Properties of nanoparticles affecting simulation of fibrous gas filter performance

Computational Fluid Dynamics (CFD) codes allow detailed simulation of the flow of gases through fibrous filter media. When the pattern of gas flow between fibers has been established, simulated particles of any desired size can be “injected” into the entering gas stream, and their paths under the influence of aerodynamic drag, Brownian motion and electrostatic forces tracked. Particles either collide with a fiber, or pass through the entire filter medium. They may bounce off the fiber surface, or adhere firmly to the surface or to particles previously captured. Simulated injection of many particles at random locations in the entering stream allows the average probability of capture to be calculated. Many particle properties must be available as parameters for the equations defining the forces on particles in the gas stream, at the moment of contact with a fiber, and after contact. Accurate values for all properties are needed, not only for predicting particle capture in actual service, but also to validate models for media geometries and computational procedures used in CFD. We present a survey of existing literature on the properties influencing nanoparticle dynamics and adhesion.


Introduction
The immense growth of nanotechnology in recent years means that nanoparticles will appear in industrial and research locations at levels which demand careful air pollution control. Vehicular exhausts pollute the air in cities and along highways with unacceptable aerosol concentrations, including nanoparticles. It is important to understand and quantify the details of nanoparticle by fibrous filters, to promote the development of effective, reliable and minimum-cost solutions to nanoparticle filter systems design.
The authors have previously discussed the effect of nanofiber additions to air filter media [1]. The present paper is concerned with the physical properties of nanoparticles which affect their capture and build-up in fibrous air filters, regardless of the characteristics of the fibers in the filter media.
Several studies found in our literature review had a recurring theme: the behavior of instruments based on "classic" concepts cannot necessarily be extended to aerosol particles with low-nanometer sizes. Flow patterns in differential mobility analyzers that appear unimportant for micrometer-sized particles may affect results for nanoparticles. Particle-charge neutralization in bipolar ion fields are not described by the same expressions for nanoparticles as for larger particles. Particle count devices may have very different count efficiencies for particle sizes above and below 100 nm. Agglomeration of fundamental nanoparticles can confuse results. Several studies have taken a somewhat different approach to establishing the fractal dimension and fractal prefactor of aggregates. Assuming or calculating the size and size distribution of primary particles, and fractal dimension and fractal prefactor values, they generate large numbers of images of aggregates. Various models of the agglomeration physics are possible. These simulated images frequently match the appearance of TEM or SEM images of the agglomerates studied quite well, indicating that the parameter choices were appropriate.

Nanop Propertie
[8] and [9] discuss ways in which the agreement between simulations and measurements can be quantified, and in particular, the best means to obtain reliable fractal descriptions of 3D agglomerates from 2D images.

Size distributions of nanoparticles
Many studies have shown that primary nanoparticles can exist as essentially uniform particles. More often, however, the size distributions are log-normal. The same mathematical relationships and graphical representations that are used with micrometer-scale particles apply to distributions at nanometer scale. Simple particle forms have a characteristic dimension, which for a cloud of particles can have a size-dependent distribution. Sodium chloride particles, for example are frequently cubical, characterized by the length of a side; cylindrical particles can have size distributions for both diameter and length. Agglomerates can have wide size ranges, but no easily defined size, hence no easily specified size. What can be defined and measured for agglomerates are their mobilities, aerodynamic, diffusive and electrical. Mobility is defined as: [particle velocity relative to local gas velocity] / [force on particle].
The term [force on particle] is different for aerodynamic, diffusive, and electrical mobility. These three forces and means for measuring them are discussed in sections below. Because agglomerates have no definable size, their size distributions are often stated in terms of some "equivalent mobility diameter", dependent on the method used to obtain the distribution. An alternative "size" is some measurable geometric value, obtained from SEM images. One example of SEM-measured size is the determination of the smallest rectangle able to enclose the particle. Image-analysis software packages, both commercial and open-source, are available to measure such dimensions more or less automatically, and characterize the distributions of them.

