• 대한수학회지
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• 제36권1호
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• pp.139-157
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• 1999

Consider a supercritical Bellman-Harris process evolving from one particle. We superimpose on this process the additional structure of movement. A particle whose parent was at x at its time of birth moves until it dies according to a given Markov process X starting at x. The motions of different particles are assumed independent. In this paper we show that when the movement process X is standard Brownian the proportion of particles with position $\leq${{{{ SQRT { t} }}}} b and age$\leq$a tends with probability 1 to A(a)$\Phi$(b) where A(.) and $\Phi$(.) are the stable age distribution and standard normal distribution, respectively. We also extend this result to the case when the movement process is a Levy process.

• 한국가시화정보학회:학술대회논문집
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• 한국가시화정보학회 2004년도 추계학술대회 논문집
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• pp.84-85
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• 2004

Experimental study was conducted to characterize shear-induced lateral migration of $1.0-{\mu}m-diameter$ Brownian particles flowing through a rectangular microchannel which can be used to deliver small amount of liquids, drugs, biological agents and particles in microfluidic devices. Measurements were obtained by using a mercury lamp with a light of 532-nm wavelength, an inverted epi-fluorescence microscope, and a cooled CCD camera to record particle images. Peclet number was used as a parameter to assess the lateral distribution of the particles at a fixed volume fraction of $0.1\%$. It was shown that as Pe increased, particles were moved toward the centerline of the channel, which is in good agreement with previous studies.

• 대한기계학회논문집B
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• 제26권12호
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• pp.1715-1721
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• 2002

Numerical analysis was conducted to characterize the gas flow field and particle deposition on a horizontal freestanding semiconductor wafer under the laminar flow field at vacuum environment. In order to calculate the properties of gas, the gas was assumed to obey the ideal gas law. The particle transport mechanisms considered were convection, Brownian diffusion and gravitational settling. The averaged particle deposition velocities and their radial distributions fnr the upper surface of the wafer were calculated from the particle concentration equation in an Eulerian frame of reference for system pressures of 1 mbar~1 atm and particle sizes of 2nm~10$^4$ nm(10 ${\mu}{\textrm}{m}$). It was observed that as the system pressure decreases, the boundary layer of gas flow becomes thicker and the deposition velocities are increased over the whole range of particle size. One thing to be noted here is that the deposition velocities are increased in the diffusion dominant particle size range with decreasing system pressure, whereas the thickness of the boundary layer is larger. This contradiction is attributed to the increase of particle mechanical mobility and the consequent increase of Brownian diffusion with decreasing the system pressure. The present numerical results showed good agreement with the results of the approximate model and the available experimental data.

• Bulletin of the Korean Chemical Society
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• 제25권12호
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• pp.1893-1897
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• 2004

Hydrodynamic simulations of mesoscopic solvent have been performed by multi-particle collision algorithm in a real dimensional system without and with the random shifting of the grid. A systematic conversion of the dimensionless units to a real dimensional system was confirmed by jump rates of solvent particles. Speed distributions of solvent particles obtained from the simulations agreed very well with the Maxwell-Boltzmann distributions. Solvent viscosities obtained from the simulations and from the conversion of units are exactly the same which confirmed the correct conversion of the units once again. The calculation of the friction coefficient of a massive Brownian particle in a mesoscopic solvent as a function of Brownian particle diameter was examined as an example.

• Korea-Australia Rheology Journal
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• 제21권1호
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• pp.1-12
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• 2009

This paper reports the suitability of a domain decomposition technique for the hybrid simulation of dilute polymer solution flows using Eulerian Brownian dynamics and Radial Basis Function Networks (RBFN) based methods. The Brownian Configuration Fields (BCF) and RBFN method incorporates the features of the BCF scheme (which render both closed form constitutive equations and a particle tracking process unnecessary) and a mesh-less method (which eliminates element-based discretisation of domains). However, when dealing with large scale problems, there appear several difficulties: the high computational time associated with the Stochastic Simulation Technique (SST), and the ill-condition of the system matrix associated with the RBFN. One way to overcome these disadvantages is to use parallel domain decomposition (DD) techniques. This approach makes the BCF-RBFN method more suitable for large scale problems.

