Transcript File

CALCULATIONS IN
NANOTECHNOLOGY
TASNEEM KAPADIA
60011115023
NANOTECHNOLOGY

Nanotechnology is the understanding and control of
matter at dimensions of roughly 1 to 100 nanometers.

This is the world of atoms, molecules, macromolecules,
quantum dots, and macromolecular assemblies.
Relationship between Nanoscience
and Quantum Mechanics
Particle size Distribution
Particle size influences many properties of
particulate materials and is a valuable indicator of
quality and performance. It determines:

appearance and gloss of paint

flavor of cocoa powder

reflectivity of highway paint

hydration rate & strength of cement

properties of die filling powder

absorption rates of pharmaceuticals

appearances of cosmetics
Particle size distribution

Number weighted distributions: Particle size
doesn’t matter only number of particles

Volume weighted distributions: The relative
contribution will be proportional to (size)3,
distribution represents the composition of the
sample in terms of its volume/mass, and therefore
its potential $ value.

Intensity weighted distributions: Dynamic light
scattering techniques will give the contribution of
each particle in the distribution relating to the
intensity of light scattered by the particle. For
example, using the Rayleigh approximation, the
relative contribution for very small particles will
be proportional to (size)6.
Mean, Median & Mode

mean – ‘average’ size of a population

median – size where 50% of the population is below/above

mode – size with highest frequency.
1.Number length mean D[1,0]:
D[1,0]= 𝐷𝑖 𝑣𝑖 /𝑁
2.Surface area moment mean D[3,2] (Sauter Mean Diameter):
D[3,2]=
3
𝑛
1 𝐷𝑖 𝑣𝑖 /
2
𝑛
1 𝐷𝑖 𝑣𝑖
3. Volume moment mean D[4, 3] (De Brouckere Mean Diameter)
ZETA POTENTIAL
Zeta potential is a measure of the magnitude of the electrostatic or charge
repulsion or attraction between particles in a liquid suspension.
It is one of the
fundamental parameters
known to affect dispersion
stability. Its measurement
brings detailed insight into
the causes of dispersion,
aggregation or flocculation,
and can be applied to
improve the formulation of
dispersions, emulsions and
suspensions.
Particle size measurement
methods

Dynamic Light Scattering (DLS)

Differential Centrifugal Sedimentation (DCS)

Transmission Electron Microscopy (TEM)

Scanning Electron Microscopy (SEM)

Asymmetric flow- field flow fractionation
(AFFF)

Particle Tracking Analysis (PTA)
DCS
DLS
AFFFF
Fluid Particle Dynamics
Fluid dynamic mechanism
F= 𝒎𝒑 𝒈;
→ Gravitational force
𝑭𝑮 =
𝝆𝑷 𝝅𝒅𝒑 𝟑 𝒈
𝟔
→ Buoyant force
𝑭𝑩 =
𝝆𝒂 𝝅𝒅𝒑 𝟑 𝒈
𝟔
→ Drag force
𝝆 𝒂 𝒗𝟐
𝑭𝑫 = (
)𝑨𝑷 𝑪𝑫
𝟐𝒈𝒄
𝑚 𝑑𝑣
𝐹𝑅 = 𝐹𝐺 − 𝐹𝐵 − 𝐹𝐷 =
𝑔𝑐 𝑑𝑡
Terminal Particle Settling Velocity

If particle is not accelerating, velocity must be constant.
This velocity where all the forces balance out, is called
terminal settling velocity.
𝑭𝑹 = 𝟎 &
Solving,



