I want to get through four topics, we'll see. Going home at 2am.
Poker tournament tomorrow at DTD so won't get much done. hopefully bust early. Can be at uni early then.
Getting really scared.
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There are three different types of transport movement, advection, diffusion and dispersion.
ADVECTION
Starting on Advection:
Darcys law dictates the flow through soil and strata horizontally.
Q=-Aki where i is teh rate of change of head = DeltaH/L
k is the permeability.
This can be used to get the velocity through the soil
v=-ki
This is not the actual velocity in the pores though so it must be devided by the porosity which is always less than 1.
v_s=-ki/n where n=V_voids/V_total
Therefore the transit time, the time for one particle of water to move from one area to another, is t=L/v_s
Advective Flux: this is teh rate of contaminanet movement
F_A=vC=v_s.n.C
Permneability of soil if not water passing through:
K=k.gamma.mu (gamme is the unit weight of the liquid and mu is the dynamic/absolute viscosity)
K=k.ro.g/mu = g.nu (nu is the kinematic viscosity)
DIFFUSION
Flcisk law is the main thing used here:
F_D=-D_o(deltaC/deltaL)
Where deltaC/deltaL is the concentration gradient, this usually changes with time but in this is assumed to be constant. It also assumes concentration doesn't change as contaminant moves
When in static water a contaminent will diffuse to tryh and get equal conentration, this is due to the concentration gradient., in moving water it will both flow and diffuse.
Effective diffusion coems from the gfact that the pathway for a contaminent to diffuse is actually alot longer than a straight line due to the nature of uneven particle layers in the soil:
F_D=-D*.n.(deltaC/deltaL) where D*=omega.D_o
As the conentration gradient is not going to be constant unless more conentration is added constantly, the conc. gradient will change with time thus:
-n.(deltaC/deltat)=-D*.n.(delta^2C/deltaL^2)
Which is integrated to give:
C{L,t}=C_o.E_c(L/(2.SQRT(D*t)) Where E_c is the complementary error function and the brackets are related to the normal distribution=sigma^2/2t
C/C_o will always be less than 1, usually it will balance at around 0.5
DISPERSION
Dispersion is the mechanicle distribution of contaminent due to the tortuous nature of the particles inthe soil.
Again it uses Flick's law:
F_m=-D_m.n.(deltaC/deltaL)
Where D_m=alpha_L.v_s^beta
Where alpha is the londitudinal dispersivity (m) which can be found from the graph, This is usually 4-6 times larger when in-situ because the soil is more compacted obviously.
In this case C/C_o will eventually reach 1, at the point where it reaches 0.5 this is known as the breakthrough time.
There are three different ways in which a contaminent can disperse:
- Through fractured flow
- Through Longitudinal Dispersion
- Through transverse dispersion
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Most of the time these movement mechanisms work together:
Combing the fluxs gives:
F=F_A+F_D+F_m
But F_D is alot smaller than F_m and F_A and so F=F_m+F_A
where diffusion is taken in by F_m
GENERAL ADVECTION-DISPERSION EQUATION
Form the above:
F=n.v_s.C-D_h.n.(deltaC/deltaL)
Where D_h=D*+D_m this is thge hydromatic dispersion coefficient
Obviously like before this becomes time dependet as the contamination gradient changes:
F=n.(deltaC/delta t)=D_h.n.(delta^2 C/delta L^2)-n.v_s.(deltaC/deltaL)
PLUMES
The aboves equation applies to line sources, but point sources give a 3D movement and so the previous equation does not apply.
For 1 D movement:
C=C_o/2(E_c((L-V_s.t)/(2SQRT(D_h.t)))-...)
The ... tends to zero with distacne/time.
RETARDATION
This works against the spread of the contaminant as the contaminant in lower concentration flows has ana ffinity to the soil solids and so is lost and will no,longer move, lowering the future contamination in front.
R=1+(ro.k_d)/n
Where k_d=C_soil/C_water
Thus :
(deltaC/deltaL) =(D_h/R)(delta^2 C/delta L^2)-(v_s/R)(deltaC/deltaL)
THIS APPLIES AT EQUILIBRIUM ONLY!
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So at this point it is 11.53pm after having to do a load of stuff to get my head around the next sextion so I am going to write it up then go home to go to sleep probably.
Soil Physics & Chemistry
Properties
Soil is:
- Continuous - It has ill defined boundaries
- Variable
- Anisotropic (directionally dependent)
- Stress dependent (current stress and historical stress)
- Environmentally dependent
- Temp
- Moisture
- Pore Fluid Chemistry
- 3 phases
- Solid
- Clay -> Boulders
- Liquid
- Water, oils etc.
- Gas
- Air, methane, etc.
- Small particles mean a larger surface area
- Contaminants react on solid surfaces and so the larger the surface area the more reactions ( this is due to Adsorption. Therefore clay is very important (Small particles = big SA)
Clay Minerology
Clay is a silicate layer, it is a sheet of silicate, metal cations as part of a mineral structure, inonic inbalances occur.
The silicate layer = Si(4+) + 2O_2(2-) ->SiO_4
It is in a tetrahedra shape (trianle based piramid with the O at the points and Si in the center.
These join together in sheets of ionic bonds, with O in lop layer, Si middle layer and O bottom layer.
These sheets are balances but AL(2+) can sometimes take the place of Si (4+) as it has the same fit but can only go in the edge and givesa net -ive charge.
REAL TETRAHEDRAL SHEETS
They consist of groups of 5O(2-) + 2Si(4+) giving a -2 charge, these can be balances by joining in a mirror image to create 8O(2-) + 4Si(4+) or can be balanced by supplying external cations.
These sheets are known as Smectite
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Octrahedral sheets can also be created using both Aluminium and Magnesium:
Al(3+)
This has no ionic imbalance but it has holes in the structure which can take atoms.
This is called Gibbsite
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Mg(2+)
This also has no ionic imbalance and has no holes in the structure so is very stable.
This is called Brucite
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In practice these sheets can change properties atthe edges due to broken bonds and exchanging of cations that can change the ionic balance. Therefore sheets can join together.
These joined sheets at the boundaries can either have strong bonds from shared atoms or weak bonds from charge differences.
This is it for tonight, There will be more tomorrow after poker, I will continue on the bottom of this until the topic is finished then start a new one for the next two topics tomorrow.
Au revioir
Bon chance pour tomorrow.
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