The closure issue related to liquid-cell mass transfer and substrate uptake dynamics in biological systems.

An original dynamic model for substrate uptake under transient conditions is established and used to simulate a variety of biological responses to external perturbations. The actual uptake and growth rates, treated as cell properties, are part of the model variables as well as the substrate concentration at the cell-liquid interface. Several regulatory loops inspired by the structure of the glycolytic chain are considered to establish a set of ordinary differential equations. The uptake rate evolves so as to reach an equilibrium between the cell demand and the environmental supply. This model does not contain any of the usual algebraic closure laws relating to the instantaneous uptake, growth rates, and the substrate concentration, nor does it enforce the continuity of mass fluxes at the liquid-cell interface. However, these relationships are found in the steady-state solution. Previously unexplained experimental observations are well reproduced by this model. Also, the model structure is suitable for further coupling with flux-based metabolic models and fluid-flow equations.

Computational Study of the Effect of Homogeneous and Heterogeneous Bubbly Flows on Bulk Gas-Liquid Heat Transfer.

A numerical investigation is performed on buoyancy-driven homogeneous and heterogeneous bubbly flows to compare the bulk gas-liquid heat transfer effectiveness for Prandtl (Pr) numbers 0.2-20 and void fractions 〈 α g 〉 0.3-0.5. For this purpose, transient two-fluid model simulations of bubbles rising in a stagnant pool of liquid are conducted in a rectangular box by applying periodic boundary conditions to all the sides. The temperature difference ( Δ T ) between gas and liquid phase is averaged over the rectangular box and monitored with respect to time, the heat transfer rate is studied based on the time at which the Δ T tends to zero. The results of numerical study show that at low Pr numbers, faster decay of Δ T is observed for homogeneous flow of bubbles indicating higher heat transfer rate in comparison with the heterogeneous flow of bubbles for the same void fraction. On the contrary, for high Pr numbers, higher heat transfer rate is observed in heterogeneous flow compared to the homogeneous. The comparison of heat transfer behavior between different void fractions for heterogeneous flow show that, for low Pr numbers higher heat transfer rate is achieved for void fraction 0.4 in comparison with void fraction 0.5. And for high Pr numbers, higher heat transfer is observed for void fraction 0.5 in comparison with void fraction 0.4.

Theoretical study of the pyrolysis of methyltrichlorosilane in the gas phase. 3. Reaction rate constant calculations.

The rate constants for the gas-phase reactions in the silicon carbide chemical vapor deposition of methyltrichlorosilane (Ge, Y. B.; Gordon, M. S.; Battaglia, F.; Fox, R. O. J. Phys. Chem. A 2007, 111, 1462.) were calculated. Transition state theory was applied to the reactions with a well-defined transition state; canonical variational transition state theory was applied to the barrierless reactions by finding the generalized transition state with the maximum Gibbs free energy along the reaction path. Geometry optimizations were carried out with second-order perturbation theory (MP2) and the cc-pVDZ basis set. The partition functions were calculated within the harmonic oscillator and rigid rotor approximations. The final potential energy surfaces were obtained using the left-eigenstate coupled-cluster theory, CR-CC(2,3) with the cc-pVTZ basis set. The high-pressure approximation was applied to the unimolecular reactions. The predicted rate constants for more than 50 reactions were compared with the experimental ones at various temperatures and pressures; the deviations are generally less than 1 order of magnitude. Theory is found to be in reasonable agreement with the experiments.

Turbulence in a microscale planar confined impinging-jets reactor.

Confined impinging-jets reactors (CIJR) offer many advantages for rapid chemical processing at the microscale in applications such as precipitation and the production of organic nanoparticles. It has been demonstrated that computational fluid dynamics (CFD) is a promising tool for "experiment-free" design and scale-up of such reactors. However, validation of the CFD model used for the microscale turbulence applications requires detailed experimental data on the unsteady flow, the availability of which has until now been very limited. In this work, microscopic particle-image velocimetry (microPIV) techniques were employed to measure the instantaneous velocity field for various Reynolds numbers in a planar CIJR. In order to illustrate the validation procedure, the performance of a particular CFD model, the two-layer k-epsilon model, was evaluated by comparing the predicted flow field with the experimental data. To our knowledge, this study represents the first attempt to directly measure and quantify velocity and turbulence in a microreactor and to use the results to validate a CFD model for microscale turbulent flows.

A critical analysis of Powell's results on the interdivision time distribution.

