Filtration Theory On removing little particles with big particles

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Filtration Theory

Filtration Outline

  • Filters galore

    • Range of applicability
  • Particle Capture theory

    • Transport
    • Dimensional Analysis
    • Model predictions

Filters Galore

Categorizing Filters

  • Straining

    • Particles to be removed are larger than the pore size
    • Clog rapidly
  • Depth Filtration

    • Particles to be removed may be much smaller than the pore size
    • Require attachment
    • Can handle more solids before developing excessive head loss
    • Filtration model coming…

The “if it is dirty, filter it” Myth

  • The common misconception is that if the water is dirty then you should filter it to clean it

  • But filters can’t handle very dirty water without clogging quickly

Filter range of applicability

Developing a Filtration Model

  • Iwasaki (1937) developed relationships describing the performance of deep bed filters.

Graphing Filter Performance

Particle Removal Mechanisms in Filters

Filtration Performance: Dimensional Analysis

  • What is the parameter we are interested in measuring? _________________

  • How could we make performance dimensionless? ____________

  • What are the important forces?

Dimensionless Force Ratios

  • Reynolds Number

  • Froude Number

  • Weber Number

  • Mach Number

  • Pressure/Drag Coefficients

    • (dependent parameters that we measure experimentally)

What is the Reynolds number for filtration flow?

  • What are the possible length scales?

    • Void size (collector size) max of 0.7 mm in RSF
    • Particle size
  • Velocities

    • V0 varies between 0.1 m/hr (SSF) and 10 m/hr (RSF)
  • Take the largest length scale and highest velocity to find max Re

  • For particle transport the length scale is the particle size and that is much smaller than the collector size

Choose viscosity!

  • In Fluid Mechanics inertia is a significant “force” for most problems

  • In porous media filtration viscosity is more important that inertia.

  • We will use viscosity as the repeating parameter and get a different set of dimensionless force ratios


Diffusion (Brownian Motion)

London van der Waals

  • The London Group is a measure of the attractive force

  • It is only effective at extremely short range (less than 1 nm) and thus is NOT responsible for transport to the collector

    • H is the Hamaker’s constant

What about Electrostatic repulsion/attraction?

  • Modelers have not succeeded in describing filter performance when electrostatic repulsion is significant

  • Models tend to predict no particle removal if electrostatic repulsion is significant.

  • Electrostatic repulsion/attraction is only effective at very short distances and thus is involved in attachment, not transport

Geometric Parameters

  • What are the length scales that are related to particle capture by a filter?

    • ______________
    • __________________________
    • ______________
    • Porosity (void volume/filter volume) ()
  • Create dimensionless groups

    • Choose the repeating length ________

Write the functional relationship

Numerical Models

  • Trajectory analysis

  • A series of modeling attempts with refinements over the past decades

  • Began with a “single collector” model that modeled London and electrostatic forces as an attachment efficiency term ()

Filtration Model

Transport Equations

Filtration Technologies

  • Slow (Filters→English→Slow sand→“Biosand”)

    • First filters used for municipal water treatment
    • Were unable to treat the turbid waters of the Ohio and Mississippi Rivers
    • Can be used after Roughing filters
  • Rapid (Mechanical→American→Rapid sand)

    • Used in Conventional Water Treatment Facilities
    • Used after coagulation/flocculation/sedimentation
    • High flow rates→clog daily→hydraulic cleaning
  • Ceramic

Rapid Sand Filter (Conventional US Treatment)

Filter Design

  • Filter media

    • silica sand and anthracite coal
    • non-uniform media will stratify with _______ particles at the top
  • Flow rates

    • 60 - 240 m/day
  • Backwash rates

    • set to obtain a bed porosity of 0.65 to 0.70
    • typically 1200 m/day


  • Wash water is treated water!

  • WHY?

Rapid Sand predicted performance

Slow Sand Filtration

  • First filters to be used on a widespread basis

  • Fine sand with an effective size of 0.2 mm

  • Low flow rates (2.5-10 m/day)

  • Schmutzdecke (_____ ____) forms on top of the filter

    • causes high head loss
    • must be removed periodically
  • Used without coagulation/flocculation!

  • Turbidity should always be less than 50 NTU with a much lower average to prevent rapid clogging

Slow Sand Filtration Mechanisms

  • Protozoan predators (only effective for bacteria removal, not virus or protozoan removal)

  • Aluminum (natural sticky coatings)

  • Attachment to previously removed particles

  • No evidence of removal by biofilms

Typical Performance of SSF Fed Cayuga Lake Water

Particle Removal by Size

Techniques to Increase Particle Attachment Efficiency

  • Make the particles stickier

    • The technique used in conventional water treatment plants
    • Control coagulant dose and other coagulant aids (cationic polymers)
  • Make the filter media stickier

    • Biofilms in slow sand filters?
    • Mystery sticky agent present in surface waters that is imported into slow sand filters?

