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# 3. The Motion of Particles Drag force d particle diameter V flow velocity Spherical particle, Re < 1 Drag coefficient A projected area.

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3. The Motion of Particles Drag force d particle diameter V flow velocity Spherical particle, Re < 1 Drag coefficient A projected area

Case 1: With slip is Cunningham correction factor For d > 0.1  m For d > 0.01  m

Case 2: High Re, Re > 1

Case 3: Nonspherical particle is shape factor is equivalent volume diameter Shape/type spherical fiber (L/d = 4) quartz dust fused alumina talcum (platelet) 1 1.32 (axis perpendicular to flow) 1.07 (axis parallel to flow) 1.36 1.04-1.49 2.04

Motion under gravity

Equation of motion Particle relaxation time or time constant Terminal settling velocity

Mechanical mobility Terminal settling velocity with slip, shape factor

Motion under electrical forces q particle charge n number of charge e electron charge = 1.6x10 -19 C E electric field

In equilibrium Terminal electrical velocity Electrical mobility

Relation between V TE and E for two particle sizes

Motion under thermal gradients Thermophoretic force -> Temperature gradient Thermophoretic velocity

Motion under no external force Equation of motion Velocity Traveling distance

Stopping distance, t >> 

Similarity in particle motion 1. Reynolds number (Re) must be equal With slip 2. Stokes number (Stk) must be equal

Particle motion for several values of Stokes number

3. When gravity is important, gravitational parameter (G) must be equal To determine if inertia or gravity is more important, use Froude number (Fr)

Aerodynamic diameter Aerodynamic diameter (d a ) is the diameter of a spherical particle of density  0 = 1 g/cm 3 which has the same terminal settling velocity in air as the particle of interest. Stokes diameter (d s ) is the diameter of a spherical particle that has the same density and terminal settling velocity in air as the particle of interest. is the bulk density

Comparison of equivalent volume diameter, Stokes diameter, and aerodynamic diameter.

Inertial impaction Stokes number is the jet diameter

Collection efficiency characteristics of an impactor

Collection efficiency characteristics of an impactor: Ideal -v- real

Diffusion (Brownian motion) Random motion of an aerosol particle in still air is the particle flux (# particles per unit area per unit time) is the diffusion coefficient is the number of particles is the direction of motion Fick’s first law Stokes-Einstein derivation

RMS and average velocity

Diffusion-related properties of standard-density spheres at 293 K

Deposition by diffusion Fick’s second law Aerosol particle collides and sticks to the surface Boundary and initial conditions

Solution Concentration profile for a stagnant aerosol of 0.05-mm particles near a wall

General form of the concentration profile near a wall

Cumulative number of particle deposited per unit area during time t Deposition velocity: velocity that particles move to a surface and is analogous to the terminal settling velocity due to gravity.

Cumulative deposition of particles on a horizontal surface during 100 sec.

Diffusion of aerosol particles on the tube wall Penetration for circular tube Deposition parameter is the length of the tube is the diameter of the tube is the average velocity is the flow rate

Peclet number: another dimensionless parameter used in diffusion motion is the characteristic length Penetration for rectangular tube

Penetration of aerosol particles in a tube.

Fractional loss to the walls by diffusion for an aerosol flowing through a 1-m-long tube

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