Some comments on von Smoluchowski theory of rapid coagulation

1982 ◽  
Vol 260 (12) ◽  
pp. 1151-1152 ◽  
Author(s):  
H. Gedan ◽  
H. Lichtenfeld ◽  
H. Sonntag
Keyword(s):  
Rapid Coagulation ◽  
Smoluchowski Theory

scholarly journals Determination of the Rate of Salt-Induced Rapid Coagulation of Polystyrene Latex Particles in Turbulent Flow Using Small Stirred Vessel

2018 ◽  
Vol 3 (1) ◽  
pp. 5
Author(s):  
Oktaviani Oktaviani ◽  
Yasuhisa Adachi
Keyword(s):  
Ad Hoc ◽  
Coupling Effect ◽  
Particle Diameter ◽  
Polystyrene Latex ◽  
Stirred Vessel ◽  
Colloidal Spheres ◽  
Rapid Coagulation ◽  
Mixing Intensity ◽  
Mixing Rates ◽  
Different Diameters

In our study, we revisited a previously reported method for evaluating the mixing intensity of uniform colloidal spheres in terms of their collision frequency, with the aim of evaluating the validity of this method in the case of a small stirred vessel equipped with an impeller with four paddles. The rates of the salt-induced rapid coagulation of polystyrene latex (PSL) particles with five different diameters were measured as functions of the rotation rate. The ad-hoc assumption of the linear additivity of the perikinetics and the orthokinetics of the coagulation process was used for the analysis. Our previously proposed equation for the rate of turbulent coagulation as a function of the particle diameter, determined for an end-over-end rotation mixing device, was confirmed to be valid. However, it was found that, for small particles and low-mixing rates, i.e., for low Peclet numbers, the rate of coagulation becomes larger than that predicted on the basis of linear additivity because of the coupling effect of Brownian motion and the fluid flow during turbulent mixing. This increase occurred even though the rate was lowered by the wall effect, which resulted in an inhomogeneous distribution of the mixing intensity.

Generalised concentration fluctuations under diffusion equilibrium

1964 ◽  
Vol 1 (1) ◽  
pp. 47-68 ◽  
Author(s):  
Harold Ruben
Keyword(s):  
Total Concentration ◽  
Point Of View ◽  
Temporal Fluctuation ◽  
Classical Analysis ◽  
Occupation Numbers ◽  
Single Region ◽  
Rigorous Test ◽  
Smoluchowski Theory ◽  
Fixed Region ◽  
Number Of Particles

Smoluchowski's classical analysis of the temporal fluctuation, under diffusion equilibrium, of the number of particles in a fixed region R of space is generalised to a set of disjoint regions; specifically, the single Smoluchowski region is divided into a finite number of non-intersecting subregions. The generalisation allows a more rigorous test of some of the consequences of the Einstein-Smoluchowski theory of Brownian motion to be carried out, and at the same time enables the Avogadro constant to be estimated with greater precision than is possible with the single region. In particular, the reversibility paradox of Loschmidt and the recurrence paradox of Zermelo are reexamined from the point of view of the fluctuation of configurations (a configuration being defined as the set of occupation numbers for the various subregions) rather than that of total concentration for the single region.

scholarly journals Spatially-extended nucleation-aggregation-fragmentation models for the dynamics of prion-like neurodegenerative protein-spreading in the brain and its connectome

2019 ◽  
Author(s):  
Sveva Fornari ◽  
Amelie Schäfer ◽  
Ellen Kuhl ◽  
Alain Goriely
Keyword(s):  
Anisotropic Diffusion ◽  
Transport Processes ◽  
Misfolded Proteins ◽  
Size Distributions ◽  
Discrete Laplacian ◽  
Brain Connectome ◽  
Spatially Extended ◽  
Smoluchowski Theory ◽  
The Brain ◽  
Disease Specific

AbstractThe prion-like hypothesis of neurodegenerative diseases states that the accumulation of misfolded proteins in the form of aggregates is responsible for tissue death and its associated neurodegenerative pathology and cognitive decline. Some disease-specific misfolded proteins can interact with healthy proteins to form long chains that are transported through the brain along axonal pathways. Since aggregates of different sizes have different transport properties and toxicity, it is important to follow independently their evolution in space and time. Here, we model the spreading and propagation of aggregates of misfolded proteins in the brain using the general Smoluchowski theory of nucleation, aggregation, and fragmentation. The transport processes considered here are either anisotropic diffusion along axonal bundles or discrete Laplacian transport along a network. In particular, we model the spreading and aggregation of both amyloid-β and τ molecules in the brain connectome. We show that these two models lead to different size distributions and different propagation along the network. A detailed analysis of these two models reveals the existence of four different stages with different dynamics and invasive properties.

