Discrete-element modeling of particulate aerosol flows

Abstract

A multiple-time step computational approach is presented for efficient discrete-element modeling of aerosol flows containing adhesive solid particles. Adhesive aerosol particulates are found in numerous dust and smoke contamination problems, including smoke particle transport in the lungs, particle clogging of heat exchangers in construction vehicles, industrial nanoparticle transport and filtration systems, and dust fouling of electronic systems and MEMS components. Dust fouling of equipment is of particular concern for potential human occupation on dusty planets, such as Mars. The discrete-element method presented in this paper can be used for prediction of aggregate structure and breakup, for prediction of the effect of aggregate formation on the bulk fluid flow, and for prediction of the effects of small-scale flow features (e.g., due to surface roughness or MEMS patterning) on the aggregate formation. After presentation of the overall computational structure, the forces and torques acting on the particles resulting from fluid motion, particle–particle collision, and adhesion under van der Waals forces are reviewed. The effect of various parameters of normal collision and adhesion of two particles are examined in detail. The method is then used to examine aggregate formation and particle clogging in pipe and channel flow.

Introduction

Fluid flows containing adhesive aerosol particles occur in a wide range of natural and engineering problems. Inhaled smoke particles with diameters ranging from 100 to 1000 nm can penetrate throughout the lungs, even down to the alveoli, leading to numerous respiratory diseases. Dust particle clogging is a cause of frequent system maintenance in many industrial systems. For instance, construction vehicles operating in dusty environments experience rapid dust clogging of the radiator and other heat exchangers associated with the vehicle cooling system, leading to the need for frequent vehicle down time. Dust fouling has long been a major maintenance concern for electronic equipment in general, where small dust particles adhering to electrical circuit boards can short out an electrical system. Similar concerns arise with MEMS systems, which are sensitive to small amounts of contamination and provide large surface area for dust adhesion. Ability to predict dust fouling is of particular importance for preparation for human and robotic exploration of dusty planets, such as Mars. Production of nanoparticles is of growing interest for various industrial applications, including use in anti-abrasion coatings, as fillers for advanced composite materials, and as coatings for advanced sensors, catalysts and battery electrodes. For flame-generated nanoparticle production processes in particular [28], processes such as particle transport, filtration, and dispersion all require an ability to predict aggregate formation in various fluid flows and its effect on the flow.

Computational models available for solution of flows with adhesive particles are quite varied in approach, but for the purposes of this introduction these models are divided into two general classes – population-based models and discrete-element models (DEM). Population-based models are typified by the Smoluchowski population balance equation [37], or later variants of this equation [6], [19], [44], which relates the rate of change of the number of aggregates of a certain size, n_i, to various effects that lead to generation or elimination of aggregates of size n_i, resulting from aggregate collision and breakup processes. Expressions for each of these source/sink terms are developed using either deterministic physical models [37] or statistical arguments, such as those based on extensions of kinetic theory to granular media [23]. Population balance approaches have been sufficiently refined to provide reasonably accurate prediction of aggregate size distribution in different types of flow fields, but they cannot yield predictions of the micromechanics and microstructure of the aggregates or of their interactions with each other and with immersed surfaces in the flow. Of particular interest are situations where the flow length scale may approach the aggregate size and situations where aggregates become attached to solid surfaces in the flow, such as a channel wall or a fiber. Both of these types of situations are common in microfluidic flows.

The second general approach for simulation of adhesive particle flows is discrete-element models (DEM), wherein the transport and interactions of each particle are computationally followed. Discrete-element models have been used extensively for large-size particles, where adhesion effects are negligible, as well as for nanoscale particles, in which the particle size is compatible with the adhesion length scales, so the molecular dynamics approach can be directly applied. In between these two extremes is found a regime involving particles with diameter d much larger than the adhesion length scale but still small enough to exhibit significant particle adhesion, which for dry aerosols corresponds roughly to 0.1 μm < d < 100 μm. Computational models for particles in this range exhibit high stiffness, due to the large difference between the several time scales involved in the problem, ranging from the fluid advection time at the upper end to the time associated with particle adhesion forces at the lower end. A second challenge for models of this sort is the necessity to include in the computational model a wide range of forces and torques acting on the particles, due to both fluid flow and to collision events. Among the latter include the elastic and dissipative normal forces and the resistance from particle sliding, twisting and rolling motions. Many of the collision forces and torques are significantly affected by the adhesive force. In development of discrete-element models for adhesive particles, both the physical and computational modeling issues must be accounted for in tandem, since in many cases models exist for these various forces which, while accurate, would not be computational feasible for large numbers of particles. At the same time, the interests of computational efficiency leads some studies of adhesive particle flows to neglect effects, such as rolling resistance, which play a critical role in the aggregate dynamics and breakup.

An early DEM study for adhesive particle flows is presented by Mikami et al. [30], who consider cohesive powders subject to liquid bridging force. Dominik and Tielens [13] present a DEM with van der Waals forces [42], which they use to examine impact of ice particles in space. Many of these previous DEM studies for adhesive particle flows report results only for two-dimensional flows and with relatively small number of particles, due in large part to the time step restriction caused by the stiffness of the governing equations for particle adhesion force. One option to partially circumvent the problem of a small time step was proposed by Weber et al. [43], who replace the van der Waals potential with a square-well potential and use a hard-sphere model for the particle collisions, in which particles collide both with their respective surfaces and with the outer surface of the cohesive energy well surrounding each particle. The minimum time step for this method is on the order of the time required for the particle surface to cross the thickness of the adhesive energy well.

The present paper presents a computational discrete-element model for efficient, physically-accurate evolution of particulate aerosol flows with micron-size particles. The model involves both physical and computational modeling components, which are developed to be true to the physics of collision- and fluid-induced forces and torques acting on the particles, while at the same time consistent with the demands of rapid computation for large numbers of particles. The method is presented for small particles immersed in a fluid flow subject to van der Waals adhesive forces, but it has been extended in on-going work for other adhesive forces, including liquid bridging and ligand-receptor bonding. Computationally efficient models for the various forces and torques on the particles due to fluid flow effects and to collision and adhesion with other particles are critically reviewed. The model is then applied to examine aggregate formation for pipe and channel flows subject to different conditions, with investigations focusing on the role of the channel walls on particle capture and the aggregate formation process.

The structure of the computational algorithm is described in Section 2. Fluid-particle coupling is described in Section 3. The particle forces and torques resulting from collisions are reviewed in Section 4, including normal impact force and resistance for sliding, twisting and rolling motions. Modifications to the collision forces and torques arising from van der Waals adhesion are discussed in Section 5. The behavior of the computational model is examined for two particle collisions in Section 6. The method is applied in Section 7 to examine the process of particle aggregate formation in pipe and channel flows. Conclusions are given in Section 8.