3. The Motion of Particles. Drag force. Spherical particle, Re < 1. d particle diameter V flow velocity. Drag coefficient. A projected area. Case 1: With slip. is Cunningham correction factor. For d > 0.1 m m. For d > 0.01 m m. Case 2: High Re, Re > 1.
3. The Motion of Particles Drag force Spherical particle, Re < 1 d particle diameter V flow velocity Drag coefficient A projected area
Case 1: With slip is Cunningham correction factor For d > 0.1 mm For d > 0.01 mm
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
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
Motion under thermal gradients Thermophoretic force -> Temperature gradient Thermophoretic velocity
Motion under no external force Equation of motion Velocity Traveling distance
Similarity in particle motion 1. Reynolds number (Re) must be equal 2. Stokes number (Stk) must be equal With slip
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 (da) is the diameter of a spherical particle of density r0 = 1 g/cm3 which has the same terminal settling velocity in air as the particle of interest. Stokes diameter (ds) 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
Diffusion (Brownian motion) Random motion of an aerosol particle in still air Fick’s first law 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 Stokes-Einstein derivation
Deposition by diffusion Aerosol particle collides and sticks to the surface Fick’s second law Boundary and initial conditions
Solution Concentration profile for a stagnant aerosol of 0.05-mm particles 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
Penetration for rectangular tube Peclet number: another dimensionless parameter used in diffusion motion is the characteristic length
Fractional loss to the walls by diffusion for an aerosol flowing through a 1-m-long tube