Simultaneous Coagulation Research Articles

Modelling the Aggregation and Break-up of Fractal Aggregates in a Shear Flow

A population balance model has been proposed to describe simultaneous coagulation and fragmentation of fractal aggregates during shear-flocculation induced by means of a Couette-flow system. Given enough time, a floc-size distribution achieves the steady state, which reflects the balance between coagulation and fragmentation forces. Experimental results obtained recently show that higher shear rate values shift the steady state to smaller aggregate sizes. Also, for a fixed value of the shear rate, when the volume fraction of the particles increases, the steady state size increases if the flow is laminar, and decreases if the flow is turbulent. In order to model the fragmentation of the aggregates, a power dependence between the breakage rate coefficient and the shear rate has been proposed. The model is adjusted by using two different parameters: the effective probability of success for collisions αeff, and the break up coefficient for shear fragmentation, B′. The dependence of these two parameters on the shear rate and the volume fraction of the particles is discussed.

Coagulation and fragmentation: Universal steady‐state particle‐size distribution

AbstractA population balance model presented describes simultaneous coagulation and fragmentation during shear‐induced flocculation. Given sufficient time, a floc‐size distribution reaches steady state that reflects the balance between coagulation and fragmentation. The model agrees with experimental data for the evolution of the average floc size. Higher shear shifts the steady‐state size distribution to smaller sizes. When the steady‐state size distributions obtained at various shear rates are scaled with the average floc size, however, they collapse onto a single line. This indicates that the steady‐state floc‐size distribution is self‐preserving with respect to fluid shear. This distribution is universal for the employed coagulation and fragmentation rates provided that less than 5% (by number) of the particles remain unflocculated. This result is supported with experimental data on shear‐induced flocculation of polystyrene particles, although a detailed quantitative comparison is limited by the irregular structure of the flocs.

On the steady-state equation for particles undergoing simultaneous Brownian diffusion and coagulation

An earlier calculation of the solution of the time-independent equation for the diffusion of coagulating particles is modified to take into account the correct dependence of the Brownian diffusion coefficient on particle size. Explicit analytic results are obtained for the spatial dependence of the particle number density N and the volume fraction of particulate matter .

Ultrapulse carbon dioxide laser resurfacing and facial cosmetic surgery

Over 100 patients have been treated with the ultrapulse carbon dioxide laser since July 1994. The high power square wave pulse of 600 watts at less than 1 msec (which is less than the thermal relaxation time of tissue) dissipates heat during vaporization, thus producing a ‘cold beam’ and decreasing thermal injury. Similarly, hemostatic incision may be achieved by the focus beam at short repetition rates allowing incision with simultaneous coagulation of small vessels. Seventy-four patients underwent resurfacing for rhytides and photo aging with excellent cosmetic results and no texture or pigmentary change. Facial cosmetic surgery (facelift/eyelid lift/forehead lift) was accomplished in 41 patients using the laser scalpel. Patient selection, preparation, sequence of the laserbrasion and incisional techniques are summarized.

Simultaneous diffusion, coagulation and evaporation of aerosols in annular diffusion denuders

Simultaneous diffusion, coagulation and evaporation of aerosols in annular diffusion denuders

Simulating Condensational Growth, Evaporation, and Coagulation of Aerosols Using a Combined Moving and Stationary Size Grid

We present a numerical method of simulating the aerosol processes of coagulation, condensational growth, and evaporation over a hybrid size grid. In the hybrid grid, the volume of involatile core material is constant for each size bin, but the volume of volatile material fluctuates. Since particles in each bin grow and evaporate at their own pace, particles from one bin can obtain the same volume as those from another bin while maintaining different composition. Similarly, particles from different bins that grow to the same size can evaporate back to their respective original core sizes. Allowing independent growth of particles inhibits numerical diffusion since particles in each bin grow or evaporate to their actual sizes. When two particles coagulate, they form a new particle with core volume between the core volumes of particles in two other bins. We partition the new particle and its total volume between these two bins. Similarly, we adapt other processes, such as nucleation, emissions, and transport to the hybrid grid structure. The condensational growth equations developed conserve mass between the gas phase and size-distributed aerosol phase. Because the equations result in sparse matrices of partial derivatives, SMVGEAR, a sparse-matrix Gear-type integrator, solves them quickly. Furthermore, the semi-implicit coagulation equations used here conserve volume exactly, are absolutely stable, and require no iteration. Finally, we compared model solutions to both analytical and other integrated numerical solutions. To obtain numerical solutions, we developed and integrated equations that simulate simultaneous coagulation and growth of multicomponent particles.

