1. Colloid Transport Project Project Advisors: Timothy R. Ginn, Professor, Department of Civil and Environmental Engineering, University of California Davis, Daniel M. Tartakovsky, Professor, Department of Mechanical and Aerospace Engineering University of Patricia J. Culligan, Professor, Department of Civil Engineering and Engineering Mechanics, Columbia

2. Basic Goal Examine the transport of a dilute suspension (of micron sized particles) in a saturated, rigid porous medium under uniform flow Advection Dispersion Filtration (sorption, deposition, or attachment)

3. Challenge ∂S/∂t…. Classic mathematical models used to describe ∂S/∂t are inadequate in many cases - even in very simple systems

4. Problems Involving Particle Transport through Porous Media Water treatment system –Deep Bed Filtration (DBF) –Membrane-based filtration Transport of contaminants in aquifers –Colloidal particle transport Transport of microorganisms –Pathogen transport in groundwater –Bioremediation of aquifers Clinical settings –Blood cell filtration –Bacteria and viruses filtration

5. Particle Sizes 10 -2 10 -3 10 -4 10 -5 10 -6 10 -7 10 -8 10 -9 10 -10 (diameter, m) 1 Å 1 nm 1  m 1 mm 1 cm Soils Atoms, molecules Microorganisms Blood cells Electron microscope Light microscope Human eye Depth-filtration range Red blood cell White blood cell Bacteria VirusesProtozoa GravelSand SiltClay AtomsMoleculesMacromolecules Colloids Suspended particles

6. Particle Filtration through a Porous Medium Porous Medium Particle suspension injection at C 0 Particle breakthrough L C/C o < 1 C/C o Fraction of particle mass is permanently removed by filtration

7. Idealized Description of Particle Filtration Clean-bed “ Filtration Theory ” Single collector efficiency Single “collector” represents a solid phase grain. A fraction  of the particles are brought to surface of the collector by the mechanisms of Brownian diffusion, Interception and/or Gravitational sedimentation. A fraction  of the particles that reach the collector surface attach to the surface The single collector efficiency is then scaled up to a macroscopic filtration coefficient, which can be related to first-order attachment rate of the particles to the solid phase of the medium. Filtration coefficient First-order deposition rate

8. Particle Filtration through a Porous Medium Porous Medium Particle suspension injection at C 0 Particle breakthrough L C/C o < 1 C/C o k att (and  ) is assumed to be spatially constant and dependent upon particle-solid interaction energies (DLVO theory) and system physics

9. Motivation for Work Growing body of literature that indicates that k att decreases with transport distance - points to inadequacies in the filtration-theory Various solutions to fixing these inadequacies –More complex macroscopic models? –Modeling at the micro-scale? Examine solutions in context of a unique data set that has resolved particle concentrations in the interior of a porous medium in real time

10. Generation of Data Set Translucent porous medium – glass beads saturated with water Laser induced fluorescent particles –Micro-size Fluorescent Particles: Excitation wavelength 511- 532nm, Emission wavelength 570-595nm. –Laser : 6W Argon-ion Laser Digital image processing –Captured images in real-time with CCD camera –Image processing software

11. Particles  Acrylic particles with organic fluorescent dyes (fluorecein, rhodamine) embedded.  Specific gravity = 1.1  Particle size  Range: 1-25  m, d 50 =7  m  Surface potential  zeta-potential = -109.97mV. Unlikely to attach to the glass bead surface due to the repulsive electrostatic force

12. Experimental Set Up

13. Particle Fluorescence is related to Particle Concentration Particle concentration had a linear relationship with fluorescent light intensity. Pixel by pixel calibration eliminated the optical distortion caused by the camera and the lens.

14. Basic Experiment Inject 10 Pore Volumes (PVs) of particle suspension at C = 50 mg/l Follow with injection of 10 Pore Volumes (PVs) of non-particle suspension at C = 0 mg/l Series of data for tests in similar porous media at difference values of u f

15. Data Available: Particle Breakthrough Curve at Column Base Particle density versus time in fluid phase at base - C versus t at a fixed z

16. Particle Concentration Inside the Medium (C + S) versus time at various locations within the medium

17. Microscopic Observations: Physical Insight Flow direction Particles are irreversibly attached at the solid-solid contact points (contact filtration) and at the top surface of the beads (surface filtration). The particles are also reversibly attached at the surface of the beads and possibly at the contact points. (a)to (c) Particle injection (d) to (e) Particle flushing

18. Contact Filtration Particles moving near bead- bead contact points were physically strained. Bead-bead contacts Bead- glass plate contacts Flow direction

19. Surface Filtration Some of the particles that approached the surface of the beads became “ irreversibly ” attached. Considering the highly negative zeta-potentials of the particles and beads, surface filtration must be “physical” - hypothesized that surface roughness held the particles against the drag force. Flow direction

20. Project Tasks Understand the data set Model data using traditional filtration-theory Understand the inadequacies of this theory Model data set using “more-complex” macroscopic balance equation Can any of the coefficients in this balance equation be given a physical meaning? Can micro-scale modeling techniques be applied and used to capture some of the observed behavior

21. What you will be given Data sets for three experiments - each at different average fluid velocity Experimental information - set-up plus parameters etc. A library of background literature Guidance, encouragement, hints (?)

22. What you will Deliver? Project report = technical article that discusses the shortcomings of existing modeling approaches and explores avenues for improvements based on (a) macroscopic modeling approaches and (b) microscopic approaches