• Journal of the Korean Data and Information Science Society
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• v.7 no.1
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• pp.69-78
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• 1996

Consider a natural model for stochastic flow systems is Brownian motion, which is Brownian motion on the positive real line with constant drift and constant diffusion coefficient, modified by an impenetrable reflecting barrier at $x_{0}$. In this paper, we investigate the joint distribution functions and study on the distribution of the first-passage time. Also we find out the distribution of ${\mu}-RBMPx_{0}$.

• Computers and Concrete
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• v.30 no.2
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• pp.143-150
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• 2022

In this paper, the non-linear mathematical problem is solved via numerical scheme by utilizing shooting method. Brownian diffusion and thermophoresis along mass and heat transfer are accounted for. Non-linear expression is reduced via non-dimensional variables. The simplified ordinary differential equations are tackled by shooting technique. Behavior of distinct influential parameters is investigated graphically and analyzed for temperature and concentration profile. Our finding indicates that temperature profile is enhanced for the thermophoresis, Brownian motion coefficient, Prandtl number, Eckert number and temperature slip parameter. Comparison of numerical technique with the extant literature is made and an acceptable agreement is attained. Graphs are plotted to examine the influence of these parameters.

• Membrane Journal
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• v.12 no.4
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• pp.207-215
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• 2002

The hindered diffusion in confined spaces is an important phenomenon to understand in a micro-scale the filtration mechanism determined by the particle motion in membrane pores. Compared to the case of spherical colloids, both the theoretical investigations and the experiments on the hindered diffusion of polyelectrolytes is actually more difficult, due to lots of relevant parameters resulting from the complicated conformational properties of the polyelectrolyte chain. We have successfully performed the Brownian dynamics simulations upon a single polyeiectrolyte confined in a slit-like pore, where a coarse-grained bead-spring model incorporated with Debye-Huckel interaction is properly adopted. For the given sizes of both the polyelectrolyte and the pore width, the hindered diffusion coefficient decreases as the solution ionic concentration decreases. It is evident that a charge effect of the pore wall enhances the hindered diffusion of polyelectrolyte. Simulation results allow us to make sense of the diffusive transport through the micro-pore, which is restricted by the influences of the steric hindrance of polyelectrolytes as well as the electrostatic repulsion between the polyelectrolytes and pore wall.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.32 no.6
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• pp.706-712
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• 1999

PSD (particle size distribution) for 2,000 mg/$\ell$ natural loess in seawater showed normal distribution cure at 0 minute settling time, accompanying with very large particle distribution range with its mean particle diameter of 31.6 $\mu$m and coencient of variance of $72.6\%$, With elapsed time it showed that the PSD was rapidly changed from normal distribution cure to abnormal distribution curve, steepened the right-hand side of it and its coefficient of variance was getting increased because of rapid settling of large size particles, Cumulative weight distribution showed that 2,000 mg/$\ell$ natural loess in seawater was almost $100\%$ constituted of particles bigger than 20 $\mu$m in diameter. Ratio of $V_s/(D_{bm})^{1/2}$ for loess particles in seawater was increased with increase of particle size in geometrical progression. Almost all loess particles in seawater had Stokes settling velocity not less than 2,255 times of Brownian diffusion coefficient, There was almost to EDL (about 0.4 nm) around natural loess particles in seawater, Thus, there was always LVDW attractive force between loess particles approaching each other in seawater, and almost no EDL repulsive force. Loess particles were not always in the condition of easy floe formation. Concentration of natural loess in seawater increasing from 400 mg/$\ell$ to 10,000 mg/$\ell$, characteristics of the settling was changed from Type I settling (discrete settling) to Type II settling (flocculation settling). PVD (particle volume distribution) showed that natural loess particles in seawater were largely constituted of two types of particles, such as rapidly settling particles and suspended and dispersed particles for a long time. Amount of the latter was much less than that of the former.