Gravity Classifier (PlittFlintoff)
Description
This article describes a model of gravity classifiers proposed by Plitt and Flintoff (1985).^{[1]}^{[2]}
Gravity classifiers use the differential settling velocity of particles in a pool to separate feed pulp into coarse and fine product streams.
Mechanical gravity classifiers use a mechanical action to both agitate pulp in the pool and convey the gravitysettled coarse particles away from the machine and the remaining fine particles in the overflow. Examples of mechanical gravity classifiers include spiral, rake and bowl machines.
Nonmechanical gravity classifiers rely on free or hindered settling against a rising current and draw settled coarse particles through an underflow spigot. Finer particles report to the overflow. Examples of nonmechanical gravity classifiers include devices variously referred to as hydraulic classifiers, elutriators, hydrospearators, hydrosizers, upcurrent classifiers, teeterbed separators, hinderedbed separators, or cone classifiers.
Model theory
Plitt and Flintoff proposed a model that describes the classification of particles based on a consideration of settling velocity and flow conditions in gravity classification devices.^{[1]}
Classification
Plitt and Flintoff's formulation applies the ReidPlitt (1971) efficiency curve to describe the classification of particles by size.^{[3]}^{[4]}
The ReidPlitt expression for corrected partition to underflow, (frac), is:
where:
 is the index of the size interval, , is the number of size intervals
 is the geometric mean size of particles in size interval (mm)
 is the corrected size at which 50% of the particle mass reports to underflow and 50% to overflow (mm)
 is the sharpness parameter that determines the steepness of the partition curve ()
The actual partition to underflow , (frac), is computed as:
where is the fraction of fines and/or feed liquids split to the underflow (frac).
Determination of the corrected cut size () and water recovery () terms of the ReidPlitt equation are described below.
The value of the sharpness parameter, , can be specified for a given application, or estimated as described below.
Corrected cut size
Plitt and Flintoff assume the corrected cut size () is the size of a particle which has a settling velocity equal to the mean upward rising velocity of pulp, (m/h), i.e.:
where:
 is the volumetric flow rate of pulp in the overflow (m^{3}/h)
 is the effective settling pool area of the classifier (m^{2})
 is the density of solids (t/m^{3})
 is acceleration due to gravity (m/s^{2})
The effective density of slurry in the classifier, (t/m^{3}), is assumed to be the mean of the feed slurry density, (t/m^{3}), and overflow slurry density, (t/m^{3}), i.e.:
The apparent viscosity of slurry in the classifier, (Pa.s), is estimated by the classical KriegerDougherty (1959) equation:^{[5]}
where:
 is the viscosity of the carrier fluid, i.e. water (Pa.s)
 is maximum packing fraction of particles (v/v), assumed to be 0.64
 is a particle shape constant, assumed to be 2.5
The effective volume solids fraction in the classier, (v/v), is assumed to be the mean of the feed solids volume fraction, (v/v), and the overflow solids volume fraction, (v/v), i.e.:
The parameters and are related to the particle shape, as shown in Table 1.
Table 1. Particle shape types Index Particle shape Example mineral 0 Spheres 0.942 3.03 1 Perfect cubes Galena, sylvite 1.038 3.01 2 Conchoidal fracture Quartz 1.022 4.008 3 Dodecahedral Sphalerite 1.05 5.9 4 Plates 10x thickness 2.43 4.7 5 Plates 100x thickness Mica 7.69 12.29 6 Irregular fracture Arsenopyrite 1.00 12.98
The term is implicit in the settling velocity equation. Therefore a numerical rootfinding algorithm is applied to approximate the value of for a given settling velocity and pulp conditions.
Water recovery
The Plitt and Flintoff model requires the volume fraction of solids in the underflow, (v/v), to be specified as an input.
The recovery of feed water to the underflow, , is thus a function of the recovery of solids to the underflow, which is in turn determined by the ReidPlitt classification equation.
The ReidPlitt classification equation itself features the term, and therefore an iterative scheme is required to fully compute the Plitt and Flintoff model.
Sharpness estimation
Plitt and Flintoff suggest using the following relationship to estimate values of , the separation sharpness:
where is the ratio of volumetric flowrates of pulp in the underflow (sands) and overflow streams, i.e. .
Plitt (1971) found the value of was in the range of 1  3.8 for classifiers. As such, the sharpness estimation above may not be appropriate for larger values of , depending on the application. User caution is recommended.
Densityspecific classification
Plitt and Flintoff's original model formulation purposely assumed that a mixture of particles of differing densities could be represented by a singular solid density value ().
This implementation can retain Plitt and Flintoff singular density value assumption, or compute classification curves separately for each density class, (t/m^{3}), where and is the number of density classes (or ore types, minerals etc).
