Dust in mines dynamics of a particle-

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.

3. 2
• Other physical properties of dust such as
optical, electrical etc. are also
utilized for sampling, separation etc

4. 3
• Small particles have a relatively high
surface area per unit mass.
• If a centimeter cube of quartz is crushed
to particles of micro meter cube size,
there will be 1012 particles with a total
surface area of 6 m2
• compared to only 6 cm2 surface area of
the original cube.

5. 4
• 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.

6. 5
• 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.

7. 6
• The terminal velocity of fine particles is
very small being if 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.

8. 7

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10. 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
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.
• This equation is valid for all subsonic particle motion, from cannon
balls to aerosol particles (or for instance, apples...assuming they're
spherical).

11. 10
• 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.

12. 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

13. 12
WherehD - diameter of
the particle.
and
Pa – density of air

14. 13

15. 13
• For Re <3.0, CD can be taken to vary
inversely with Re given by the equation
CD = 24/ Re for spherical particles.
R=24µ Π

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18. 17
Terminal Settling Velocities
• As has been said earlier, a falling particle
attains the terminal velocity when the
gravitational force balances the air
resistance.

19. 18
• The forces acting on an aerosol particle in
still air are
• Gravitational Force, W
• Bouyancy Force,
• Drag Force,

20. Bouyancy Force19
• The bouyant force exerted on a floating
body is equal to the weight of the fluid
displaced by the body.

21. 20

22. 21
• Gravitational Force
• The weight of a spherical particle of
diameter d is expressed as
• where p is the density of the particle and
g is the acceleration due to gravity.

23. 22
• Bouyancy Force
• According to Archimedes' Bouyancy Principle,
• the bouyant force exerted on a floating body is
equal to the weight of the fluid displaced by the
body.
• The Bouyancy Force exerted on a spherical
particle is:
• F= Π D3 *ρg ÷ 6
• Where ρ is the gas density.

24. 23
• The forces acting on an aerosol particle in still air are:
• Gravitational Force, W
• Bouyancy Force,
• Drag Force,

25. 24

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