Fast Coagulation Rate

2016 ◽  
Author(s):  
Stanislaw Slomkowski ◽  
José V. Alemán ◽  
Robert G. Gilbert ◽  
Michael Hess ◽  
Kazuyuki Horie ◽  
...  
Keyword(s):  
Coagulation Rate ◽  
Fast Coagulation

Fast Coagulation Rate Coefficient

2016 ◽  
Author(s):  
Stanislaw Slomkowski ◽  
José V. Alemán ◽  
Robert G. Gilbert ◽  
Michael Hess ◽  
Kazuyuki Horie ◽  
...  
Keyword(s):  
Rate Coefficient ◽  
Coagulation Rate ◽  
Fast Coagulation

scholarly journals Stationary Non-equilibrium Solutions for Coagulation Systems

2021 ◽  
Vol 240 (2) ◽  
pp. 809-875
Author(s):  
Marina A. Ferreira ◽  
Jani Lukkarinen ◽  
Alessia Nota ◽  
Juan J. L. Velázquez
Keyword(s):  
Power Law ◽  
Source Term ◽  
Continuous Model ◽  
Stationary Solutions ◽  
Weight Functions ◽  
Equilibrium Solutions ◽  
Coagulation Rate ◽  
Diffusion Limited Aggregation ◽  
Coagulation Equations ◽  
Non Equilibrium

AbstractWe study coagulation equations under non-equilibrium conditions which are induced by the addition of a source term for small cluster sizes. We consider both discrete and continuous coagulation equations, and allow for a large class of coagulation rate kernels, with the main restriction being boundedness from above and below by certain weight functions. The weight functions depend on two power law parameters, and the assumptions cover, in particular, the commonly used free molecular and diffusion limited aggregation coagulation kernels. Our main result shows that the two weight function parameters already determine whether there exists a stationary solution under the presence of a source term. In particular, we find that the diffusive kernel allows for the existence of stationary solutions while there cannot be any such solutions for the free molecular kernel. The argument to prove the non-existence of solutions relies on a novel power law lower bound, valid in the appropriate parameter regime, for the decay of stationary solutions with a constant flux. We obtain optimal lower and upper estimates of the solutions for large cluster sizes, and prove that the solutions of the discrete model behave asymptotically as solutions of the continuous model.

The Coagulation Rate of the Blood in Epileptics

1907 ◽  
Vol 53 (224) ◽  
pp. 766-794 ◽  
Author(s):  
John Turner
Keyword(s):  
Coagulation Rate ◽  
Healthy Women ◽  
Systematic Examination

THE following is an account of a systematic examination of the coagulation rate of the blood of nine female epileptics and seven healthy women.

A RHEOLOGICAL EXPRESSION OF COAGULATION RATE THEORY

1982 ◽  
Vol 3 (2) ◽  
pp. 129-145 ◽  
Author(s):  
Kenichi Hattori ◽  
Kaichi Izumi
Keyword(s):  
Rate Theory ◽  
Coagulation Rate

Drop Coagulation in Cross-Over Pipe Flows of Wet Steam

1979 ◽  
Vol 21 (5) ◽  
pp. 357-360 ◽  
Author(s):  
J. J. E. Williams ◽  
R. I. Crane
Keyword(s):  
Drop Size ◽  
Chemical Engineering ◽  
Numerical Technique ◽  
Wet Steam ◽  
Coagulation Rate ◽  
Two Phase ◽  
Size Spectra ◽  
Pipe Flows ◽  
The Core ◽  
Median Diameter

A numerical technique is developed for predicting the evolution of drop-size spectra in turbulent, two-phase pipe flows. While relevant to many chemical engineering processes, it is applied here to the crossover pipes of a nuclear wet-steam turbine. Valid expressions for turbulent coagulation rate in the cross-over pipes are available only for drops below about 10 μm diameter in the core flow, and for those exceeding about 20 μm near the pipe wall. Using these expressions, it is found that the rapid formation of large drops in the core allows prediction for only a small fraction of the typical residence time in the pipe, but near the wall the volume median diameter of an initial 20 μm monodispersion can double in 100 ms. Further work is required to validate the technique and extend it to handle the intervening ranges of drop size and turbulence parameters.

