriate modeling of the local flotation (bubble-particle attachment) rate is the basic constituent for global modeling and prediction of flotation equipment efficiency. Existing approaches for the local flotation rate are limited to specific set of conditions like high or low turbulence. In addition, the combined effects of buoyant bubble rise and/or particle gravity settling are usually ignored. The situation is even vaguer for the computation of collision and attachment efficiencies which are usually computed using the gravity induced velocities although the dominant mode of flotation is the turbulent one. The scope of this work is clear: the development of a general expression for the flotation rate in a turbulent flow field which will cover in a unified and consistent way all possible sets of the problem parameters. This is achieved by using concepts from statistical approach to homogeneous turbulence and gas kinetic theory.     

Heavy traffic limits associated with >M/G/∞ input processes

We study the heavy traffic regime of a discrete-time queue driven by correlated inputs, namely the M/G/ input processes of Cox. We distinguish between M/G/ processes with short- and long-range dependence, identifying in each case the appropriate heavy traffic scaling that results in a nondegenerate limit. As expected, the limits we obtain for short-range dependent inputs involve the standard Brownian motion. Of particular interest are the conclusions for the long-range dependent case: the normalized queue length can be expressed as a function not of a fractional Brownian motion, but of an -stable, 1/ self-similar independent increment Lévy process. The resulting buffer content distribution in heavy traffic is expressed through a Mittag–Leffler special function and displays a hyperbolic decay of power 1-. Thus, M/G/ processes already demonstrate that under long-range dependence, fractional Brownian motion does not necessarily assume the ubiquitous role that standard Brownian motion plays in the short-range dependence setup.     

Asymptotic optimality of the Round–Robin policy in multipath routing with resequencing

We consider a model of a multipath routing system where arriving customers are routed to a set of identical, parallel, single server queues according to balancing policies operating without state information. After completion of service, customers are required to leave the system in their order of arrival, thus incurring an additional resequencing delay. We are interested in minimizing the end-to-end delay (including time at the resequencing buffer) experienced by arriving customers. To that end we establish the optimality of the Round–Robin routing assignment in two asymptotic regimes, namely heavy and light traffic: In heavy traffic, the Round–Robin customer assignment is shown to achieve the smallest (in the increasing convex stochastic ordering) end-to-end delay amongst all routing policies operating without queue state information. In light traffic, and for the special case of Poisson arrivals, we show that Round–Robin is again an optimal (in the strong stochastic ordering) routing policy. We illustrate the stochastic comparison results by several simulation examples. The work of the first author was supported through an ARCHIMEDES grant by the Greek Ministry of Education. The work of the second author was prepared through collaborative participation in the Communications and Networks Consortium sponsored by the U.S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government.     

Electrical conductance study of theta-liquid bridges

This work investigates the behavior of small liquid bridges that are formed between two horizontal supporting surfaces, aligned at the vertical direction. The contact lines of the liquid bridges are not edge-pinned but free to move across the supporting surfaces with the contact angle as a parameter (theta-bridges). An a.c. electrical conductance technique coupled with high resolution optical images is used to characterize the geometrical details of constant volume liquid bridges when their length is increased gradually until rupture. A mathematical framework is developed for the identification of the geometrical characteristics of theta-liquid bridges explicitly from conductance data. Theoretical predictions show good agreement with measurements for most of the bridge lengths (separation distance between supports) except close to the rupture point where the bridge is highly stretched. It is further shown that for short and moderate separation distances the present model can be used with confidence to determine the bridge volume and neck radius from the electrical signal.