Laminar regime
Transition regime
Turbulent regime
𝑭𝑩 = 𝟎
𝑭𝑮 = 𝑭𝑫
𝒗𝒕 =
𝒗𝒕 =
𝒈𝝆𝒑 𝒅𝒑 𝟐
𝟏𝟖𝝁
𝟎.𝟏𝟓𝟑𝒈𝟎.𝟕𝟏 𝒅𝒑 𝟏.𝟏𝟒
𝝁𝟎.𝟒𝟑 𝒆𝟎.𝟐𝟗
𝒗𝒕 = 𝟏. 𝟕𝟒
𝒈𝒅𝒑 𝒆𝒑 𝟎.𝟓
(
)
𝒆
Determination of flow regime
To calculate 𝑣𝑡 , 𝑎 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝐾 𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒𝑠 𝑡ℎ𝑒 appropriate range
of the fluid-particle dynamic laws that apply.
K=𝑑𝑝 (
𝑔𝜌𝑝 𝜌 1
𝜇2
)3
→ 𝐾 < 3.3: 𝑆𝑡𝑜𝑘𝑒 ′ 𝑠 𝑙𝑎𝑤 𝑟𝑎𝑛𝑔𝑒: 𝑅𝑒 ≤ 2.2 → Laminar regime
→ 3.3 < 𝐾 < 43.6; 𝐼𝑛𝑡𝑒𝑟𝑚𝑒𝑑𝑖𝑎𝑡𝑒 𝑙𝑎𝑤 𝑟𝑎𝑛𝑔𝑒, 2 ≤ 𝑅𝑒 ≤ 500 → Transition regime
→ 43.6 < 𝑘 < 2360; 𝑁𝑒𝑤𝑡𝑜𝑛′ 𝑠 𝑙𝑎𝑤 𝑟𝑎𝑛𝑔𝑒, 𝑅𝑒 > 500 → Turbulent regime
Larocca and Theodore defined a dimensionless value W that would
enable one to calculate diameter of a particle if terminal velocity is known.
W= 𝑣 3 𝜌2 /𝑔𝜇𝜌𝑝
→ 𝑊 < 0.2222; 𝑆𝑡𝑜𝑘𝑒 ′ 𝑠 𝑙𝑎𝑤
→ 0.2222<W<1514; Intermediate’s law
→ 1514< W; Newton’s law
Cunnigham correction factor
At very low reynold numbers, when the particle size is comparable with the
mean free path of fluid molecules, the medium is no longer continuous. The
particles fall between the molecules at a faster rate than explained by
aerodynamics. To allow this slip, Cunningham introduced a factor to Stoke’s
equation,
Where, Cunningham correction factor
The modified stoke’s- Cunningham equation is
On further simplification with kinetic theory of gases:
Brownian Motion
• Particles suspended in a gas or liquid seem to
move around randomly as they are pushed to
and fro by collisions with the atoms that
comprise the gas or liquid.
• Brownian motion of a particle in the fluid is a
result of thermal fluctuations surrounding the
particle
Particle collection mechanism
The overall collection/removal process for particulates in a
fluid takes place in 4 steps:

Application of external force  velocity  directs of
retrieval section,

Retention at the retrieval area,

As particles get accumulated, they are subsequently
removed,

Ultimate disposition completes the process.
Particle collection mechanism
and efficiency
Brownian motion :
Diffusion occurs when smaller particles having Brownian motion hit
the surface of the fibers
Centrifugal force:
The shape of the collector
causes the gas to rotate. The
Heavier particles move
towards the wall and lose
kinetic energy and hence
Fall down and get separated.
The drift velocity, number of
Rotations and residence time
affects the efficiency.
Interception: Interception occurs
when particles do not depart from
the streamlines. The inertia or
Brownian motion of particles is
negligible. Particles following
streamlines arrive at the fibers and
get "intercepted" on the fiber
surface.
Interception parameter NR=Dp (particle diameter)/Df (fiber diameter)
Inertia impaction: This occurs when
particles cannot adjust to the "sudden"
change of streamlines near fibers, and,
due to inertia, depart from the streamlines
and impact on the fiber surface.
Inertia impaction parameter, Ni= C
𝑑𝑝 2 𝑣𝜌𝑝
18𝜇𝑑𝑐
Thermophoretic and diffusiophoretics forces:
These are classified as flux forces because they are dependent
on temperature and concentration gradients respectively. the
thermal and diffusiophoretic forces, acting on a body suspended
in a gas not in equilibrium, originates from interaction of gas
molecules with solid surface.

Thermal: moves from hot to cold

Diffusiophoretics: moves in the direction of heavier partices
in the fluid

The gas solid interaction is defined by ‘Ratio of mean free
path length to particle radius’ called Knudsen number Kn.

Ratio 𝑁𝐹𝐷 is flux deposition number,

Single collection efficiency due to any flux force is
η = 4𝑁𝐹𝐷
Electrostatic attraction:
The charged particles are
subjected to a strong electrical
field to overcome the drag force
of the fluid. Combined effect of
direct impaction, interception
and electrostatic attraction.
Electrostatic force, Fe=q Ep,
where, q:particle charge
Ep: collection field intensity
Gravity: When the only significant
force acting on a particle is the
gravity, then this mode of deposition
is called sedimentation, or
gravitational settling.
THANK YOU!