This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: x C D J ∂ ∂- = Dt x rms 2 = Diffusion is defined as the movement of solute molecules from a higher to A lower concentration gradient Occurs by a “ random walk ” mechanism in which molecules are continually colliding with each other while moving “on average” towards a particular direction Brownie in motion – “ random walk ” – random movement of a molecule by its energy state – molecules colliding with each other And gradually diffuse out as it goes on The diffusive flux, mass per unit time of solute movement Where dC/dx is the concentration gradient in the direction of solute movement And D is the constant of proportionality and is defined as the Diffusion constant or Diffusion coefficient root mean square displacement; X is the distance (length) Diffusion constant depends on what the solute is, where it is (liquid, water, oil) A property of the solute, but depends on what the solute is Depends on temperature Diffusion prop. To energy you give it Provide heat energy, collides more, moves more Negative sign in front? By convention, if movement is high to low, direction of solute movement, the concentration decreases You use microscopy techniques to follow its random movement over time. If diffusion coeff. Is high -> diffuse much more distance If diffusion coeff. Is low diffuse much less Flux proportional to conc. Gradient It is a steady state condition. You let it sit for a long period of time, and you see what it looks like. Doesn’t give you a time dependent flux. Not dependent on time. A flux is coming in (3), each flux you are dividing it by the x, y, and z directions respectively. z y x t C a y x J J z x J J z y J J z z z y y y x x x ∆ ∆ ∆ ∂ ∂ = + ∆ ∆-- ∆ ∆-- ∆ ∆-- ∆ + ∆ + ∆ + ) ( ] [ ] [ ] [ ψ ..(2) .......... ) ( t C a z J y J x J z y x ∂ ∂ = + ∂ ∂- ∂ ∂- ∂ ∂- ψ .(3) .......... ) ( ] [ 2 2 2 2 2 2 t C a z C y C x C D ∂ ∂ = + ∂ ∂...
View Full Document
This note was uploaded on 02/01/2011 for the course BME 314 taught by Professor Frey during the Spring '08 term at University of Texas.
- Spring '08