scholarly journals Turbulent Coagulation of Aerosol Particles: New Insights From Direct Numerical Simulations and Holographic Imaging Experiments

2003 ◽  
Author(s):  
Lance R. Collins ◽  
Hui Meng ◽  
Aruj Ahluwalia ◽  
Lujie Cao ◽  
Gang Pan
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Search Algorithm ◽  
Concentration Field ◽  
Direct Numerical Simulations ◽  
Three Dimensions ◽  
Collision Kernel ◽  
Coagulation Rate ◽  
Subsequent Work ◽  
Turbulent Fluctuations

Particle collisions driven by turbulent fluctuations play a key role in such diverse problems as cloud formation, aerosol powder manufacturing and inhalation drug therapy to name a few. In all of these examples (and many others) turbulent fluctuations increase the rate of collisions relative to the background collision rate driven by Brownian motion. Furthermore, turbulence can spontaneously generate very large fluctuations in the particle concentration field. This “clustering” is caused by the inertial mismatch between the heavy particles and the lighter surrounding gas; vortices in the flow “centrifuge” the heavier particles out of vortex cores and into the straining regions that lie in between the vortices. Because collision is a binary process, concentration fluctuations further enhance the turbulent coagulation rate by as much as two orders of magnitude. An effect of this size must be accounted for in a rational model of turbulent coagulation. Sundaram & Collins (J. Fluid Mech. 1997) showed that the radial distribution function (RDF) of the particle population, evaluated at contact, precisely corrects the collision kernel for clustering. Subsequent work has explored the dependence of the RDF on the system parameters (e.g., particle size, concentration, response time and Reynolds number) using direct numerical simulations. These results have improved our understanding and ability to predict the effect of the first three parameters; however, owing to the limited range of Reynolds number that can be reached in a numerical simulation, questions remain over the scaling of the RDF with Reynolds number. This is a critical issue for high-Reynolds-number applications such as cloud physics, where values of the Reynolds number can be 1–2 orders of magnitude greater than can be simulated. We will present our highest Reynolds number simulations to date and show our attempts to resolve this issue. Recently, the ability to measure three-dimensional particle positions using holography has been realized (e.g., Meng & Pu, J. Opt. Soc. Am. 2003). With holography, the optical image that is produced contains fringes that, upon inverting the laser, reproduce the original image in three dimensions. The hologram can then be scanned using a digital camera to obtain the particle positions. An important consideration with this study is the need to differentiate individual particles. We developed a search algorithm that locates particle centers, even in the presence of optical aberations and speckle noise. The algorithm has been used to obtain the first experimental RDF measurements to date. Thus far we see good agreement between the experimentally obtained RDF and the simulations. Besides validating the simulations, experiments can span a much broader range of Reynolds numbers, providing critical data that may help resolve the open questions associated with this parameter.

scholarly journals New Results on the Coagulation Equation

1987 ◽  
Vol 115 ◽  
pp. 547-547
Author(s):  
Pierre Bastien ◽  
Claude Lejeune
Keyword(s):  
Mass Spectrum ◽  
Time Dependence ◽  
Star Clusters ◽  
Mass Function ◽  
Mass Dependence ◽  
Coagulation Rate ◽  
Precise Form ◽  
Explicit Time Dependence ◽  
Coagulation Equation ◽  
Free Parameters

In attempting to reproduce the initial stellar mass function, we solved analytically the coagulation equation with an explicit time dependence in the coagulation rate in order to simulate the gravitational collapse of the fragments upon themselves as they move within the progenitor cloud. Two separate cases have been studied, with and without a mass dependence in the coagulation rate. The solution show that (1) inclusion of self-gravitation is very important and can change the results to the point of preventing coalescence to work altogether, depending on the values of the two free parameters, (2) the precise form of the mass dependence of the coagulation rate is not of prime importance in most situations of astrophysical interest, and (3) coagulation alone is not sufficient to yield a realistic mass spectrum and fragmentation must also be taken into account. Coagulation is more efficient for massive fragments and fragmentation for the smaller ones. These results are applied to different regions: star clusters, associations, and starburst regions.

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