The cell-age and interdivision-time probability density functions (PDFs) have been extensively investigated since the 1940s due to their fundamental role in cell growth. The pioneering work of Powell established the first relationship between the interdivision-time and cell-age PDFs. In the literature, two definitions for the interdivision-time PDF have been proposed. One stands for the age-at-rupture PDF and is experimentally observable, whereas the other is the probability density that a cell divides at a certain age and is unobservable. From Powell's results pertaining to the unobservable interdivision-time PDF, Painter and Marr derived an inequality that is true but is incorrectly used by experimentalists to analyse single-cell data. Unfortunately, the confusion between these two PDFs persists. To dissipate this confusion, exact relationships between the cell-age and the interdivision-time PDFs are derived in this work from an age-structured model, which can be used by experimentalists to analyse cell growth in batch and continuous culture modes.

Destructive aggregation: aggregation with collision-induced breakage.

Mean-field population balance equations are used to describe the evolution of particle size distributions in a wide variety of systems undergoing simultaneous aggregation and breakage. In this paper we develop a population balance that includes aggregation combined with collision-induced particle breakage for arbitrary fragment distribution functions, provided that this distribution function depends only on the total mass of the particles undergoing a collision. We then develop a specific distribution function for arbitrary two-body collisions by postulating that each collision produces a transition-state aggregate having the morphology of a linear polymer. The behavior of the resulting equation is then analyzed for the case in which the collision kernel is a constant, and partial analytical solutions are derived and compared to corresponding Monte-Carlo simulation results. The computer simulations are then used to validate a proposed scaling law for the steady-state particle size distribution. Lastly, the behavior of the aggregation with collision-induced-breakage population balance equation is compared and contrasted with the behavior of an analogous aggregation with linear-breakage population balance equation.

CFD simulation of shear-induced aggregation and breakage in turbulent Taylor-Couette flow.

An experimental and computational investigation of the effects of local fluid shear rate on the aggregation and breakage of approximately 10 microm latex spheres suspended in an aqueous solution undergoing turbulent Taylor-Couette flow was carried out. First, computational fluid dynamics (CFD) simulations were performed and the flow field predictions were validated with data from particle image velocimetry experiments. Subsequently, the quadrature method of moments (QMOM) was implemented into the CFD code to obtain predictions for mean particle size that account for the effects of local shear rate on the aggregation and breakage. These predictions were then compared with experimental data for latex sphere aggregates (using an in situ optical imaging method). Excellent agreement between the CFD-QMOM and experimental results was observed for two Reynolds numbers in the turbulent-flow regime.

Quadrature method of moments for aggregation-breakage processes.

Investigation of particulate systems often requires the solution of a population balance, which is a continuity statement written in terms of the number density function. In turn, the number density function is defined in terms of an internal coordinate (e.g., particle length, particle volume) and it generates integral and derivative terms. Different methods exist for numerically solving the population balance equation. For many processes of industrial significance, due to the strong coupling between particle interactions and fluid dynamics, the population balance must be solved as part of a computational fluid dynamics (CFD) simulation. Such an approach requires the addition of a large number of scalars and the associated transport equations. This increases the CPU time required for the simulation, and thus it is clear that it is very important to use as few scalars as possible. In this work the quadrature method of moments (QMOM) is used. The QMOM has already been validated for crystal growth and aggregation; here the method is extended to include breakage. QMOM performance is tested for 10 different cases in which the competition between aggregation and breakage leads to asymptotic solutions.

Micromixing visualization and quantification in a microscale multi-inlet vortex nanoprecipitation reactor using confocal-based reactive micro laser-induced fluorescence.

