The verification of the Taylor-expansion moment method for the nanoparticle coagulation in the entire size regime due to Brownian motion

2010 ◽  
Vol 13 (5) ◽  
pp. 2007-2020 ◽  
Author(s):  
Mingzhou Yu ◽  
Jianzhong Lin ◽  
Hanhui Jin ◽  
Ying Jiang
Keyword(s):  
Brownian Motion ◽  
Moment Method ◽  
Taylor Expansion ◽  
Size Regime

scholarly journals Numerical modeling of fine particle fractal aggregates in turbulent flow

2015 ◽  
Vol 19 (4) ◽  
pp. 1189-1193
Author(s):  
Feifeng Cao ◽  
Zhanhong Wan ◽  
Minmin Wang ◽  
Zhenjiang You ◽  
Zongfu Ren
Keyword(s):  
Numerical Modeling ◽  
Turbulent Flow ◽  
Moment Method ◽  
Particle Transport ◽  
Fine Particle ◽  
Taylor Expansion ◽  
Fine Particles ◽  
Particle Dynamics ◽  
Fractal Aggregates

A method for prediction of fine particle transport in a turbulent flow is proposed, the interaction between particles and fluid is studied numerically, and fractal agglomerate of fine particles is analyzed using Taylor-expansion moment method. The paper provides a better understanding of fine particle dynamics in the evolved flows.

Method of Taylor Expansion Moment Incorporating Fractal Theories for Brownian Coagulation of Fine Particles

2012 ◽  
Vol 13 (7-8) ◽  
Author(s):  
Zhanhong Wan ◽  
Zhenjiang You ◽  
Zhilin Sun ◽  
Wenbin Yin
Keyword(s):  
Fractal Dimension ◽  
Moment Method ◽  
Taylor Expansion ◽  
Fine Particles ◽  
Second Order ◽  
New Method ◽  
Particle Removal ◽  
Brownian Coagulation ◽  
Combination Process ◽  
Laguerre Method

AbstractFine particles aggregating into larger units or flocculation body is a random combination process. Increasing the size and density of flocculation body is the main approach to rapid particle removal or sedimentation in water. Aiming at the Brownian coagulation of fine particles, a new method of Taylor expansion moment construction of fractal flocs has been developed in this paper, incorporating the Taylor expansion approach based on the moment method and the fractal dimension of the floc structure originated from fractal theories. This method successfully overcomes the limit of previous moment methods that require pre-assumed particle size distribution. Results of the zero and second order moments of Brownian flocs from the proposed method are compared with those from the Laguerre method, integral moment method and finite element method. It is found that the higher accuracy and efficiency of computation have been achieved by the new method, compared to the previous ones. Effects of the fractal dimension on the zero and second order moments, geometric average volume and standard deviation are also analyzed using this method. The self-conservation characteristics of particle distribution is observed without presumption of initial distributions.

scholarly journals On fluctuations for random band Toeplitz matrices

2015 ◽  
Vol 04 (03) ◽  
pp. 1550012 ◽  
Author(s):  
Yiting Li ◽  
Xin Sun
Keyword(s):  
Brownian Motion ◽  
Moment Method ◽  
Toeplitz Matrices ◽  
Covariance Structure ◽  
Independent Random Variables ◽  
Homogeneous Polynomials ◽  
Empirical Measures ◽  
Main Method ◽  
The Moment ◽  
Random Band

In this paper, we study two one-parameter families of random band Toeplitz matrices: [Formula: see text] where (1) a0 = 0, {a1, a2, …} in An(t) are independent random variables and a-i = ai; (2) a0(t) = 0, {a1(t), a2(t), …} in Bn(t) are independent copies of the standard Brownian motion at time t and a-i(t) = ai(t). As t varies, the empirical measures μ(An(t)) and μ(Bn(t)) are measure valued stochastic processes. The purpose of this paper is to study the fluctuations of μ(An(t)) and μ(Bn(t)) as n goes to ∞. Given a monomial f(x) = xp with p ≥ 2, the corresponding rescaled fluctuations of μ(An(t)) and μ(Bn(t)) are [Formula: see text] respectively. We will prove that the above equations converge to centered Gaussian families {Zp(t)} and {Wp(t)} respectively. The covariance structure 𝔼[Zp(t1)Zq(t2)] and 𝔼[Wp(t1)Wq(t2)] are obtained for all p, q ≥ 2, t1, t2 ≥ 0, and are both homogeneous polynomials of t1 and t2 for fixed p, q. In particular, Z2(t) is the Brownian motion and Z3(t) is the same as W2(t) up to a constant. The main method of this paper is the moment method.

scholarly journals Fractal aggregation and breakup of fine particles

2016 ◽  
Vol 20 (3) ◽  
pp. 797-801 ◽  
Author(s):  
Bingru Li ◽  
Feifeng Cao ◽  
Zhanhong Wan ◽  
Zhigang Feng ◽  
Honghao Zheng
Keyword(s):  
Fluid Dynamics ◽  
Moment Method ◽  
Taylor Expansion ◽  
Fine Particles ◽  
Size Distributions ◽  
Number Density ◽  
Dynamics Modeling ◽  
Particle Size Distributions ◽  
Particle Volume ◽  
Computational Fluid Dynamics Modeling

Breakup may exert a controlling influence on particle size distributions and particles either are fractured or are eroded particle-by-particle through shear. The shear-induced breakage of fine particles in turbulent conditions is investigated using Taylor-expansion moment method. Their equations have been derived in continuous form in terms of the number density function with particle volume. It suitable for future implementation in computational fluid dynamics modeling.

Research on the coagulation law of dielectric nanoparticles in Stokes regime via Taylor expansion moment method

2020 ◽  
Vol 31 (48) ◽  
pp. 485402
Author(s):  
Kai Zhang ◽  
Zhihan Gao ◽  
Qing Zhang ◽  
Mingyue Yang ◽  
Guangxue Zhang
Keyword(s):  
Moment Method ◽  
Taylor Expansion

scholarly journals The verification of the Taylor-expansion moment method in solving aerosol breakage

2012 ◽  
Vol 16 (5) ◽  
pp. 1424-1428 ◽  
Author(s):  
Ming-Zhou Yu ◽  
Kai Zhang
Keyword(s):  
Moment Method ◽  
Taylor Expansion ◽  
High Efficiency ◽  
Population Balance ◽  
Moment Equation ◽  
Method Of Moment ◽  
Balance Equations ◽  
Particle Population ◽  
The Moment ◽  
Linear Integral

The combination of the method of moment, characterizing the particle population balance, and the computational fluid dynamics has been an emerging research issue in the studies on the aerosol science and on the multiphase flow science. The difficulty of solving the moment equation arises mainly from the closure of some fractal moment variables which appears in the transform from the non-linear integral-differential population balance equation to the moment equations. Within the Taylor-expansion moment method, the breakage-dominated Taylor-expansion moment equation is first derived here when the symmetric fragmentation mechanism is involved. Due to the high efficiency and the high precision, this proposed moment model is expected to become an important tool for solving population balance equations.

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