2. Dynamics of a particle
For dealing with the dust control in mines
a thorough understanding and utilization of
the dynamic properties of fine particles is
necessary.
2
3. • Other physical properties of dust such as
optical, electrical etc. are also
utilized for sampling, separation etc
3
4. • Small particles have a relatively high
surface area per unit mass.
• Let us consider a cube of 1 cm
• Surface area would be 6 cm2
• If the 1 cm cube is crushed to particles of
micro meter cube size, there will be 1012
particles with a total surface area of 6 m2
.
4
5. • For the motion of small particles due to the
large surface area, there is a greater
viscous resistance in air as compared to
larger ones.
5
6. • A small particle falling in the gravitational field of
the earth will be opposed by the viscous
resistance of air.
viscous resistance increases with increasing
velocity of the particle until the particle has no
acceleration.
• when viscous resistance of air balances the
gravitational force the particle falls at a constant
velocity called the terminal settling velocity.
6
7. • The terminal velocity of fine particles is
very small being of the order of
centimeters or even millimeters per hour
and that is why particles of fine dust, when
once air-borne, remain in suspension for a
long time.
7
8. Where R=Resistance
ρa = Density
A= Projected area of the particle
v= velocity of the particle relative
to the air
CD = drag coefficient
8
9. • Newton derived the general equation for the resistance
force on a sphere moving through a gas.
• theorized that a sphere must push aside a volume of gas
equal to the projected area of the sphere times its
velocity.
• The general form of Newton's resistance equation is:
• FD=CDII PA D2 V2 FD= CD
8
• where FD is the drag force on the sphere ,CD is the
drag coefficient, and V is the relative velocity between
the gas and the sphere.
9
10. • This equation is valid for all subsonic particle motion,
from cannon balls to aerosol particles (or for instance,
apples...assuming they're spherical).
• CD is not constant, but varies with the Reynolds number
and the shape of the particle.
(Reynolds number is a dimensionless parameter that
represents the ratio of viscous to inertial forces in a
fluid)
For values of Re (Reynolds number) greater than 103
(up to a maximum limit of 2.5 X 105 )
• CD is reasonably constant and has an average value of
0.44 for spheres.
10
11. This is the regime of turbulent motion where the resistance
is proportional to the square of the velocity and the
equation for viscous resistance can be written as
Where D - diameter of
the particle.
And
ρa – density of air
11
13. • For Re <3.0,
• CD can be taken to vary inversely with Re
given by the equation
CD = 24/ Re for spherical particles.
or R = 3πµD v
• This equation developed by Stokes holds
good for stream line flow where the
resistance varies directly as velocity
13
14. • But in case of turbulenmt motionthe
resistance is governed by air density and
is independent of viscosity.
• For intermediate values of Re, the
resistance depends ion both viscosity and
density of air.
• Here CD is a complex function of Re and is
given by the approximate relation
CD= 14/Re
1/2 For which
R = 5.5ρa1/2μ1/2D1/2v1/2.
14
15. 17
Terminal Settling Velocities
• A falling particle attains the terminal
velocity when the gravitational force
balances the air resistance.
15
16. • The forces acting on an aerosol particle in
still air are
• Gravitational Force, W
• Buoyancy Force,
• Drag Force,
16
17. Bouyancy Force19
• The bouyant force exerted on a floating
body is equal to the weight of the fluid
displaced by the body.
17
19. • Gravitational Force
• The weight of a spherical particle of
diameter d is expressed as
• W= πd3ρġ/6
• where p is the density of the particle and
g is the acceleration due to gravity.
19
20. • Bouyancy Force
• According to Archimedes' Buoyancy Principle,
the buoyant force exerted on a floating body is
equal to the weight of the fluid displaced by the
body.
• The Buoyancy Force exerted on a spherical
particle is:
• F= πd3ρġ/6
• Where ρ is the gas density.
20
21. • The forces acting on an aerosol particle in still air are:
• Gravitational Force, W
• Bouyancy Force,
• Drag Force,
21