A technique for visualizing and quantifying reactive mixing for laminar and turbulent flow in a microscale chemical reactor using confocal-based microscopic laser induced fluorescence (confocal µ-LIF) was demonstrated in a microscale multi-inlet vortex nanoprecipitation reactor. Unlike passive scalar µ-LIF, the reactive µ-LIF technique is able to visualize and quantify micromixing effects. The confocal imaging results indicated that the flow in the reactor was laminar and steady for inlet Reynolds numbers of 10, 53, and 93. Mixing and reaction were incomplete at each of these Reynolds numbers. The results also suggested that although mixing by diffusion was enhanced near the midplane of the reactor at Rej = 53 and 93 due to very thin bands of acidic and basic fluid forming as the fluid spiraled towards the center of the reactor, near the top, and bottom walls of the reactor, the lower velocities due to fluid friction with the walls hindered the formation of these thin bands, and, thus, resulted in large regions of unmixed and unreacted fluid. At Rej = 240, the flow was turbulent and unsteady. The mixing and reaction processes were still found to be incomplete even at this highest Reynolds number. At the reactor midplane, the flow images at Rej = 240 showed unmixed base fluid near the center of the reactor, suggesting that just as in the Rej = 53 and 93 cases, lower velocities near the top and bottom walls of the reactor hinder the mixing and rection of the acidic and basic streams. Ensemble averages of line-scan profiles for the Rej = 240 were then calculated to provide statistical quantification of the microscale mixing in the reactor. These results further demonstrate that even at this highest Reynolds number investigated, mixing and reaction are incomplete. Visualization and quantification of micromixing using this reactive µ-LIF technique can prove useful in the validation of computational fluid dynamics models of micromixing within microscale chemical reactors.

Characterization of sheared colloidal aggregation using Langevin dynamics simulation.

Aggregation of colloidal particles under shear is studied in model systems using a Langevin dynamics model with an improved interparticle interaction potential. In the absence of shear, aggregates that form are characterized by compact structure at small scales and ramified structure at larger scales. This confirms the structural crossover mechanism previously suggested by Sorensen and coworkers, that colloidal aggregation occurs due to monomer addition at small scales and due to cluster-cluster aggregation at large scales. The fractal dimension of nonsheared aggregates is scale-dependent. Smaller aggregates have a higher fractal dimension than larger ones, but the radius of gyration where this crossover occurs is independent of potential well depth for sufficiently deep wells. When these aggregates are subjected to shear they become anisotropic and form extended cigar-like structures. The size of sheared anisotropic aggregates in the direction perpendicular to the shear flow is limited by shear-induced breakage because the shear force dominates interparticle attraction for sufficiently large aggregates. Anisotropic aggregates are not completely characterized by a single radius of gyration, but rather by an inertia ellipsoid. Consequently the fractal dimension is no longer an adequate metric to properly characterize them, and to identify changes in their structure from their nonsheared isotropic counterparts. We introduce a new compactness-anisotropy analysis that characterizes the structure of anisotropic aggregates and allows us to distinguish between aggregates from sheared and nonsheared systems. Finally, using the ratio of interparticle force to the shear force f_{pot,sh} we are able to characterize different outcomes of sheared aggregation as a function of dimensionless well depth and Péclet number.

Theoretical study of the pyrolysis of methyltrichlorosilane in the gas phase. 1. Thermodynamics.

Structures and energies of the gas-phase species produced during and after the various unimolecular decomposition reactions of methyltrichlorosilane (MTS) with the presence of H2 carrier gas were determined using second-order perturbation theory (MP2). Single point energies were obtained using singles + doubles coupled cluster theory, augmented by perturbative triples, CCSD(T). Partition functions were obtained using the harmonic oscillator-rigid rotor approximation. A 114-reaction mechanism is proposed to account for the gas-phase chemistry of MTS decompositions. Reaction enthalpies, entropies, and Gibbs free energies for these reactions were obtained at 11 temperatures ranging from 0 to 2000 K including room temperature and typical chemical vapor deposition (CVD) temperatures. Calculated and experimental thermodynamic properties such as heat capacities and entropies of various species and reaction enthalpies are compared, and theory is found to provide good agreement with experiment.

Theoretical study of the pyrolysis of methyltrichlorosilane in the gas phase. 2. Reaction paths and transition states.

The kinetics for the previously proposed 114-reaction mechanism for the chemical vapor deposition (CVD) process that leads from methyltrichlorosilane (MTS) to silicon carbide (SiC) are examined. Among the 114 reactions, 41 are predicted to proceed with no intervening barrier. For the remaining 73 reactions, transition states and their corresponding barrier heights have been explored using second-order perturbation theory (MP2) with the aug-cc-pVDZ basis set. Final energies for the reaction barriers were obtained using both MP2 with the aug-cc-pVTZ basis set and coupled cluster theory (CCSD(T)) with the aug-cc-pVDZ basis set. CCSD(T)/aug-cc-pVTZ energies were estimated by assuming additivity of basis set and correlation effects. Partition functions for the computation of thermodynamic properties of the transition states were calculated with MP2/aug-cc-pVDZ. Forward and reverse Gibbs free energy barriers were obtained at 11 temperatures ranging from 0 to 2000 K. Important reaction pathways are illustrated at 0 and 1400 K.