# A Numerical Study of an Ellipsoidal Nanoparticles under High Vacuum Using the DSMC Method

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Approach

#### Drag Force in Slip Regime

## 3. Numerical Methods

#### 3.1. Direct Simulation Monte Calro

_{N}, 10

^{11}–10

^{15}). It approximates the physical phenomenon represented by the Boltzmann equation using a statistical method. In the DSMC method, flow is caused by repeating movement, collision, deposition, and chemical reactions using these representative particles, and various characteristics such as velocity, temperature, and pressure can be expressed through statistical techniques. The collision algorithms are important in DSMC methods and calculate the most complex terms of the Boltzmann or Kac probability equations. The DSMC schemes can be grouped into two groups with respect to collision treatment [32]. The first group is based on the Boltzmann equation and includes TC [33], NTC [34], NC [35], and MFS [36] methods. The second group is based on the Kac stochastic equation, and there are BT [37] and SBT [38,39] methods. In this study, we used the NTC collision scheme, which is the most widely used.

_{N}value according to the temperature and pressure conditions in the initial flow region. It also assigns an initial velocity to every particle for a given initial temperature. At this time, the magnitude of the velocity is determined according to the Maxwell–Boltzmann distribution.

#### 3.2. GPU Computing (CUDA)

## 4. Results and Discussion

#### 4.1. Microchannel Flow

#### 4.2. Nanoparticle Drag Force

_{p}).

#### 4.3. Drag Force of Ellipsoid Particle

_{x}, D

_{y}, and D

_{z}, which are in the x, y, and z-directions, respectively.

_{z}. In addition, to determine the effect of the diameter of the fine particles, the vertical diameter D

_{x}was analyzed at 50 nm and 100 nm.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**(

**a**) Velocity profiles for microchannel flow. (

**b**) Pressure profile ($Kn$ = 0.0439) of microchannel flow. (

**c**) Deviation in the pressure ($Kn$= 0.0439) of microchannel flow.

**Figure 3.**(

**a**) Schematic diagram of the calculation domain for the drag force. (

**b**) Force-per-area contour on the particle surface. (

**c**) Force per area on particle surface for various angles.

**Figure 5.**(

**a**) The shape of the ellipsoid with aspect ratio. (

**b**) Force per area on ellipsoidal particle surface for various angles.

**Figure 6.**(

**a**) Drag force for various aspect ratios (${D}_{x}=50\mathrm{nm}$). (

**b**) Drag force for various aspect ratios (${D}_{x}=100\mathrm{nm}$).

**Figure 7.**(

**a**) Normalized drag force according to various aspect ratios (${D}_{x}=50\mathrm{nm}$). (

**b**) Normalized drag force according to various aspect ratios (${D}_{x}=100\mathrm{nm}$).

Case | Inlet Pressure [Pa] | Outlet Pressure [Pa] | $\mathit{K}\mathit{n}$ |
---|---|---|---|

1 | $1.4\times {10}^{5}$ | $1.0\times {10}^{5}$ | 0.0402 |

2 | $1.2\times {10}^{5}$ | $1.0\times {10}^{5}$ | 0.0439 |

Knudsen Number | Pressure [Pa] |
---|---|

10 | 13,851 |

20 | 6925 |

50 | 2770 |

100 | 1385 |

500 | 277 |

1000 | 139 |

5000 | 28 |

10,000 | 14 |

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**MDPI and ACS Style**

Jang, J.; Son, Y.; Lee, S.
A Numerical Study of an Ellipsoidal Nanoparticles under High Vacuum Using the DSMC Method. *Micromachines* **2023**, *14*, 778.
https://doi.org/10.3390/mi14040778

**AMA Style**

Jang J, Son Y, Lee S.
A Numerical Study of an Ellipsoidal Nanoparticles under High Vacuum Using the DSMC Method. *Micromachines*. 2023; 14(4):778.
https://doi.org/10.3390/mi14040778

**Chicago/Turabian Style**

Jang, Jinwoo, Youngwoo Son, and Sanghwan Lee.
2023. "A Numerical Study of an Ellipsoidal Nanoparticles under High Vacuum Using the DSMC Method" *Micromachines* 14, no. 4: 778.
https://doi.org/10.3390/mi14040778