Effects of coagulation of thelocus coeruleus and pontine raphe nuclei on the background activity recorded from the rat cerebellar fastigial nucleus neurons

Simultaneous or separate coagulation of thelocus coeruleus (LC) and the pontine raphe nucleus (PRN) results in a significant increase of irregular-type background activity in the cerebellar fastigial nucleus neurons. There are also considerable changes in the dynamics of impulse sequences, in particular, the number of neurons with random interpulse intervals markedly increases. Destruction of theLC and/or PRN is followed by a marked drop in the mean frequency of discharges in the neurons of the fastigial nucleus.

Laparoscopic excision of endometriosis with 3-mm scissors: Comparison of operating times between sharp excision and electro-excision

To determine if laparoscopic excision of endometriosis by electrosurgery is more rapid than by sharp dissection, a retrospective comparative study was made of operative times for the two procedures. Median operating times for laparoscopic electro-excision of endometriosis were 26% to 49% faster than excision by sharp dissection. A x 2 analysis of the frequency counts of surgical intervals, and disease stage revealed this difference to be statistically significant and not due to acquired experience or differences in extent of disease in the two groups. The reduction in operating time achieved with monopolar electro-excision seems primarily associated with a more rapid cutting action with simultaneous coagulation of bleeders.

Simulation of multicomponent aerosol dynamics

A technique for numerical solution of the multicomponent aerosol general dynamic equation is developed and tested. The method is intended to obtain directly the multivariable size-composition distribution without any a priori assumptions about the nature of the distribution. In selecting the numerical method particular attention is paid to simulating simultaneous coagulation and condensation processes, although if condensation is the dominant process a scheme more suitable for pure condensation can be chosen. Numerical solutions are compared with analytical solutions for model problems of pure condensation, pure coagulation, and simultaneous condensation and coagulation.

The Aggregation Probability in Random Coagulation and Breakup Processes

AbstractA single parameter, denoted as the "aggregation probability", is introduced to represent the average potential of clustering in a suspension in which the aggregates are undergoing random and simultaneous coagulation and breakup by means of mechanical stirring. The parameter may be useful for obtaining quick estimates of the equilibrium cluster size distributions in such systems.

Evolution of the cluster-size distribution in stirred suspensions

Based on combinatorics, a simple model for predicting the steady-state cluster or drop-size distribution in suspensions undergoing simultaneous coagulation and break-up due to rapid stirring was recently proposed (R. D. Cohen, J. Chem. Soc. Faraday Trans., 1990, 86, 2433). This work extends that model to account for the evolution of the size distribution in stirred systems. The method utilizes the concept of the distribution entropy, and suggests a means for predicting the characteristics of the size distribution as the system approaches steady state. Among the important results is that the distribution functions (size, volume etc.) are path dependent. Furthermore, along the ‘most probable entropy path’, the cluster-size distribution remains closely related to the Poisson distribution up to and including steady state. Another interesting finding is that, along the mentioned path, the distribution functions are concentration specific (intensive property) as long as they are in their transient state. These ultimately become number specific (extensive property) once they reach steady state.

