### Abstract

A multiscale-linking algorithm has been developed for the efficient simulation of irreversible deposition of particles on a two-dimensional substrate. The algorithm combines Brownian dynamics simulation (BDS) for the evaluation of particle trajectories with the solution of the continuum-level conservation law for particle concentration. This allows for the use of a simulation box with relatively small dimensions in the flux direction, resulting in significant CPU-time savings. The instantaneous flux of particles into the box is computed from the solution of the transient diffusion equation with an adaptive Neumann boundary condition. The incoming particles are placed in the box in accordance with the probability distribution function associated with the motion of particles. The algorithm is applied for the simulation of irreversible monolayer deposition of noninteracting hard spheres. Results are presented for the kinetics (fractional surface coverage, θ) and the surface structure (radial distribution function, g(r), two-point probability distribution function, S_{2}(r), and void distribution function, H_{v}(r)) of the deposit for different bulk concentrations, φ. Short-time kinetics follows θ(t) = 3/2p^{1/2} φ √ t-, where t- denotes dimensionless time, consistent with the diffusion-limited deposition model. The approach to the maximum coverage (jamming limit), θ_{∞}, fits a 2/3-power law, θ_{∞} - θ = βt-^{-2/3,} consistent with theoretical predictions. By performing BDS for different φ values it is shown that β = 3/4φ^{-0.9} in the dilute regime. θ_{∞}, g(r) and S_{2}(r) are in good agreement with statistical-geometric models such as random sequential adsorption (RSA) and ballistic deposition (BD) models. However, differences exist between the predictions of BDS and RSA or BD for the blocking function, φ, that accounts for the reduction in the particle flux at the surface due to adsorption. Specifically, ^{φ}RSA < ^{φ}BDS < ^{φ}BD.

Original language | English (US) |
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Pages (from-to) | 475-500 |

Number of pages | 26 |

Journal | Multiscale Modeling and Simulation |

Volume | 2 |

Issue number | 3 |

DOIs | |

State | Published - 2004 |

Externally published | Yes |

### Keywords

- Ballistic deposition
- Blocking function
- Brownian dynamics
- Colloidal
- Irreversible deposition
- Monolayer
- Multiscale
- Random sequential adsorption

### ASJC Scopus subject areas

- Chemistry(all)
- Modeling and Simulation
- Ecological Modeling
- Physics and Astronomy(all)
- Computer Science Applications