THE CRITICAL OPALESCENCE OF ETHYLENE

1948 ◽  
Vol 26b (8) ◽  
pp. 592-603
Author(s):  
O. Maass ◽  
S. G. Mason
Keyword(s):  
Oleic Acid ◽  
Critical Temperature ◽  
Time Lag ◽  
The Other ◽  
Statistical Fluctuations ◽  
Maximum Value ◽  
Critical Opalescence ◽  
Phase Discontinuity ◽  
Two Phases ◽  
Smoluchowski Theory

The opalescence of ethylene has been investigated under various conditions in the region of the critical temperature. The opalescence of critical fillings increases as the temperature is lowered and passes through a maximum at the critical dispersion temperature Ts. When the system is heated the value depends upon the thermal history, both below and above Ts. Two types of time lag curve are observed in the irreversible region, one in which the opalescence passes through a minimum and then a maximum value, and the other through a minimum only. It is believed on the basis of previous qualitative studies that violent shaking would result in reversibility with respect to changes in temperature. Once the apparent phase discontinuity has disappeared the opalescence becomes reversible as long as condensation is prevented. The opalescence of critical fillings depends upon the density and appears to be a maximum when the two phases are present in equal volumes at Ts. Air and oleic acid present in small quantities depress Ts but do not appear to change the variation of opalescence with (T − Ts) when T > Ts. These observations appear to disagree with the classical Einstein–Smoluchowski theory based on light scattering resulting from statistical fluctuations in density. This theory predicts a maximum opalescence at the classical critical temperature, which in the case of ethylene is 0.7 °C. higher than Ts. If, however, the more recent views of the nature of the P − V isotherms near the critical point are taken into account, some of the conflict disappears.

Drift mechanism of the metal nanowires formation in liquid helium

2019 ◽  
Vol 21 (10) ◽  
pp. 5771-5779 ◽  
Author(s):  
S. V. Stovbun ◽  
A. A. Skoblin
Keyword(s):  
Heat Release ◽  
Liquid Helium ◽  
Metal Nanowires ◽  
Quantum Vortex ◽  
Rapid Coagulation

It is shown theoretically that the mechanism of the rapid coagulation of metal nanospheres into a nanowire in a quantum vortex proposed by E. B. Gordon et al. (Low Temp. Phys., 2010, 36, 590) could not be realized, due to the enormous heat release expelling the nanospheres from the vortex.

Coagulation kinetics and the stability of surfactant-free emulsion-polymerised latexes

e-Polymers ◽  
2005 ◽  
Vol 5 (1) ◽  
Author(s):  
E. Rotimi Sadiku ◽  
Ron D. Sanderson
Keyword(s):  
Dlvo Theory ◽  
Correlation Spectroscopy ◽  
Double Layers ◽  
Stability Factor ◽  
Rapid Coagulation ◽  
Nacl Concentration ◽  
Coagulation Kinetics ◽  
The Stability ◽  
Electric Double Layer Thickness ◽  
Hamaker Constants

AbstractThe stability factor of styrene/sulfopropyl methacrylate (styrene/SPM) and styrene/3-[N,N-dimethyl-N-(methacryloxyethyl)ammonium]propane sulfate (styrene/ SPE) latexes was studied using the classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory and the critical coagulation concentration, CCC, was deduced for the latexes. Photon correlation spectroscopy was used to study ionic stabilities. The stability factor was determined as the ratio of the rate constant for rapid coagulation to that of slow coagulation, obtained from the coagulation kinetics data. The log-log plot of the stability factor, W, as a function of NaCl electrolyte concentration shows an asymptotic decrease in W of both latexes. DLVO theory was successfully employed, whereby the characteristic properties of the diffuse electric double layers or the Stern layers around latex particles in terms of their Hamaker constants and diffuse potentials were determined. The electric double layer thickness decreases with increasing NaCl concentration. Stability curves revealed a higher CCC value for the styrene/SPM latex than for the styrene/SPE latex, which is in accordance with the higher surface charge density and an indication of a better stability.

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