Biomedical subjects

Haim Taitelbaum

Publications and source records attributed to Haim Taitelbaum.

8 recordsLinked to original sources

PubMed2006

Perturbation analysis for competing reactions with initially separated components.

We study a competitive reaction-diffusion system with initially separated components. In this system, two similar species on one side of the system compete to react with the species on the other side. The competition is due to significant differences in the microscopic reaction constants and the initial densities of the two competing species. In the short-time limit, each of the competitive reactions is considered as perturbation with respect to the diffusion, the latter is essential for the effective mixing of the reactants. We identify the small parameters required for the perturbation analysis of the competitive scheme. The resulting perturbative expressions provide the rich spatiotemporal reaction front patterns, which were experimentally observed for Cr3+ + Xylenol Orange (XO) --> products, where the aggregated and nonaggregated forms of Cr3+ in aqueous solution compete to react with the XO.

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PubMed2006

Reaction-diffusion front width anomalies in disordered media.

We study the front characteristics of the A + B --> C reaction-diffusion system with initially separated reactants in disordered media, exemplified by two-dimensional (2D) percolation. We investigate the front characteristics as a function of the disorder degree in this system, in particular close to criticality. We show that the front width exponent is larger than the mean-field (MF) exponent of 1/6, and at criticality it approaches 1/4, which is the one-dimensional (1D) exponent. We show that previous predictions in the literature for the 2D percolation cluster at criticality are wrong. The results are discussed in the context of other systems with attenuated transport where the front width exponent is smaller than the MF exponent. We also study the short-time behavior of the front width exponent, and discuss the validity of the scaling relations between the relevant exponents.

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PubMed2006

Effect of a slit-shaped trap on depletion kinetics within a microchannel.

The diffusion-limited trapping reaction kinetics of the growth of the depletion zone within and around a "slit-shaped" trap in a flat microchannel was studied experimentally and numerically. In the experiment, an ellipse-shaped laser beam acted as a slit trap in a long, flat capillary, and the trapping reaction is photobleaching of fluorescein dye. The parameter studied was the theta distance, i.e., the distance from the trap to the point where the reactant concentration has been locally depleted to the specific survival fraction [theta] of its initial bulk value. When the trap is perfect, then, due to the geometry of the trap and the reactor, as many as three time regimes can be found, with up to two crossover transitions. The number of crossovers is determined by the relative sizes of the trap and the microreactor. In the case of two crossovers, we show that the first crossover relates to the length of the trap, while the second crossover relates to the width of the reactor. When the slit trap is imperfect and its width cannot be neglected, as is the case in the experiments, a nontrivial early behavior is observed, followed by two regions in time, separated by a single crossover only.

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PubMed2005

Interface roughening dynamics: temporal width fluctuations and the correlation length.

In this work we study experimentally and numerically the temporal width fluctuations obtained in kinetic roughening of single interfaces. This fluctuative behavior, which results from competing mechanisms in the interface growth process, is shown to contain information on the growth process of the specific interface. We define a measure of the temporal interface width fluctuations in order to extract the correlation length of the interface from the fluctuating data. We study numerically the quenched Kardar-Parisi-Zhang (QKPZ) equation for single interfaces in order to assess the role of the different mechanisms, such as normal growth and surface tension, on the fluctuations. We analyze experimental data of mercury droplets spreading on various metal films (silver and gold) in various thicknesses, as well as data of water spreading on paper (imbibition), in order to demonstrate the validity of our method in a wide range of growing interfaces.

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PubMed2005

Depletion kinetics in the photobleaching trapping reaction inside a flat microchannel.

The diffusion-limited kinetics of the growth of a depletion zone around a static point trap in a thin, long channel geometry was studied using a laser photobleaching experiment of fluorescein dye inside a flat rectangular capillary. The dynamics of the depletion zone was monitored by the theta distance, defined as the distance from the trap to the point where the reactant concentration has been locally depleted to the specified survival fraction (theta) of its initial bulk value. A dimensional crossover from two dimensions to one dimension, due to the finite width of the reaction zone, was observed. We define a "parallel" and a "perpendicular" theta distance, along the slab long and short dimensions, respectively, and study their time development as a means to study the asymmetrical nature of the slab geometry. For all theta values, the crossover occurs concurrently for both theta distances when the depletion zone touches the boundary for the first time. We derive theoretical expressions for this geometry and compare them with the experimental data. We also obtain important insight from the ratio of the reactant concentration profiles in the parallel and perpendicular directions. Exact enumeration and Monte Carlo simulations support the anomalous depletion scaling results. Nevertheless, the crossover time (tau(c)) is still found to scale with the width (W) of the rectangular reaction zone as tau(c) approximately W2 , as expected from the basic Einstein diffusion law.

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PubMed2004

Roughness and growth in a continuous fluid invasion model.

We have studied interface characteristics in a continuous fluid invasion model, first introduced by Phys. Rev. Lett. 60, 2042 (1988)]. In this model, the interface grows as a response to an applied quasistatic pressure, which induces various types of instabilities. We suggest a variant of the model, which differs from the original model by the order of instabilities treatment. This order represents the relative importance of the physical mechanisms involved in the system. This variant predicts the existence of a third, intermediate regime, in the behavior of the roughness exponent as a function of the wetting properties of the system. The gradual increase of the roughness exponent in this third regime can explain the scattered experimental data for the roughness exponent in the literature. The growth exponent in this model was found to be around zero, due to the initial rough interface.

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PubMed2003

Dynamics of the depletion zone at a finite-sized imperfect trap in two dimensions: photobleaching experiments and simulations.

The kinetics of the growth of depletion zones around a static trap in an effective two-dimensional geometry were studied experimentally with photobleaching of fluorescein dye by a focused laser beam. The phototrap served as an imperfect trap with a finite size. The growth of the depletion zone was monitored by the theta distance, defined as the distance from the trap to the point where the concentration of the reactants reaches a given arbitrary fraction theta (0<theta<1) of its initial value, which could be directly measured experimentally. At the asymptotic limit, the results confirm the theoretical nonuniversal t(theta/2) scaling behavior for the theta distance. We also find an effect of fast expansion at an early time of the depletion zone inside an imperfect trap. Both the imperfect trapping strength and the finite trap size are found to control the early-time behavior, while the trap shape does not much affect the dynamics of the theta distance. A dimensional crossover was found for a perfect trap with a finite radius, when the theta distance was measured from the trap surface. The actual trapping efficiency was determined for different laser powers of the phototrap. Results are supported by analytical equations, exact enumerations, and Monte Carlo simulations.

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PubMed2003

Anomalous growth of the depletion zone in the photobleaching trapping reaction.

We study the anomalous growth of the depletion zone at a single trap, as observed in a photobleaching trapping reaction in confined geometry. We provide experimental evidence for a nonuniversal growth of this depletion. We also find an early-time behavior of the depletion zone, owing to the finite size of the trap. Various laser powers are used in order to study the effects of trapping strength, interpreted theoretically in terms of an imperfect trap. The results are supported by numerical calculations. Comparison with other trapping reactions provides insight into finite-size traps.

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