Hindered Systems & Thickening

Chapter 6 in Fundamentals

Professor Richard Holdich

R.G.Holdich@Lboro.ac.uk

Watch this lecture at http://www.vimeo.com/10201270

Visit http://www.midlandit.co.uk/particletechnology.htm

for further resources.

Introduction

Hindered settling

Porosity/voidage and

Concentration

Introduction

Hindered settling - thickener design

Hindered settling – pharma crystallisation

Hindered Systems & Thickening

Buoyancy correction – p61 Viscosity correction – p61 Hindered settling relations – p55 Zones in batch sedimentation – p57 Kynch's analysis – p60 Flux theory & thickener designs –

p57/8

Buoyancy Correction

Archimede’s Principle When a body is wholly, or partially,

immersed in a fluid it experiences an upthrust equal to the weight of fluid displaced.

Buoyancy - hence buoyed weight is:

gxF sW )(6

3

Buoyancy Correction

However, when measuring the buoyancy in a continuum consisting of suspended particles Archimede’s Principle tells us that the buoyancy correction is the density of the continuum not fluid alone (e.g. for a hydrometer in a slurry):

gxF msW )(6

3

)1( CC sm where

Viscosity correction

When a body is moving relative to a suspension made of others (usually finer).

NOT appropriate for sedimentation and filtration of a homogeneous suspension.

Krieger’s equation:K

e KC /)1( K is crowding factor 1/CMAX, and equal to 1.56 for spheres

eta is intrinsic viscosity, which is 2.5 for spheres

Viscosity correction

Hindered settling relations

Free settling

Hindered settling relations

Hindered settling

Hindered settling relations

Hindered settling

Hindered settling relations

Hindered settling

U = Ut (1-C)n

Richardson and Zaki’s equations

Zones in batch sedimentation

Hindered settling

Zones in batch sedimentation

Time

Height

t

At time t:

Supernatant

Originalconcentration

Variableconcentration

Sediment

Zones:

Co

Zones in batch sedimentation

Height

Supernatant

OriginalconcentrationVariableconcentration

Sediment

Zones:

Concentration

Co

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Kynch's analysis

Material balance on thickening element:

hsCUA

sAhhCUCU d/)(d

Kynch's analysis

Material balance on thickening element:

Input:

Output:

Accumulation:

Giving:

sCUA

sAhhCUCU d/)(d

hAt

Cs

d

d

C

CU

t

h

d

)(d

d

d

Kynch's analysis

Material balance on thickening element:

Time

HeightGiving:

C

CU

t

h

d

)(d

d

d

The rate at which the concentration propagates up the vessel is equal to the differential of the ‘solids flux’ withrespect to solids concentration.

Kynch's analysis

Experimental measurements:

Introduction

Hindered settling - thickener design

Flux theory & thickener design

Thickeners - hindered settling

Flux theory & thickener design

Thickeners - hindered settling

Picket fence rake - plunging feed

Flux theory

Settling curves

Batch flux curveCU

Flux theory

Flux?

sACU m2 v/v m s-1 kg m-3 i.e. kg s-1

sCU v/v m s-1 kg m-3 i.e. kg m-2 s-1

or

i.e. mass flow rate of solids (per unit area) - input & output.

Area and solid density are assumed to be constant - hence simply velocity by concentration (v/v) are used.

Flux theory

Batch flux curve

Flux theory

Flux theory

Underflow withdrawal flux

Flux theory

Composite flux

Flux theory

Limiting flux

Flux theory

Limiting flux F m3/s

A

Coe and Clevenger

Flux at any point:

G = (U + T) A C

Flux in underflow: G = (Uu + T) A Cu

Flux in feed:

G = F Co

Rearrange equations for T then G gives:

U

O

CCCU

FCA

11

)(

Coe and Clevenger

U

O

CCCU

FCA

11

)(

Where U(C) is U at values of C between Co and Cu. Solve the above equations for various values of C and U(C) and select the area that is the greatest for the design.

Thickener designs - others

Lamella settler - increased capacity:

Thickener designs - others

Lamella settler - increased capacity:

Thickener designs - others

Potable (drinking) water treatment - floc bed clarifier:

Upward flow clarification, coagulation using ferric sulphate or polyectrolyte. Solids collected in the blanket are removed by cone de-sludging.

Sedimentation

Stokes law ok for small particles Particles of given size settle fastest

in free settling Increasing concentration slows

particles - hindered settling If a PSD then smaller particles

dragged down by the larger ones Empirically relate U=f(C): U=Ut(1-C)n

Recap:

Sedimentation

On line thickener design available on the www (freely available) using Coe and Clevenger technique:

http://www.filtration-and-separation.com

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