Aerodynamic drag of nanoparticles
The aerodynamic drag F drag of a sphere with low Reynolds number moving in a gas stream is given by Stokes law with the Cunningham correction: Where µ = gas dynamic viscosity; d p = sphere diameter; u g = gas velocity; u p = particle velocity; m p = particle mass; and C c = Cunningham's correction for slip at the particle surface, a function of gas type, temperature and pressure. With λ = gas mean-free-path and Knudsen Number defined as "neutral" aerosol cloud is not charge-free; each individual particle in the cloud carries some number of elementary charges, ranging from zero to N elementary charges, either positive or negative. For an aged aerosol, the Boltzmann equilibrium distribution will be approached. Aerosols freshly generated in the laboratory are passed through clouds of mixed positive and negative ions to reach equilibrium quickly. The ion-production devices of such neutralizers can depend on radioactive sources (Kr-85 or Po-210), soft X-rays, or high-voltage corona discharge to produce the bipolar ion clouds needed. Covert, Wiedensohler and Russell [26] critique neutralizing devices. Like so many things in aerosol experimentation, care in choosing a neutralizer adequate for the conditions of an experiment is essential.
Fuchs [27] developed the basic form of the distribution of charges on aerosols exposed to a balanced bipolar ion cloud (one with equal numbers of positive and negative ions). Hoppel and Frick [28] extended the analysis to nanometer-size particles, and provided plots of the Boltzmann equilibrium distribution of charge on particles with radii 1 nm to 4µm. Stommel and Riebel [29] found errors in these earlier works, and provide corrections. The limited results of their corrections deviate slightly from the plot from Hoppel and Frick (figure 4).

Evaporation of liquid nanoparticles
The literature on nanoparticle evaporation is chiefly related to high-temperature evaporation of metal particles. Li and Davis [30] conducted experiments on evaporation of dibutyl-phthalate particle evaporation in air at pressures decreasing from 13.7 kPa to 0.016 kPa. Their results are expressed as evaporation rates as a function of Knudsen Number, so may be applicable to nanoparticles at normal pressures. Their experimental conditions involved values of Kn as high as 2. Sutter et.al. [31] studied the evaporation of n-hexadecane particles with mass-mean diameters as small as 1.5 µm actually on filter fibers. Evaporation rates were substantially lower than predicted by traditional mass-transfer theory (Fick's Law). The mass of nanoparticle aerosols is very small, so evaporation may not result in appreciable health hazards.

Counting of nanoparticles for filtration studies
Light-scattering aerosol spectrometers, widely used for counting particles of micrometer dimensions, have lower detection limits of about 90 nm, hence limited application in nanoparticle studies. Nanoparticles can be examined by a transmission electron microscope (TEM) or scanning electron microscope (SEM), and the number of particles counted. Nuclear track-etched polycarbonate membrane filters provide a relatively featureless image background, allowing some automation of the counting process when SEM images are obtained. Preparation of nanoparticle samples for these imaging processes is more difficult than for light microscopy; the samples must be given a thin conductive coating, usually of a gold/palladium alloy, in an ion sputtering device.
Image-analysis computer programs are available to assist the particle counting process, including an open-source one (fraclac, an add-on for imagej). Electron microscope imaging is essentially the reference method for evaluating all other devices used to study aerosol particle geometry. It avoids the assumptions about particle charging, aerodynamic drag and diffusion effects necessary for interpreting the results of data from instruments such as the MOUDI, ELPI, DMA, SMPS, and APM.
The usual device for nanoparticle counting in gas flows is the condensation particle counter (CPC), which increases the size of individual particles by condensing a vapor onto them, then counting the enlarged particles by light-scattering. While the counting efficiency of a CPC is not 100% for all size particles, the efficiency values are reasonably stable and predictable, and useful counts can be obtained for particles below 10 nm diameter. The accuracy of results decreases as the size detected decreases.
Particle capture efficiency measurements for filter media require simultaneous upstream and downstream sampling, or very stable aerosol generation. In addition, it is essential that the sampling systems upstream and downstream, and the two flow rates, be as nearly identical as possible, so that particle losses in the two sampling systems are the same.