Ch. E and Biomolecular E.Kyu Hyun

ž Maxwell theory (Kinetic theory of gas)

d

Rigid, nonattracting spherical molecules

Diameter=dMass=m

ž Average molecular velocity

ž The frequency of molecular bombardment per unit area

ž Mean free path (the average distance traveled by a molecule between successive collisions)

ž Collision distance : given very roughly by

ž Combining (1.4-2), (1.4-6) and (1.4-5)

ž Combining (1.1-2) and (1.4-7)

ž Combining (1.4-1), (1-4-3) and (1.4-8)

d

d

∝

It is necessary to replace the rigid-sphere model by one that portrays the attractive and repulsive forces more accurately

ž Chapman-Enskog Theory (Lennard-Jones Potential) ž Pure monatomic gases

612 rB

rArVLJ -=)(

Lenard-Jones diameter of the spherical molecule, larger than real diameterLenard-Jones diameter of the spherical molecule, larger than real diameter

collision integral : Rigid molecules=1collision integral : Rigid molecules=1

ž Lenard Jones Potential : the attractive and repulsive forces

ž Chapman-Enskog Theory (Lennard-Jones Potential) ž Pure monatomic gases

ž Gas Mixture

ž Eyring and coworkers (vs. Kirkwood and coworker) : less well grounded theoretically

Energy barrier of height

Nonlinear relationship= non-Newtoninan flow

What happen to viscosity when solid particle added?

ž Einstein equation for dilute suspension:

ž Monney equation for concentrated suspensions (1)

ž Graham equation for concentrated suspensions (2)

Depending on the particular shape

ž Krieger-Dougherty equation (concentrated suspension of nonshperical particles):

ž Taylor equation for emulsions or suspensions of tiny droplets:

ž Smoluchowski equation for dilute suspensions of charged droplets

ž The mean translational energy per molecule under equilibrium

ž The molar heat capacity at constant volume

ž The heat flux across any plane of constant y

ž The heat flux

ž Thermal conductivity

ž Thermal conductivity of a dilute gas

Maxwell equation=Viscosity of monatomic gas∝and

ž Chapman-Enskog Theory

ž Eucken formula for Polyatomic Gas (semiempirical)¡ Vibrational and rotational energy

ž Example 9.3-1

ž Example 9.3-2

ž Bridgeman’s Equation

ž The calculation of the sonic velocity

“revised by experiment”

ž In crystalline materials¡ The phase and crystallite size are important

ž In amorphous solids¡ The degree of molecular orientation

ž In porous solids¡ The void fraction, the pore size, the fluid contained in the

pores

ž Metal > Nonmetal, Crystalline > Amorphousè Depending on Orientation!!

ž Dry porous solids are very poor heat conductorè”Excellent” for thermal insulation

ž Thermal and electrical conductivity go hand in hand (the rules of thumb)

ž Low-k materials (nanoporous)

l Pure solids è Homogeneous

l Composite solids è Heterogeneous è

The Stefan–Boltzmann law, also known as Stefan's law, states that the total energy radiated per unit surface area of a black body in unit time

Diffusion from a microscopic and macroscopic point of view. Initially, there are solute molecules on the left side of a barrier (purple line) and none on the right. The barrier is removed, and the solute diffuses to fill the whole container. Top: A single molecule moves around randomly.Middle: With more molecules, there is a clear trend where the solute fills the container more and more evenly. Bottom: With an enormous number of solute molecules, the randomness is gone: The solute appears to move smoothly and systematically from high-concentration areas to low-concentration areas, following Fick's laws.

ž Gas containing molecular species A and A*ž The net mass flux of species A crossing a unit area

ž The combined mass flux (=convective + molecular mass flux)

ž Formula for two different species A and B

ž The Chapman-Enskog kinetic theory

ž The Schmidt number

ž The kinetic theory for diffusion in simple liquids is not as well developed as that for dilute gases.

ž The hydrodynamic theory¡ The diffusivity of a single particle or solute molecule A

through a stationary medium B

ž The Eyring activated-state theory

ž Because of the unsatisfactory nature of the theory for diffusion in liquids

ž Wilke-Chang equation (empirical equation)

ž When the spheres of A are sufficiently small, the collisions between the spheres and the molecules of B will result in an erratic motion.

è Brownian motionž Langevin equation

Stoke’s law drag force

Irregular Brownian motion

ž Langevin equation

probability

probability

ž Dilute solution of a polymer A in a solvent B¡ The polymer molecules are modeled as bead-spring

ž Self diffusion in an undiluted polymer

With hydrodynamic interaction

Without hydrodynamic interaction

Rigid bead

Hookean spring