scholarly journals Evaluation of the Uncertainties Caused by the Forward Scattering in Turbidity Measurement of the Coagulation Rate

Langmuir ◽  
2010 ◽  
Vol 26 (10) ◽  
pp. 6908-6918 ◽  
Author(s):  
Shenghua Xu ◽  
Zhiwei Sun
Keyword(s):  
Forward Scattering ◽  
Coagulation Rate ◽  
Turbidity Measurement

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.

Forward scattering of light in thin opal films

2004 ◽  
Vol 69 (4) ◽  
Author(s):  
S. G. Romanov ◽  
C. M. Sotomayor Torres
Keyword(s):  
Forward Scattering ◽  
Scattering Of Light

Optical forward-scattering for detection of Listeria monocytogenes and other Listeria species

2007 ◽  
Vol 22 (8) ◽  
pp. 1664-1671 ◽  
Author(s):  
Padmapriya P. Banada ◽  
Songling Guo ◽  
Bulent Bayraktar ◽  
Euiwon Bae ◽  
Bartek Rajwa ◽  
...  
Keyword(s):  
Listeria Monocytogenes ◽  
Forward Scattering ◽  
Listeria Species
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