
Transformations
Chemical or biological modifications that influence the composition of a system or structure of a molecule

Transport
the physical displacement (or movement) of a chemical/ biological species over characteristic distances and timescales

fate
fate= transport (movement) +transformation (reactions)

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.

overall flux
the sum of the advective, diffusive, and dispersive movements.
units: mass (or Mol)/ area*time

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)

Osmosis
Diffusion of water (only) water molecules move up salt gradients and down water gradients

Ficks law
J_{diffusivity}is proportional to  change in concentration gradient/ change in distance
J_{diff}= D (dc/dx)
diffusivity is chemical dependent

Characteristic distance
the distance, x, a molecule or particle will travel in a time t

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

C_{c}
the cunningham slip correction factor

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/ C_{c}

diffusion occurs faster in?
air than water

How does transfer occur at boundries
Through diffusion b/c advective velocities approach zero at those interfaces

k
 k_{m}
 k is the mass transfer coefficient

If J_{boundary} < 0
then C_{boundary} > C_{bulk} and flux is from boundary to bulk fluid

If J_{boundary}_{ }>0
C_{boundary}< C_{bulk} and flux is from bulk fluid to boundary

Diffusion through a stagnant layer
 If J_{bound}= k_{m} (C_{bulk}C_{bound})= J_{diff}
 then k_{m}= D/L where D is diffusivity and L is the boundary layer thickness
J _{diff}

Diffusion through settling particles that stick to the interface
 C_{bulk}=C
 C_{bound} =0
 J_{g}= velocity* (C_{bulk}C_{bound} ) = velocity * C
 therefore k_{m }= velocity

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=L ^{2}/ 20 (ie the time when constant concentration gradient has not yet been established)
 a time dependent process
 k_{m}=(D/pie*t)^{1/2 } instantaneous K_{m }
k _{m}= 2 (D/pie*t _{2}t _{1}) ^{1/2 } Averaged k _{m} where t _{2}t _{1} is the time interval of interest

film theory
a time dependent process

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
k _{m}= 0.323(u/x) ^{1/2}*v ^{1/6}D ^{2/3} 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
 k_{m}=0.646 (u/L)^{1/2} *v^{1/6}*D^{2/3}

porosity
 porosity= pore volume/ total volume porosity of air

Density
solids density, p _{s}= mass solids/ volume of solids
bulk density, p _{b}= mass solids/ total volume
p _{b}=p _{s}(1 )

hydraulic conductivity
K
 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

Darcy's Law
where K is hydraulic conductivity and A is area and Q is flow


Find velocity in a water saturated porous media
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

Find velocity in any fluidsaturated media
 where U =linear velocity
 k= intrinsic permeability
 = viscosity
 dp/dl= the pressure derivative

If U_{water}=U_{any fluid}
K(dh/dl)= (k/mu)(dp/dl)
where dP=p_{w}*g (dw)
K=k/mu
where mu is viscosity of water and k is intrinsic permeability

When can you optimize K? hydraulic conductivity?
where K =hydraulic conductivity, k+ intrinsic permeability, pw=pressure of water, g=gravity and mu is viscosity of water

Aquifers
water in a saturated zone that exists in the subsurface

recharge area
 where surface water can infiltrate the ground. Not much runoff
 has high permeability

Confined aquifer well
will pressure water up

How to determine direction of water flow?
find hydraulic head ( h) height

hydraulic head
 h=h_{p}+z
 h_{p}= pressure head
 z= elevation head ( distance between some zero level and the bottom of the well where the zero level is deeper)

How do you find the water level?
 h_{A}= h_{pA}+z_{A} where h_{pA}= pressure head for well A and z_{A}=elevation head for well A
 _{}

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= where hA is water level, and xAxB is distance the wells are apart

Pressure head
 symbolized as hp
 It is found by the total length of the wellthe length of the well before water

elevation head
distance between some zero level and the bottom of the well, where the zero level is deeper

Diffusion in Porous media
J _{diffusion}= D _{effective diffusivity}*(dc/dx)
D _{effective diffusivity}= where theta a is airfilled porosity

Dispersion in porous media
J _{dispersion }=  _{effective difusivity}*(dc/dx)
_{eff}= _{h}=D _{eff} +U
where is dispersivity in porous media, D _{eff}= effective diffusivity, U= filtration velocity


2nd order reaction
rxn=k[reactant]C_{w}

accumulation rate
accumulation rate=inputsoutputs+formation rxnrxn
dC/dt=Q_{in}C_{in}+v_{s}C_{air}A Q_{out}C_{w} kC_{w}V

