Active and Passive States of Stress
Active State
Passive State
Experimental and Theoretical average
Vertical Stresses during silo discharge:
comparison of measured (points) and
calculated (lines) values [after Shamlou,
1990 and Walker, 1966].
Liquid: Pre

2. Powder Statics: Exact stress analysis
We consider the powder to be a continuum with
constant and homogeneous properties. The field
equations that characterize such a continuum are:
a. Conservation of mass
b. Conservation of momentum
c. Conservation of

Part II : Continuum Powder Mechanics
1. Powder Statics - Introduction
1. Definition of stress and strain.
L0
x
Consider the specimen of
area, A, pulled by a force, F,
in the , x, direction. The
stress is defined as:
A
F
= F/A
If under the action of the
f

3. Theoretical Models of Powder Beds.
1. The Granular and the Capillary views
Imagine a pack (pile) of powder in a tube between two
screens:
One can picture the
powder particles (or
grains) as making up
the pile so that they
touch
at
distinct
points and

9. Application: Analysis of particle size, size distribution
and shape using computer imaging
Gain-control and camera system is added to a PC.
Gain Control
Unit: Dage -MTI
RC300
CCD CAMERA
Dage -MTI
CCD300 B&W
Computer
Software:
LENS
Matrox Inspector
Part

Application: The minimum fluidization velocity of a
Fluidized bed.
Consider a packed bed of particles of diameter, dp,
situated in a tube of area, A, with gas flowing upward.
We increase gas flow from zero to the point when all
particles are suspended in

5. Yield function and the Plastic potential
The yield function is a more rigorous, mathematical way
to express the yield condition. It is denoted by, Y, and
takes the form:
Y=0
where Y = - tan or Y = q p sin , for a cohesionless Coulomb powder or Y = - ta

12. Mass flow Funnel flow in a Hopper
Industrial practice with flow in a hopper shows the
existence of two distinctive regimes of flow depending
largely on the half-angle, of the hopper:
Mass-flow characterized by a uniform, radial-like
flow that acceler

2. Powder Dynamics
1. Regimes of Powder Flow
There are several different regimes of powder flow,
presented here in order of increasing shear rate:
a. Quasi-static
b. Slow or so-called frictional
c. Intermediate
d. Rapid-Granular
a. It is assumed that the

2. Packings of Particle and their Properties
1. Porosity or Void Fraction, ().
Porosity or void fraction of a pack of powder is defined as
the ratio of volume occupied by void (in most cases
interstitial gas) to the total (bulk) volume of the powder.
vB

Powder Science
and Technology
an undergraduate graduate course
by
Gabriel I. Tardos
Department of Chemical Engineering
The City College of
The City University of New York
Convent Ave at 140 Street
New York NY 10036
1
Course Content
Part: I. Fundamentals o

Powder Science
and Technology
an undergraduate graduate course
by
Gabriel I. Tardos
Department of Chemical Engineering
The City College of
The City University of New York
Convent Ave at 140 Street
New York NY 10036
1
Course Content
Part: I. Fundamentals o

DEPARTMENT OF CHEMICAL ENGINEERING
ChE 45200
Open Book !
1.5 Hours
December 21, 2004
Final Examination
Answer all Questions
1. Calculate the minimum fluidization velocity u mf of a bed of identical
spherical particle with diameter 500 micrometers at a por

DEPARTMENT OF CHEMICAL ENGINEERING
ChE 452/5752
December 18, 2002
Examination
Open Book !
1.5 Hours
Answer all Questions
=
1. Calculate the free fall velocity, uT of a spherical particle with diameter
500 micrometers in air. Take the particle density as 2