The Relationship between Clinical Signs and Hypercoagulable State in Toxemia of Pregnancy

The hypercoagulable state in patients with toxemia of pregnancy was investigated in comparison with normal pregnant women using new coagulation parameters, mainly thrombin-antithrombin III (TAT) complexes, alpha 2-antiplasmin-plasmin complexes (PIP), and D-dimer FDP. When the patients were categorized by the classification of the WHO Study Group (1985), significant increases of TAT complexes and alpha 2-PIP complexes with decreases of the ATIII level were observed in the groups with preeclampsia and severe gestational hypertensive disease as compared to normal pregnant women. A significant increase of D-dimer FDP was observed in a group with severe gestational hypertensive disease. Additionally, the relationship between clinical signs and the hypercoagulable state in the patients was analyzed using canonical correlation analysis as a multivariate analysis. The clinical signs and coagulation parameters had a significantly high correlation of lambda 1 = 0.7219, p less than 0.01. The results showed that clinical signs were associated with simultaneous coagulation abnormalities. The indices obtained from the results of canonical correlation analysis, which were called the clinical index and the coagulation index, should be useful in evaluating the efficacy of anticoagulation therapy.

On the collision efficiency approach to flocculation

The collision efficiency approach to flocculation is analyzed on the basis of a model describing the probability of aggregation by polymer bridging. The model allows for the effect of the randomness of distribution of polymer over particles as well as the effect of simultaneous coagulation and weak flocculation. It is argued that the collision efficiency approach is applicable to a rather limited range of experimental systems and provides a qualitative understanding rather than a quantitative theory of the relationship between flocculation and adsorption.

Soot Coagulation with Surface Growth Kinetics

Abstract A generalized system of rate equations governing simultaneous coagulation, surface growth and nucleation of a homogeneous soot dispersion is presented. Coagulation is modeled by free molecule Brownian collision kinetics and surface growth is treated in terms of a global chemical reaction scheme. Particle nucleation is neglected and the equations are numerically integrated to yield the time dependence of particle number density, mean size and size distribution standard deviation. A time dependent lognormal particle volume distribution function (PVDF) is assumed. For coagulation only, the asymptotic lognormal PVDF (i.e., standard deviation = 0.912) is shown to be almost identical to the self-preserving distribution function based on comparison of their respective moments. Particle coagulation is found to strongly influence net particle growth via its effect on particle surface area. The major effect of surface growth on coagulation dynamics is a tendency to narrow the particle size distribution

レーザー深部照射による肝動脈、門脈同時塞栓術。(肝梗塞部の経時的組織変化に関する検討)

We made peripheral liver infarction in normal canine livers by simultaneous coagulation of the potal vein and hepatic artery using Nd-YAG Laser in depth radiation. Three weeks after irradiation, this infarction was surrounded by fibrous tissue. and in four weeks, it was organized instead of falling into abscess.Our method is useful for making small selective infarctions of the liver and should become a new method of treatment for hepatoma to eliminate of TAE faults.

Soot aerosol dynamics in a stagnation point diffusion flame

A soot aerosol undergoing simultaneous growth and coagulation in a stagnation point propane diffusion flame has been simulated numerically. The detailed thermochemical flame structure has been calculated by solving for a conserved scalar, the fuel atom mass fraction, and using empirical data to derive temperature and species concentrations. With the computed flow field and flame structure, soot aerosol behaviour was simulated with free molecular coagulation rates and assumed particle source terms near the flame reaction zone. Forty discrete classes of particle size were used and C3H8, C2H4 and C2H2 were permitted to contribute to surface growth with simplified kinetics. The general features of the computed soot volume fraction, size and number density were in agreement with measurements. Interpretation of the results on the basis of a light scattering experiment showed that use of a monodisperse assumption overestimated mean particle diameties by 50% and underestimated number densities by a factor of 2.6. A self-preserving size distribution (SPSD) was able to yield a reasonable correction to number densities obtained with the monodisperse assumption towards the end of the aerosol history. At earlier times the aerosolcould not be described in either self-preserving or lognormal forms, indicating the need for independent measurements of size distributions in regions of particle production and growth. It was found that particle production rates had a weak effect on overall soot loadings. However, with simultaneous growth and coagulation the effect is not negligible and in some circumstances it could account for observed variations in soot loading.