Cayuga Lake Seston Extract

  • Concentrate particles from Cayuga Lake

  • Acidify with 1 N HCl

  • Centrifuge

  • Centrate contains polymer

  • Neutralize to form flocs

Seston Extract Analysis

E. coli Removal as a Function of Time and Al Application Rate

Slow Sand Filtration Predictions

How deep must a filter (SSF) be to remove 99.9999% of bacteria?

  • Assume  is 1 and dc is 0.2 mm, V0 = 10 cm/hr

  • pC* is ____

  • z is ________________

  • What does this mean?

Head Loss Produced by Aluminum

Aluminum feed methods

  • Alum must be dissolved until it is blended with the main filter feed above the filter column

  • Alum flocs are ineffective at enhancing filter performance

  • The diffusion dilemma (alum microflocs will diffuse efficiently and be removed at the top of the filter)

Performance Deterioration after Al feed stops?

  • Hypotheses

    • Decays with time
    • Sites are used up
    • Washes out of filter
  • Research results

    • Not yet clear which mechanism is responsible – further testing required

Sticky Media vs. Sticky Particles

  • Sticky Media

    • Potentially treat filter media at the beginning of each filter run
    • No need to add coagulants to water for low turbidity waters
    • Filter will capture particles much more efficiently

The BioSand Filter Craze

  • Patented “new idea” of slow sand filtration without flow control and called it “BioSand”

  • Filters are being installed around the world as Point of Use treatment devices

  • Cost is somewhere between $25 and $150 per household ($13/person based on project near Copan Ruins, Honduras)

  • The per person cost is comparable to the cost to build centralized treatment using the AguaClara model

“BioSand” Performance

“BioSand” Performance

  • Pore volume is 18 Liters

  • Volume of a bucket is ____________

  • Highly variable field performance even after initial ripening period

Field Performance of “BioSand”

Potters for Peace Pots

  • Colloidal silver-enhanced ceramic water purifier (CWP)

  • After firing the filter is coated with colloidal silver.

  • This combination of fine pore size, and the bactericidal properties of colloidal silver produce an effective filter

  • Filter units are sold for about $10-15 with the basic plastic receptacle

  • Replacement filter elements cost about $4.00

Horizontal Roughing Filters

  • 1m/hr filtration rate (through 5+ m of media)

  • Usage of HRFs for large schemes has been limited due to high capital cost and operational problems in cleaning the filters.

Roughing Filters

  • Filtration through roughing gravity filters at low filtration rates (12-48 m/day) produces water with low particulate concentrations, which allow for further treatment in slow sand filters without the danger of solids overload.

  • In large-scale horizontal-flow filter plants, the large pores enable particles to be most efficiently transported downward, although particle transport causes part of the agglomerated solids to move down towards the filter bottom. Thus, the pore space at the bottom starts to act as a sludge storage basin, and the roughing filters need to be drained periodically. Further development of drainage methods is needed to improve efficiency in this area.

Roughing Filters

  • Roughing filters remove particulate of colloidal size without addition of flocculants, large solids storage capacity at low head loss, and a simple technology.

  • But there are only 11 articles on the topic listed in

  • (see articles per year)

  • They have not devised a cleaning method that works

Multistage Filtration

  • The “Other” low tech option for communities using surface waters

  • Uses no coagulants

  • Gravel roughing filters

  • Polished with slow sand filters

  • Large capital costs for construction

  • No chemical costs

  • Labor intensive operation


  • Many different filtration technologies are available, especially for POU

  • Filters are well suited for taking clean water and making it cleaner. They are not able to treat very turbid surface waters

  • Pretreat using flocculation/sedimentation (AguaClara) or roughing filters (high capital cost and maintenance problems)


  • Filters could remove particles more efficiently if the _________ efficiency were increased

  • SSF remove particles by two mechanisms

    • ____________
    • ______________________________________
    • Completely at the mercy of the raw water!
  • We need to learn what is required to make ALL of the filter media “sticky” in SSF and in RSF


  • Tufenkji, N. and M. Elimelech (2004). "Correlation equation for predicting single-collector efficiency in physicochemical filtration in saturated porous media." Environmental-Science-and-Technology 38(2): 529-536.

  • Cushing, R. S. and D. F. Lawler (1998). "Depth Filtration: Fundamental Investigation through Three-Dimensional Trajectory Analysis." Environmental Science and Technology 32(23): 3793 -3801.

  • Tobiason, J. E. and C. R. O'Melia (1988). "Physicochemical Aspects of Particle Removal in Depth Filtration." Journal American Water Works Association 80(12): 54-64.

  • Yao, K.-M., M. T. Habibian, et al. (1971). "Water and Waste Water Filtration: Concepts and Applications." Environmental Science and Technology 5(11): 1105.

  • M.A. Elliott*, C.E. Stauber, F. Koksal, K.R. Liang, D.K. Huslage, F.A. DiGiano, M.D. Sobsey. (2006) The operation, flow conditions and microbial reductions of an intermittently operated, household-scale slow sand filter

Contact Points

Polymer Accumulation in a Pore

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