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Development and Demonstration of a General-Purpose Model for Brownian Motion
Endres, Derek

2011, Master of Science, Ohio State University, Mechanical Engineering.

Brownian motion is an important phenomena demonstrated by sub-micron sized particles in fluids. The objective of the current work is to develop a general-purpose numerical model to simulate Brownian motion and explore it for various applications of practical interest. To accomplish this goal, a model based on the Langevin equation was developed and implemented. The resulting stochastic ordinary differential equations were solved using the Newton-Raphson method after backward Euler discretization. In order to track the particles through the background fluid, a three-dimensional (3-D) tracking algorithm was developed. The solver is applicable to arbitrary two-dimensional (2-D) and 3-D geometries discretized using unstructured mesh topology. The Brownian motion solver was fully coupled to the carrier fluid flow solver, enabling unsteady flows to be simulated. In order to apply the model to various applications, viscous drag, Brownian forces, lift, and thermophoretic forces were considered. These forces all contribute to the particle’s velocity and resulting motion. The Brownian motion model was first validated against analytical results and then explored for various applications where Brownian motion is important. From the simulations, it is shown that Brownian motion is increased by decreasing the particle size, increasing the fluid temperature, or decreasing the fluid viscosity. One application where Brownian motion is taken advantage of is in micro-scale filters. By simulating micro-scale filters, they can be optimized so that capture efficiencies can be improved. It is shown by performing simulations under different operating conditions, that the capture efficiency of micro-filters can be increased for a given particle diameter by increasing fluid temperature or decreasing fluid viscosity. Another application investigated in this work is the chemical vapor deposition (CVD) of Aluminum Nitride (AlN). During this process, it has been experimentally observed that particles are formed as suspended solids in the gas above the epitaxial film. Numerical simulations are conducted to shed light on the trajectory of these sub-micron particles as they travel through the reactor. Thermophoretic forces are found to be the dominant forces acting on such particles in steady CVD, and as experimentally observed; these forces prevent the AlN particles from getting incorporated in the epitaxial film. It is shown that Brownian motion has a much more significant contribution to the trajectory of formed AlN particles in pulsed AlN CVD than steady AlN CVD.

In summary there are three main contributions of this thesis. First is the development of a fully coupled 3-D Brownian motion model based on the Langevin equation along with a particle tracking algorithm that is applicable to any mesh topology, including unstructured meshes. The second contribution is simulation-based optimization of H-filters and cylindrical filters. The final contribution is simulation-based understanding of the fate of AlN particle within CVD reactors of various configurations and under various operating conditions.

Sandip Mazumder, Dr. (Advisor)
Shaurta Prakash, Dr (Committee Member)
127 p.

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Endres, D. (2011). Development and Demonstration of a General-Purpose Model for Brownian Motion. (Electronic Thesis or Dissertation). Retrieved from

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Endres, Derek. "Development and Demonstration of a General-Purpose Model for Brownian Motion." Electronic Thesis or Dissertation. Ohio State University, 2011. OhioLINK Electronic Theses and Dissertations Center. 21 Apr 2018.

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Endres, Derek "Development and Demonstration of a General-Purpose Model for Brownian Motion." Electronic Thesis or Dissertation. Ohio State University, 2011.


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