1. Transformations
    Chemical or biological modifications that influence the composition of a system or structure of a molecule
  2. Transport
    the physical displacement (or movement) of a chemical/ biological species over characteristic distances and timescales
  3. fate
    fate= transport (movement) +transformation (reactions)
  4. Advection
    • Fluid acts as a carrier for the material dissolved (molecules) or superspended (particles) in it
    • Def: the transport of material caused by the net flow of the fluid in which a material is suspended (particles) or dissolved (molecules)

    • Formulas:Concentration*Volume/ area *time
    • or concentration*distance traveled*area/ area* distance traveled/ velocity
    • which is concentration*velocity. 
  5. overall flux
    the sum of the advective, diffusive, and dispersive movements.

    units: mass (or Mol)/ area*time
  6. Diffusion
    • molecular diffusion:
    • The net movement of material from a region of high concentration to a region of low concentration caused by the random motion of material

    • Influenced by
    • 1.) Temperature
    • 2.) size
    • 3.) median (^ density, then lower diffusivities)
  7. Osmosis
    Diffusion of water (only) -water molecules move up salt gradients and down water gradients
  8. Ficks law
    Jdiffusivityis proportional to - change in concentration gradient/ change in distance

    Jdiff= -D (dc/dx)

    diffusivity is chemical dependent
  9. Characteristic distance
    Image Upload 1

    the distance, x, a molecule or particle will travel in a time t
  10. Diffusion/ Brownian motion
    • 1.) results from random motion of the particle and collions with other particles
    • 2.) movement from high to low concentrations
    • 3.) much slower than molecular diffusion because particles are larger relative to molecules
    • 4.) Fick's law applies, but d is more complex
  11. Cc
    the cunningham slip correction factor
  12. Stoakes Einstein Relation
    D=K*T/F   where K is the boltzman constant, f is the friction coefficient and T is the temp in Kelvin

    F= 3*pie*fluid viscosity*particle diameter/ Cc
  13. diffusion occurs faster in?
    air than water
  14. How does transfer occur at boundries
    Through diffusion b/c advective velocities approach zero at those interfaces
  15. k
    • km 
    • k is the mass transfer coefficient
  16. If Jboundary < 0
    then Cboundary > Cbulk and flux is from boundary to bulk fluid
  17. If Jboundary >0
    Cboundary< Cbulk   and flux is from bulk fluid to boundary
  18. Diffusion through a stagnant layer
    • If Jbound= km (Cbulk-Cbound)= -Jdiff
    • then km= D/L   where D is diffusivity and L is the boundary layer thickness

    JdiffImage Upload 2
  19. Diffusion through  settling particles that stick to the interface
    • Cbulk=C
    • Cbound =0
    • Jg= velocity* (Cbulk-Cbound ) = velocity * C
    • therefore k= velocity
  20. penetration theory
    accounts for the temporal varience in the concentration gradient as material is lost to the medium

    Use when contact time b/w the boundary layer and the bulk fluid is less than t=L2/ 20  (ie the time when constant concentration gradient has not yet been established)

    • a time dependent process
    • km=(D/pie*t)1/2   instantaneous K

    km= 2 (D/pie*t2-t1)1/2   Averaged km where t2-t1 is the time interval of interest
  21. film theory
    a time dependent process
  22. Boundary layer Theory
    • 1.) accounts for advection and diffusion 
    • 2.) in reality, both adv and diffusion happen simulataneously 
    • advection dominates far from boundary layer
    • diffusion dominates close to boundary layer

    km= 0.323(u/x)1/2*v-1/6D2/3   at a position x, where u is fluid velocity, x=position, D=diffusivity, v= dynamic fluid viscosity/fluid density

    • Boundary layer averaged over length L
    • km=0.646 (u/L)1/2 *v-1/6*D2/3
  23. porosity
    • porosity= pore volume/ total volumeImage Upload 3 porosity of air
    • Image Upload 4
  24. Density
    solids density, ps= mass solids/ volume of solids

    bulk density, pb= mass solids/ total volume

    pb=ps(1- Image Upload 5)
  25. hydraulic conductivity

    • the stuff that is resisting the flow in the tube
    • it is measured in Length/time
    • it is constant for a particular soil/sand
    • depends on the sand pore size/ grain size
    • Image Upload 6Image Upload 7
  26. Darcy's Law
    Image Upload 8 where K is hydraulic conductivity and A is area and Q is flow
  27. velocity
    Image Upload 9
  28. Find velocity in a water saturated porous media
    Image Upload 10  where U= linear velocity, K=hydraulic conductivity and dh/dl is change in height/ change in length

    it is - to remind that flow is down the hydraulic gradient
  29. Find velocity in any fluid-saturated media
    • Image Upload 11
    • where U =linear velocity
    • k= intrinsic permeability
    • Image Upload 12 = viscosity
    • dp/dl= the pressure derivative
  30. If Uwater=Uany fluid 
    -K(dh/dl)= (-k/mu)(dp/dl) 

    where dP=pw*g (dw)
    where mu is viscosity of water and k is intrinsic permeability
  31. When can you optimize K? hydraulic conductivity?
    Image Upload 13 where K =hydraulic conductivity, k+ intrinsic permeability, pw=pressure of water, g=gravity and mu is viscosity of water
  32. Aquifers
    water in a saturated zone that exists in the subsurface
  33. recharge area
    • where surface water can infiltrate the ground. Not much runoff
    • -has high permeability
  34. Confined aquifer well
    will pressure water up
  35. How to determine direction of water flow?
    find hydraulic head (Image Upload 14h) -height
  36. hydraulic head
    • h=hp+z
    • hp= pressure head
    • z= elevation head ( distance between some zero level and the bottom of the well where the zero level is deeper)
  37. How do you find the water level?
    • hA= hpA+zA   where hpA= pressure head for well A and zA=elevation head for well A
  38. What is the hydraulic gradient?
    With regard to an aquifer, the rate of change of pressure head per unit of distance of flow at a given point and in a given direction. 

    dh/dl= Image Upload 15   where hA is water level, and xA-xB is distance  the wells are apart
  39. Pressure head
    • symbolized as hp
    • It is found by the total length of the well-the length of the well before water
  40. elevation head
    distance between some zero level and the bottom of the well, where the zero level is deeper
  41. Diffusion in Porous media
    Jdiffusion= -Deffective diffusivity*(dc/dx)

    Deffective diffusivity=Image Upload 16  where theta a is air-filled porosity
  42. Dispersion in porous media
    Jdispersion = -Image Upload 17effective difusivity*(dc/dx) 

    Image Upload 18eff=Image Upload 19h=Deff +UImage Upload 20 

    where Image Upload 21 is dispersivity in porous media, Deff= effective diffusivity, U= filtration velocity
  43. 1st order reaction
    • -rxn=-kCw
  44. 2nd order reaction
  45. accumulation rate
    accumulation rate=inputs-outputs+formation rxn-rxn

    dC/dt=QinCin+vsCairA- QoutCw- kCwV
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