Diffusion characteristics of the industrial submicron particle under Brownian motion and turbulent diffusion

The industrial release of submicron aerosol particles at workplace could cause undue health effect on workers. To effectively capture and remove airborne particles, we need to study the characteristics of various interactive particle motion forces (drag force, Brownian force, Saffman lift force, etc.) and the dispersion of these aerosol particles in indoor air. In this study, the dominant force of submicron particles was determined by calculating the acting forces with different particle sizes. Then, a Discrete Particle Model (DPM) was used to calculate the trajectory of particle movement in turbulent thermal plume flow. Horizontal dispersity ( DH) was defined to evaluate the horizontal diffusion of the particulate matter. The impact of different particle diameters, heat source temperatures and initial relative velocities on DH was investigated. This study showed that the main acting forces for submicron aerosol particles were drag force, Brownian force, Saffman lift force and thermophoresis force. Brownian force cannot be ignored when the particle diameter was below 0.3 µm, which would promote the irregular movement of particles in space and enhance their diffusion ability. The smaller the particle size, the higher the heat source temperature and the lower the particles' initial velocity would lead to the increase of DH.

Fast Stokesian dynamics

We present a new method for large scale dynamic simulation of colloidal particles with hydrodynamic interactions and Brownian forces, which we call fast Stokesian dynamics (FSD). The approach for modelling the hydrodynamic interactions between particles is based on the Stokesian dynamics (SD) algorithm (J. Fluid Mech., vol. 448, 2001, pp. 115–146), which decomposes the interactions into near-field (short-ranged, pairwise additive and diverging) and far-field (long-ranged many-body) contributions. In FSD, the standard system of linear equations for SD is reformulated using a single saddle point matrix. We show that this reformulation is generalizable to a host of particular simulation methods enabling the self-consistent inclusion of a wide range of constraints, geometries and physics in the SD simulation scheme. Importantly for fast, large scale simulations, we show that the saddle point equation is solved very efficiently by iterative methods for which novel preconditioners are derived. In contrast to existing approaches to accelerating SD algorithms, the FSD algorithm avoids explicit inversion of ill-conditioned hydrodynamic operators without adequate preconditioning, which drastically reduces computation time. Furthermore, the FSD formulation is combined with advanced sampling techniques in order to rapidly generate the stochastic forces required for Brownian motion. Specifically, we adopt the standard approach of decomposing the stochastic forces into near-field and far-field parts. The near-field Brownian force is readily computed using an iterative Krylov subspace method, for which a novel preconditioner is developed, while the far-field Brownian force is efficiently computed by linearly transforming those forces into a fluctuating velocity field, computed easily using the positively split Ewald approach (J. Chem. Phys., vol. 146, 2017, 124116). The resultant effect of this field on the particle motion is determined through solution of a system of linear equations using the same saddle point matrix used for deterministic calculations. Thus, this calculation is also very efficient. Additionally, application of the saddle point formulation to develop high-resolution hydrodynamic models from constrained collections of particles (similar to the immersed boundary method) is demonstrated and the convergence of such models is discussed in detail. Finally, an optimized graphics processing unit implementation of FSD for mono-disperse spherical particles is used to demonstrated performance and accuracy of dynamic simulations of $O(10^{5})$ particles, and an open source plugin for the HOOMD-blue suite of molecular dynamics software is included in the supplementary material.

New weight factor for Brownian force exerted on micro/nano-particles in air flow

In order to effectively describe the effect of Brownian force exerted on the micro/nano-particles in air flow, a new weight factor, which is defined as the ratio of the characteristic velocity of the Brownian motion to the macroscopic velocity, is proposed and applied to the particle settlement under gravity. Results show that the weight factor can quantitatively evaluate the effect of Brownian force on the particle motion. Moreover, the value of the weight factor can also be used to judge the particle motion pattern and determine whether the Brownian force should be taken into account.

Preferential frequency and size effect of the Brownian force acting on a nanoparticle

The Brownian motion of a nanoparticle in fluid depends on the molecular forces acting on it. Because of the small size and the high frequency, it is difficult to make experimental measurements of these forces. In the present work, Brownian forces acting on a nanoparticle are numerically investigated with the molecular dynamics method. Some new phenomena are disclosed. (i) The probability distribution shows that the Brownian forces conform to the Gaussian distribution and self-similarity of the probability distribution is also found for different $1/Kn$ numbers which are characterized with the particle radius and the mean path $\unicode[STIX]{x1D706}$ of the gas molecule $(1/Kn=R/\unicode[STIX]{x1D706})$. (ii) The frequency spectrum distribution of the Brownian force is not a white noise spectrum, which is different from the assumption commonly used in Langevin model. The preferential frequency of the Brownian force is found. (iii) The size effect relating to the Brownian forces is not monotonically varying with $1/Kn=R/\unicode[STIX]{x1D706}$ and is also found. It first increases and then decreases after it reaches the maximum value at $1/Kn\approx 250$. The variation process for $1/Kn<250$ observed in the present work has not been reported in previous research to date.