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Abstract
Although the fundamental concepts of fibrous filters are clearly understood for the capture of micron and submicron sized particles, basic questions arise when the particles to be captured are nanometer-sized. The purpose of this article is to compile an inventory of knowledge on the performance of fibrous media for capturing nanoparticles.
In the first part of this review, the classical theory of fibrous filters is described for media in general, with a focus on the principles that apply to nanoparticles filtration. The recent breakthroughs reviewed include theoretical and empirical models for single fiber efficiency. In the second part, we present the classical models of pressure drop for both clean and clogged flat fibrous media as applied to nanoparticles filtration. We also include an extensive discussion about pressure drop across a particle deposit (cake) during surface filtration. In the third part, the impact of several parameters such as air flow rate, humidity, particle shape and morphology, fibers diameter, heterogeneous fibers, electrostatic forces, upstream particle concentration and temperature are reviewed in detail.
Nomenclature
| a | = | Contact radius (m) |
| ag | = | Particle specific area (m− 1) |
| Cd | = | Gas slip correction factor for diffusion (−) |
| Cr | = | Gas slip correction factor for interception (−) |
| = | Correction factor to lower the efficiency for diffusion (−) | |
| Cc | = | Cunningham correction factor (−) |
| Co | = | Overlap parameter (−) |
| CT | = | Drag coefficient for a fiber (−) |
| CTm(l, t) | = | Drag coefficient for a fiber loaded with particles (−) |
| D | = | Diffusion coefficient (m2.s− 1) |
| Dn | = | Diffusion coefficient of neutral nanoparticles (m2.s− 1) |
| dp | = | Particle diameter (m) |
| dm | = | Particle mobility diameter (m) |
| dg | = | Gas molecule diameter (m) |
| = | Mean particle diameter (m) | |
| df | = | Fiber diameter (m) |
| dagg | = | Aggregated or agglomerated particle size (m) |
| dpG | = | Count median diameter (m) |
| dvg | = | Geometric mean size of the volume equivalent diameter (m) |
| deq | = | Pore diameter (m) |
| dfm(l, t) | = | Diameter of the fiber loaded with particles (m) |
| E | = | Electric field (V. m− 1) |
| E∑ | = | Total single fiber efficiency (−) |
| Em | = | Single fiber efficiency due to mechanical mechanism (−) |
| ED | = | Single fiber efficiency due to diffusion (−) |
| ER | = | Single fiber efficiency due to interception (−) |
| EDR | = | Single fiber efficiency due to interception of diffused particles (−) |
| EI | = | Single fiber efficiency due to impaction (−) |
| Ee | = | Single fiber efficiency due to electrostatic mechanism (−) |
| EIM | = | Single fiber efficiency due to image force (−) |
| EP | = | Single fiber efficiency due to polarization force (−) |
| EC | = | Single fiber efficiency due to columbic force (−) |
| e | = | Elementary charge (1.602 × 10− 19C) |
| F | = | Drag coefficient (−) |
| hk | = | Kozeny constant (−) |
| HFan | = | Hydrodynamic factor for the “fan” model (−) |
| HKu | = | Hydrodynamic factor according to Kuwabara (−) |
| HLa | = | Hydrodynamic factor according to Lamb (−) |
| k | = | media penetration factor (−) |
| Knf | = | Fiber Knudsen number (−) |
| Knp | = | Particle Knudsen number (−) |
| Kb | = | Boltzmann constant (1.381 × 10− 23 J. K− 1) |
| L | = | Medium thickness (m) |
| L* | = | Medium corrected thickness (m) |
| Lf′ | = | Total length of fibers per unit volume (m− 2) |
| Lp′ | = | Length of the chain of particles per unit volume (m− 2) |
| m | = | Particle mass (kg) |
| Mp | = | Molecular weight of nanoparticles (kg.mol− 1) |
| Mg | = | Molecular weight of carrier gas (kg.mol− 1) |
| N | = | Number concentration of gas molecules (#/m3) |
| n | = | Number of elementary charges (−) |
| Pe | = | Peclet number (−) |
| q | = | Charge carried by particle (C) |
| Qf | = | Quality factor (−) |
| R | = | Interception parameter (−) |
| Ref | = | Fiber Reynolds number (−) |
| T | = | Absolute temperature (K) |
| U0 | = | Face velocity (m. s− 1) |
| U | = | Flow velocity inside the medium (m. s− 1) |
| v | = | Velocity of gas molecule (m. s− 1) |
| = | Root mean square velocity of gas (m. s− 1) | |
| Zp | = | Electrical mobility of particle (m2.s− 1.V− 1) |
| αf | = | Packing density of medium (−) |
| αp | = | Packing density of collected particles (−) |
| αpc | = | Particle deposit (cake) packing density (−) |
| β | = | Size dependent parameter (−) |
| ϵ0 | = | Permittivity of vacuum (8.84 × 10− 12F.m− 1) |
| ϵp | = | Particle dielectric constant (−) |
| ϵf | = | Fiber dielectric constant (−) |
| µ | = | Air dynamic viscosity (Pa. s) |
| κ | = | Dynamic shape factor of particles (−) |
| η | = | Filtration efficiency (−) |
| λ | = | Mean free path of gas molecules (m) |
| λq | = | Linear charge of fiber (C. m− 1) |
| ρp | = | Particle density (kg. m− 3) |
| ν(αpc) | = | Void function (−) |
| σg | = | Geometric standard deviation of particle size distribution (−) |
| Ω | = | Filtration area (m2) |
| Δp | = | Pressure drop (Pa) |
| Δp0 | = | Pressure drop of clean medium (Pa) |