Deposition and Removal Particle Transport, Deposition and Removal Mass Diffusion Goodarz Ahmadi Department of Mechanical and Aeronautical Engineering Clarkson University Potsdam, NY 13699-5725

! Deposition Velocity, Diffusion Boundary Layer, Diffusion Force Outline ! Diffusivity ! Diffusion Equation ! Diffusion to a Wall ! Deposition Velocity, Diffusion Boundary Layer, Diffusion Force ! Diffusion to a Flat Plate ! Diffusion in Tube ! Taylor Diffusion

Brownian Diffusion and Fick's Law Diffusion Equation Diffusivity

Table of Particle Mass Diffusivity

Mean Square Displacement Particle Diffusion Mean Square Displacement Brownian Motion of Rotation Particle Fluctuation Energy Concentration in gravitational field

Effect of Particle Mass Particle Mean Free Path Particle Diffusion Effect of Particle Mass Particle Mean Free Path

Particle Diffusion to a Wall Similarity Variable

Particle Diffusion to a Wall Similarity Equation

Particle Diffusion to a Wall

Particle Diffusion to a Wall tD=0.0025 tD=0.062 tD=0.25 tD=1 tD=4 y Variation of concentration profile with time.

Particle Diffusion to a Wall Diffusion Boundary Layer Diffusion Velocity Diffusion Boundary Layer Diffusion Force

Number Deposited in Time dt Total Deposited in Time Interval (0,t) Particle Diffusion to a Wall Number Deposited in Time dt Total Deposited in Time Interval (0,t)

Tube Deposition

Tube Deposition Concentration Ratio Detailed Analysis

Tube Deposition

Convective Diffusion to a Flat Plate Uo Uo Co y  x c

Convective Diffusion to a Flat Plate Momentum Mass Concentration

Flat Plate - Similarity Variables Momentum/Mass Concentration Blasius Equation

Flat Plate - Similarity Variables Boundary Conditions Blasius Solution Near the Plate

Concentration Profile

Concentration Profile

Diffusion to a Flat Plate Diffusion Boundary Layer Total Diffusion

Diffusion in a Tube Flow c R y r z c Laminar Flow

Diffusion in a Tube Flow Diffusion Equation Similarity Variable Boundary Condition

Solution for Diffusion in a Tube Flow Concentration Profile Wall Flux

Solution for Diffusion in a Tube Flow Diffusion Boundary layer Total Flux Diffusion Boundary layer

Taylor Diffusion

Neglecting Axial Diffusion Taylor Diffusion Neglecting Axial Diffusion

Diffusion In Moving Frame Taylor Diffusion Moving Frame For Diffusion In Moving Frame Solution

Taylor Diffusion Concentration Total Flux

Effective (Taylor) Diffusivity Taylor Diffusion Flux Per Unit Area Effective (Taylor) Diffusivity Range of Validity

Taylor Diffusion

Taylor Diffusion Variations of concentration along the tube at different times.

! Mass diffusion decreases with size Summary ! Mass diffusion decreases with size ! Diffusion Boundary Layer is generally smaller that momentum boundary layer ! Convective diffusion in a tube ! Taylor diffusion in a tube

Thank you! Questions?