Self-similar asymptotic behavior for the solutions of a linear coagulation equation

In this paper we consider the long-time asymptotics of a linear version of the Smoluchowski equation which describes the evolution of a tagged particle moving in a random distribution of fixed particles. The volumes v of these particles are independently distributed according to a probability distribution which decays asymptotically as a power law $v^{?\sigma }$. The validity of the equation has been rigorously proved in [22] taking as a starting point a particle model and for values of the exponent $\sigma >3$, but the model can be expected to be valid, on heuristic grounds, for $\sigma >\frac{5}{3}$. The resulting equation is a non-local linear degenerate parabolic equation. The solutions of this equation display a rich structure of different asymptotic behaviors according to the different values of the exponent σ. Here we show that for $\frac{5}{3}<\sigma <2$ the linear Smoluchowski equation is well-posed and that there exists a unique self-similar profile which is asymptotically stable.     

Electrophoresis and stability of nano-colloids: History,theory and experimental examples

The paper contains an extended historical overview of research activities focused on determining interfacial potential and charge of dispersed particles from electrophoretic and coagulation dynamic measurements. Particular attention is paid to nano-suspensions for which application of Standard Electrokinetic Model (SEM) to analysis of experimental data encounters difficulties, especially, when the solutions contain more than two ions, the particle charge depends on the solution composition and zeta-potentials are high. Detailed statements of Standard Electrokinetic and DLVO Models are given in the forms that are capable of addressing electrophoresis and interaction of particles for arbitrary ratios of the particle to Debye radius, interfacial potentials and electrolyte compositions. The experimental part of the study consists of two groups of measurements conducted for Pt/C nano-suspensions, namely, the electrophoretic and coagulation dynamic studies, with various electrolyte compositions. The obtained experimental data are processed by using numerical algorithms based on the formulated models for obtaining interfacial potential and charge. While analyzing the dependencies of interfacial potential and charge on the electrolyte compositions, conclusions are made regarding the mechanisms of charge formation. It is established that the behavior of system stability is in a qualitative agreement with the results computed from the electrophoretic data. The verification of quantitative applicability of the employed models is conducted by calculating the Hamaker constant from experimental data. It is proposed how to explain the observed variations of predicted Hamaker constant and its unusually high value.     

A rheological approach to the study of concentrated milk clotting

The aim of the present work is to analyze the complex phenomena involved in the concentrated milk clotting process in order to define general criteria applicable to the design of a continuous coagulator. A full characterization of the rheological properties of completely hydrolyzed milk as a function of two different parameters, i.e., the coagulator temperature and the concentration degree of the milk, is presented. The dynamic evolution of loss, G′′, and storage, G′, moduli has been obtained at different frequency values and for different concentration degrees during the clotting process. Time cure tests have been performed on completely hydrolyzed milk samples showing that the rate of curing is very high and that the time for rheological experiments is much too short for testing Winter's theory of gelation. To overcome this problem, the intersect of loss and storage moduli was used for estimating the coagulation. Coagulation is faster when higher temperatures are used and the consistency of the final curd is greater if a more concentrated milk is used. A tentative physical explanation based on the network theories is presented. If an observation time far enough from the crossover point is chosen it can be seen that the curd strength estimated at 40 °C is about 50 times higher than that one evaluated at 25 °C. Among the considered temperatures, a good processing value was evaluated at 40 °C. Received: 6 February 2000 Accepted: 24 October 2000     

Modelling silicosis: Existence,uniqueness and basic properties of solutions

We present a model for the silicosis disease mechanism following the original proposal by Tran et al. (1995), as modified recently by da Costa et al. (2020). The model consists in an infinite ordinary differential equation system of coagulation–fragmentation–death type. Results of existence, uniqueness, continuous dependence on the initial data and differentiability of solutions are proved for the initial value problem.     

Kinetic Limit for a System of Coagulating Planar Brownian Particles

We study a model of mass-bearing coagulating planar Brownian particles. The coagulation occurs when two particles are within a distance of order ε. We assume that the initial number of particles N is of order |logε|. Under suitable assumptions of the initial distribution of particles and the microscopic coagulation propensities, we show that the macroscopic particle densities satisfy a Smoluchowski-type equation.     

Propagation of light inside shear flows: a remote sensing method to retrieve velocity fields

Inside a moving dielectric medium a wave perceives the matter as an effective gravitational field. The medium and its velocity field alter the way in which an electromagnetism field propagates. We propose an optical method for remote sensing of the velocity fields inside shear flows by angular scanning.     

Monte Carlo simulation of cluster kinetics in three-dimensional Ising model

Simulations in lattices of size 100³ at the critical point of the three-dimensional Glauber kinetic Ising model indicate that the 1935 Becker-Doring equation no longer works there: The growth rates decay in time. These conclusions confirm those in two dimensions.     

Lyotropic effect in surface charge,electrokinetics, and coagulation of a rutile dispersion

Potentiometric, electrokinetic, and coagulation experiments with a rutile dispersion in the pH region above the point of zero charge exhibit an inverse lyotropic sequence for counterions: Li⁺>K⁺>Cs⁺. The potentiometric and electrokinetic data were interpreted by a surface complexation model assuming the Stern-Gouy-Chapman structure of the interfacial layer, which yielded the values of inner layer capacitances,C, and the intrinsic equilibrium constants,K _ass ⁰ , characterizing the specificity of each counterion. These parameters were used to explain the order of lyotropic sequences in the adsorption, coagulation, and electrokinetic phenomena.     

醋酸十二铵的吸附和SiO2悬浮液的稳定性

（1）测定了醋酸十二烷基铵（DAA）在CAB－O－SIL上的吸附，其等温线属双平台或LS型[1－3，5]；（2）NaCl的存在使DAA的吸附增加．但不影响其低浓度下第一平台的吸附量；HCl的存在则在全浓度范围内抑制了DAA的吸附，（3）测定了CAB－O－SIL颗粒在上述各溶液中的悬浮液的稳定性；（4）根据表面形成小胶团的吸附理论（即二步模型产）[2，3，5，]，并借助电导跟踪溶液中发生的变化，满意地解释了吸附和聚沉的实验结果．     

Comparison of planar SDS-PAGE,CGE-on-a-chip,and MALDI-TOF mass spectrometry for analysis of the enzymatic de-<Emphasis Type="Italic">N</Emphasis>-glycosylation of antithrombin III and coagulation factor IX with PNGase F

Three different analytical techniques (planar SDS-PAGE, CGE-on-a-chip and MALDI-TOF-MS) applied for determination of the molecular weight of intact and partly and completely de-N-glycosylated human serum glycoproteins (antithrombin III and coagulation factor IX) have been compared. N-Glycans were removed from the protein backbone of both complex glycoproteins using PNGase F, which cleaves all types of asparagine-attached N-glycan provided the oligosaccharide has at least the length of a chitobiose core unit. Two of the applied techniques were based on gel electrophoretic separation in the liquid phase while the third technique was the gas-phase technique mass spectrometry. It was demonstrated that the enzymatic de-N-glycosylation generally worked well (completely or partially) with both glycoproteins (one containing only N-glycans and the second N- and O-glycans). All three methods were suitable for monitoring the de-N-glycosylation progress. While the molecular weights determined with MALDI-TOF-MS were most accurate, both gel electrophoretic methods provided molecular weights that were too high because of the attached glycan structures. Figure CGE-on-a-chip, SDS-PAGE and MALDI mass spectrometric pattern obtained from therapeutic glycoprotein