1. Pollution spreading mechanisms
Basic question:
Where will the pollutant go, how will it behave?

2. Where will the pollutant go, how will it behave?
What kind of an answer can be satisfactory for this question?
What should I know to answer this question?

3. Today’s presentation
Solute transport = the proper term for the spreading/movement of contaminant in water
Three mechanisms contribute to the spreading of contaminant in (ground)water: diffusion, advection, dispersion
Familiarity with graphical representations of the solutions of the transport equations
which is the key dependent variable* in transport problems?

4. DIFFUSION!
~7:30 contaminant spill, nonhomogeneous distribution – variable contaminant concentrations
~9:05 same contaminant concentration everywhere

5. Diffusion Molecular phenomenon Model in one dimension: random walk
Due to the random movement of the contaminant molecules in the solution
Model in one dimension: random walk
for every time step Δt, a contaminant molecule may move left or right by Δx
let’s follow the movement of 500 molecules

6. What we saw
At t=0, 500 particles appear at x=0
t=1
t=2
t=21
t=48

7. What we saw (cont’d) σ function of the square root of time
Nepf, Heidi Transport Processes in the Environment, Fall (MIT OpenCourseWare,

8. Diffusion: the mechanism
Movement of every molecule: random
Aggregate movement of many molecules: movement from areas of high concentrations to areas of low concentrations
Diffusion: the results
Spreading of the contaminant mass
Dilution (reduction of high concentrations)
reduction of concentration differences

9. Diffusion in a glass of water (1/4)
7:27 clean water
7:29 contaminant spill

10. Diffusion in a glass of water (2/4)
7:29
7:30

11. Diffusion in a glass of water (3/4)
7:35
7:45

12. Diffusion in a glass of water (4/4)
8:37
9:06
Diffusion (through air) in everyday life: the perfume of the person sitting next to us, the smells from cooking that go from the kitchen to other rooms

13. Nature of a substance in gaseous or aqueous solution
Be careful! The solid, liquid or gas state is an emerging property that shows the relationship among the same molecules – it is not a property of each individual molecule.
Nescafé (instant coffee): suitable model/analogy for an aqueous solution
Greek coffee: inappropriate model/analogy for an aqueous solution

14. ADVECTION! Go with the flow, fast...

15. ADVECTION! (cont’d) …or slow

16. Advection Mechanical phenomenon
Contaminant movement with the average water velocity
Analogy for diffusion: a ball drops in the river and gets carried away

17. Advection: the results
The contaminant moves in the direction of the movement of (ground)water flow
There is no dilution, the contaminant moves as a “parcel”, as a “rigid body”, if the water velocity has everywhere the same magnitude and direction
it is as if Ihave placed all the contaminant molecules on a raft
Be careful! An experiment with advection only is not possible in practice

18. DISPERSION!
Search the internet for rubber duck derby

19. Many ducks start together...

20. ... but what happens along the way?

21. Dispersion Mechanical phenomenon Analogy
Advection in microscale that follows the difference in velocity from point to point (full term: mechanical dispersion)
Analogy
Many particles get dropped at the same time in a river (not just a ball, like in advection)

22. Dispersion: the results
Whereas the center of contaminant mass moves at the average water velocity, some molecules move faster, some slower
With time, differences increase (like in diffusion)
Same contaminant mass in bigger area  dilution (like in diffusion)
Because the phenomena of diffusion and dispersion produce similar results, in transport equations they are described with a common term

23. Question for understanding No 1
11:36 contaminant spill
11:36+ uniform concentration distribution “in time dt”!
What did we achieve with the spoon...
Attention! Significant difference between the movement in water we stir with a spoon and the movement of groundwater that typically moves very slowly with laminar flow.

24. The results of three mechanisms together: instantaneous release at the source

25. Αποτελέσματα τριών μηχανισμών μαζί: πηγή σταθερής συγκέντρωσης
σταθερή ταχύτητα
σταθερός συντελεστής διάχυσης-διασποράς

26. Question for understanding Νο 2
Thought experiment. Consider the picture in the video of the previous slide showing the spreading of the contaminant. How would it be different without diffusion and dispersion? Complete the concentration-time graph for each one of the points Α, Β και C.

27. Which difference would you pick to describe as the most significant at Α?
Instantaneous release of contaminant mass at the source (example?)
Constant contaminant concentration at the source (example?)

28. Relative contribution of phenomena, source of constant concentration (1/4)
I start the simulation with default τιμές, I see what is happening with time at a particular distance from the source (blue line)

29. Relative contribution of phenomena, source of constant concentration (2/4)
I reduce diffusion-dispersion by a factor of 10 (red)...

30. Relative contribution of phenomena, source of constant concentration(3/4)
... I reduce diffusion-dispersion by a factor of 100 (green)...

31. Relative contribution of phenomena, source of constant concentration (4/4)
... I reduce diffusion-dispersion by another factor of 100 (yellow)...

32. What did I achieve with the yellow line?
To perform a numerical experiment of transport practically with advection as the only transport mechanism!

33. The effect of time
Concentration profiles at different distances from the contaminant source
10m
50 m
100m
250m

34. Συμπεράσματα για την επίδραση της ροής στην μεταφορά ρύπων
The contaminant front (constant concentration source) or the center of contaminant mass (instantaneous release & source of finite duration) will move at the average velocity of water = advection
Advection dives a satisfactory approximation of transport:
when the contribution of diffusion-dispersion is small
when the we are interested in transport at short distances and short times

35. Sources of figures
Note: the non-original material used in this presentation either it has been uploaded on the internet with a Creative Commons license, or it is publicly available on the internet (e.g. US policy for reports etc. by public agencies) and can be used with suitable attribution, or is used with license from the publisher.
Slides 6, 7, 24, 25, 27. Nepf, Heidi Transport Processes in the Environment, Fall (MIT OpenCourseWare: Massachusetts Institute of Technology), (Ημερομηνία πρόσβασης 16 Oct., 2015). License: Creative Commons BY-NC-SA
Slide 14. Waynestock (Own work), License: Creative Commons BY-SA 4.0,
Slide 15. Bureau of Land Management (Rogue WSR), License: Creative Commons BY 2.0,
Slide 19. Billh35 (Own work), License: Creative Commons BY-SA 3.0,
Slide 20. Used by permission from the photographer Denton Harryman,
Slides Results from the educational applets developed by Valocchi, A. J., C. J. Werth, J. J. Decker, G. Hammond, P. Zhou & M. Hafiz, 2014, Interactive Models for Groundwater Flow and Solute Transport, (Accessed October 16, 2015).