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CALCULATIONS IN
NANOTECHNOLOGYTASNEEM 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]=
2.Surface area moment mean D[3,2] (Sauter Mean Diameter):
D[3,2]=
3. Volume moment mean D[4, 3] (De Brouckere Mean Diameter)
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.
ZETA POTENTIAL
Zeta potential is a measure of the magnitude of the electrostatic or charge repulsion or attraction between particles in a liquid suspension.
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)
DLS
DCS
AFFFF
Fluid Particle Dynamics
Fluid dynamic mechanismF
→ Gravitational force
→ Buoyant force
→ Drag force
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.
Solving,
Laminar regime
Transition regime
Turbulent regime
Determination of flow regimeTo calculate appropriate range of the fluid-particle dynamic laws that apply.
K=
Laminar regime
Transition regime
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=
0.2222<W<1514; Intermediate’s law
1514< W; Newton’s law
Cunnigham correction factorAt 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
THE DEAD CAN DANCE TOO
• 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
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 is flux deposition number,
Single collection efficiency due to any flux force is
Gravity: When the only significant force acting on a particle is the gravity, then this mode of deposition is called sedimentation, or gravitational settling.
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
THANK YOU!