Change in size distribution of ultrafine aerosol particles undergoing brownian coagulation

Brownian coagulation in the free molecular and transition regimes has been studied. In the experiment, highly concentrated NaCl, ZnCl2, and Ag aerosol particles having geometric mean diameter of 5–40 nm and geometric standard deviation around 1.4 were passed through a metal pipe of 2.0 cm diameter in laminar state. At the inlet and the outlet of the coagulation pipe, the particle size distributions were measured by means of a differential mobility analyzer combined with a CNC and the particle number concentrations were counted independently by an ultramicroscopic system after enlarging their size in a particle size magnifier. In theoretical calculation, the coagulation rate function proposed by Fuchs was used, and the pupulation balance equation for simultaneous Brownian coagulation and diffusive deposition of aerosols in laminar pipe flow was numerically solved. It was found that the experimental results deviated from the theoretical calculation with the decrease in the particle size, that is, the enhancement of coagulation rate was observed. This will be caused by the van der Waals attractive force, which was qualitatively explained from the Marlow's theory.

Experimental study of simultaneous coagulation and diffusional loss of free molecule aerosols in turbulent pipe flow

An experimental study of simultaneous coagulation and diffusional deposition of free molecule ammonium sulfate aerosols in turbulent pipe flow is reported. Experiments were conducted at atmospheric pressure, with mean particle sizes ranging from 0.005 to 0.04 μm. Information about particle sizesand concentrations was obtained with a condensation nucleus counter (CNC)-diffusion battery combination; the particle size dependence of CNC counting efficiency was accounted for when reducing the diffusion battery data. Aerosol sizes and concentrations were varied over a wide range so that data ranged from the coagulation-dominated to the diffusional loss-dominated regimes. Data were in good agreement with the theory of Brockmann, McMurry, and Liu [ Aerosol Sci. Technol., in press] when coagulation enhancement due to London-van der Waals forces was accounted for.

On Simultaneous Coagulation and Diffusional Loss of Free Molecule Aerosols in Turbulent Pipe Flow

The population balance equations for simultaneous coagulation and deposition of free molecule aerosols in turbulent pipe flow have been cast in dimensionless form and integrated to obtain a simplified two-equation model. The relative importance of coagulation and deposition is shown to depend upon a dimensionless parameter A, which is a ratio of a characteristic deposition time to a characteristic coagulation time. Solutions to these equations are presented graphically and range from the coagulation-dominated to the deposition-dominated regime. This analysis accounts for the enhancement in coagulation rates due to London-van der Waals attractive forces; this effect is often important for free molecule aerosols. In a separate paper (Brockmann et al., 1982) experimental data are shown to be in good agreement with theoretical predictions.

Dust to planetesimals: Settling and coagulation in the solar nebula

The behavior of solid particles in a low-mass solar nebula during settling to the central plane and the formation of planetesimals is examined. Gravitational instability in a dust layer and collisional accretion are considered as possible mechanisms of planetesimal formation. Non-Keplerian rotation of the nebula results in shear between the gas and a dust layer. This shear produces turbulence within the layer which inhibits gravitational instability, unless the mean particle size exceeds a critical value, ∼1 cm at 1 AU. The size requirement is less stringent at larger heliocentric distances, suggesting a possible difference in planetesimal formation mechanisms between the inner and outer nebula. Coagulation of grains during settling is expected in the solar nebula environment. Van der Waals forces appear adequate to produce centimeter-sized aggregates. Growth is primarily due to sweepup of small particles by larger ones due to size-dependent settling velocities. A numerical model for computing simultaneous coagulation and settling is described. Relative velocities are determined by gas drag and the non-Keplerian rotation of the nebula. The settling is very nonhomologous. Most of the solid matter reaches the central plane as centimeter-sized aggregates in a few times 10 3 revolutions, but some remains suspended in the form of fine dust. Drag-induced relative velocities result in collisions. The growth of bodies in the central plane is initially rapid. After sizes reach ∼10 3 cm, relative velocities decrease and the growth rate declines. Gas drag rapidly damps the out-of-plane motions of these intermediate-sized bodies. They settle into a thin layer which is subject to gravitational instability. Kilometer-sized planetesimals are formed by this composite process.