• 대한기계학회논문집B
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• 제40권6호
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• pp.365-372
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• 2016

전산유체역학(CFD)을 이용하여 테일러 반응기 내 입자간 응집과 분해반응을 고려한 유동해석을 수행하였다. 입자크기분포를 파악하기 위하여 모멘트 적분법(QMOM)을 이용하여 집합체 균형방정식(Population Balance Equation)을 계산하였다. 초기 여섯 개의 모멘트를 이용하였으며, 응집커널은 Brownian kernel 과 turbulent kernel의 합을, 그리고 분해커널은 멱법칙 커널(power-law kernel)을 사용하였다. 입자의 초기 부피분율에 따른 최종 입자크기를 예측하였다. 그 결과, 초기 부피분율이 증가할수록 입자의 크기와 초기 성장속도가 증가하는 것을 확인하였다.

• 한국입자에어로졸학회지
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• 제11권2호
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• pp.29-36
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• 2015

The purpose of this research is to find out the collection property of nanoparticle in diffusion filter to know particle size dispersion of nanomaterial using inertial force and principle of Brownian diffusion motion. We used inertial filters which are two different type and diffusion filters made by various kinds of Wiremesh and the different pieces of filter to compare with particle size distribution using NaCl particles. Finally, We made a conclusion as follows : (1) the bigger available charging volume is and the larger specific surface area of inertial filter is, the better collection efficiency is. (2) The higher wire-mesh number of filter is, the more collection efficiency of small particle is increasing because the wire of the higher Wiremesh number filter is thinner and denser. (3) The more pieces of wire-mesh filter, the more collection efficiency is increasing because it makes the residence time longer.

• 대한기계학회논문집B
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• 제21권10호
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• pp.1284-1293
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• 1997

The electrostatic effect on particle deposition onto a heated, Horizontal free-standing wafer surface was investigated numerically. The deposition mechanisms considered were convection, Brownian and turbulent diffusion, sedimentation, thermophoresis and electrostatic force. The electric charge on particle needed to calculate the electrostatic migration velocity induced by the local electric field was assumed to be the Boltzmann equilibrium charge. The electrostatic forces acted upon the particle included the Coulombic, image, dielectrophoretic and dipole-dipole forces based on the assumption that the particle and wafer surface are conducting. The electric potential distribution needed to calculate the local electric field around the wafer was calculated from the Laplace equation. The averaged and local deposition velocities were obtained for a temperature difference of 0-10 K and an applied voltage of 0-1000 v.The numerical results were then compared with those of the present suggested approximate model and the available experimental data. The comparison showed relatively good agreement between them.

• 한국대기환경학회지
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• 제16권1호
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• pp.1-10
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• 2000

The behavior of aerosos due to gravitational coagulation was studied experimentally and numerically. In experimental study, the geometric mean particel size increased as time elapsed in a vertical tube column, while the size decreased when the tube was set horizontally. The particle size distribution was observed to maintain the lognormal form during the coagulation process. Separately, numerical calculations were performed for studying the aerosol behavior under gravitational and Brownian coagulation using the moment method. By comparing the expeimented results with the numerical predictions, the governing mechanism of the aerosol behavior proved to be gravitational coagulation.

• 대한기계학회논문집B
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• 제27권2호
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• pp.173-180
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• 2003

Effects of the electric conductivity of particles were studied for the aggregation process of charged particles with a Brownian dynamic simulation in the free molecular regime. A periodic boundary condition was used for the calculation of the aggregation process in each cell with 500 primary particles of 16 nm in diameter. We considered two extreme cases, a perfect conductor and a perfect nonconductor. The electrostatic force on a particle in the simulation cell was considered as a sum of electrostatic forces from other particles in the original cell and its replicate cells. We assumed that aggregates were only charged with pre-charged primary particles. The morphological shape of aggregates was described in terms of the fractal dimension. The fractal dimension for the uncharged aggregate was D$_{f}$= 1.761. However, the fractal dimension decreased from 1.694 to 1.360 for the case of the perfect conductor, and from 1.610 to 1.476 for the case of the perfect nonconductor, with the increase of the average number of charges on the primary particle from 0.2 to 0.3. These values were smaller than that of the centered charge case.e.