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Week # 3 MR Chapter 3 Tutorial #3 MR #3.1, 3.5, 3.9, 3.12. To be discussed on Feb 4, 2015. By either volunteer or class list. MARTIN RHODES (2008) Introduction to Particle Technology, 2nd Edition. Publisher John Wiley & Son, Chichester, West Sussex, England.

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Settling of a suspension of particles Equation (3.5)

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U fs Equation (3.6)

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Batch settling Re < 0.3: Re > 500: Equation (3.20)

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Khan & Richardson Archimedes number, Ar: Equation (*): A maximum is observed at = (n/(n+1); Inflection point at = (n-1)/(n+1) (*)

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Sharp interfaces in sedimentation Variation of dimensionless setting flux with suspension concentration Re P <0.3, n=4.65

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Concentration interface in sedimentation U PS1, U PS2 are particle volumetric flux U ps = U p * C =Up * (1- ) (a)The gradient of the curve at concentration C is the velocity of a layer of suspension of this concentration. (b) The slope of a chord joining two points at concentration C 1 and C 2 is the velocity of discontinuity or interface between suspensions of these concentrations.

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The batch settling test Determination of interface and layer velocities from a batch flux plot C2 C3 C2

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Type 1 batch settling. Zones A, B and S are zones of constant concentration. Zone A is a clear liquid; zone B is a suspension of concentration equal to the initial suspension concentration; zone S is a suspension of settled bed or sediment concentration

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Change in positions of interface AB, BS and AS with time in Type 1 batch settling

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Type 2 batch settling. Zones A, B and S are zones of constant concentration. Zone A is clear liquid; zone B is a suspension of concentration equal to the initial suspension concentration; zone S is a suspension of settled bed concentration. Zone E is a zone of variable concentration. S

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Change in positions of interface AB, BE min, E max S and AS with time in Type 2 batch settling

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Determining if settling will be Type 1 or Type 2. A line through C S tangent to the flux curve gives C B1 and C B2. Type 2 settling occurs when initial suspension concentration is between C B1 and C B2.

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Relationship between the Height-Time curve and the flux plot Analysis of batch settling test

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Analysis of batch settling; relative velocities of a plane of concentration C and the particles in the plane

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Volume of particles which have passed through this plane in time t

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Continuous settling Settling of a suspension in a flowing fluid Continuous settling; downflow only

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** Upward flow of a particle suspension in a vessel gives total downward particle flux. ** (1- ) Equation (3.41)

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Total flux plot for settling in downward flow

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Total flux plot for settling in upward flow

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A real thickener (with upflow and downflow sections) A real thickener, combining upflow and downflow (F, L and V are volumes; C F, C L and C V are concentrations)

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Total flux plot for a thickener at critical loading

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Total flux plot for an underloaded thickener

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Total flux plot for an overloaded thickener

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Alternative total flux plot shape; thickener at critical loading

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Alternative total flux plot shape; Overloaded thickener

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Section 16.5 Local Extreme Values

Section 16.5 Local Extreme Values

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