Coarse solids removal capacity
If the computed mass flowrate of solids to the underflow stream, (t/h), exceeds the solids removal capacity of the classifier, (t/h), the value is increased by a small fraction. This process repeats until the underflow mass flowrate of solids is less than the removal capacity, i.e.
This action simulates a buildup of solids in the classifier which effectively reduces the settling pool area, driving up the cut size.
Sands solid content
Plitt and Flintoff provide the following table as a guide to the volume fraction of solids that may be expected from a classifier with a given cut size:
Table 2. Sands solids content (after Plitt and Flintoff, 1985)^{[1]} (μm) Volume fraction solids (% v/v) 600 5760 420 5357 300 5254 210 53 150 52 105 51 74 49 Hydroseparators 2040
Partition metrics
Several metrics are provided to characterise the partition curve.
The , also known as the cut or separation size, is defined as the size of a particle which has an even (50%) chance of appearing in either the underflow or overflow stream. The size is estimated via a loglinear interpolation of geometric mean size () against the uncorrected partition to underflow of all solids in the feed.
The Ecart Probable, or , is a measure of the deviation of a partition curve from a perfect separation, and is typically defined for size classification as:^{[6]}
where and are the sizes of particles which have a 75% and 25% probability, respectively, of appearing in the underflow stream. The and sizes are estimated by loglinear interpolation of geometric mean size against the uncorrected partition to underflow of all solids in the feed.
The Imperfection, , is a normalised measure of the sharpness of separation, which is suggested to be independent of the magnitude of the , and is typically defined for size classification as:^{[6]}
Excel
The PlittFlintoff gravity classifier model may be invoked from the Excel formula bar with the following function call:
=mdUnit_GravityClassifier_PlittFlintoff(Parameters as Range, Size as Range, Feed as Range, OreSG as Range)
Invoking the function with no arguments will print Help text associated with the model, including a link to this page.
Inputs
The required inputs are defined below in matrix notation with elements corresponding to cells in Excel row () x column () format:
where:
 is the index to the particle shape factors in Table 1 (06)
 indicates whether to compute classification separately for each solids density class (True) or use a singular representative solids density (False)
 indicates whether to estimate the sharpness of separation () (True) or apply a userspecified value (False)
 is a userspecified value of the sharpness of separation () which is applied if is False and ignored otherwise ()
 is the size of the square mesh interval that feed mass is retained on (mm)
 is feed solids mass flow rate by size and ore type (t/h)
 is the mass flow feed rate of liquids into the classifier (t/h)
Results
The results are displayed in Excel as an array corresponding to the matrix notation below:
where:
 is the number of iterations required to converge the PlittFlintoff model
 is the mass flow rate of liquids to the overflow stream (t/h)
 is the mass flow rate of liquids to the underflow stream (t/h)
 is mass flow rate of solids to the underflow stream (t/h)
 is mass flow rate of solids to the overflow stream (t/h)
 is the actual partition of all particles of size to the underflow stream, computed as (frac)
Example
The images below show the selection of input arrays and output results in the Excel interface.
SysCAD
The sections and variable names used in the SysCAD interface are described in detail in the following tables.
MD_Classifier page
The first tab page in the access window will have this name.
Tag (Long/Short)  Input / Display  Description/Calculated Variables/Options 

Tag  Display  This name tag may be modified with the change tag option. 
Condition  Display  OK if no errors/warnings, otherwise lists errors/warnings. 
ConditionCount  Display  The current number of errors/warnings. If condition is OK, returns 0. 
GeneralDescription / GenDesc  Display  This is an automatically generated description for the unit. If the user has entered text in the 'EqpDesc' field on the Info tab (see below), this will be displayed here.
If this field is blank, then SysCAD will display the unit class ID. 
Requirements  
On  CheckBox  This enables the unit. If this box is not checked, then the MassFracToUF option appears below. 
MassFracToUF  Input  Only appears if the On field above is not checked. Specifies the fraction of feed mass that reports to the underflow stream when the model is off. 
Method  Partition (User)  The partition to underflow for each size interval is defined by the user. Different values can be used for different solids. 
Partition (ReidPlitt)  The partition to underflow for each size interval is defined by a ReidPlitt efficiency curve. Different parameters can be used for different solids.  
Partition (WhitenBeta)  The partition to underflow for each size interval is defined by a WhitenBeta efficiency curve. Different parameters can be used for different solids.  
Air Classifier (Altun)  The Altun air classifier model is used to determine the partition of solids to underflow for each size interval.  
Gravity (PlittFlintoff)  The PlittFlintoff gravity classifier model is used to determine the partition of solids to underflow for each size interval.  
Options  
ShowQFeed  CheckBox  QFeed and associated tab pages (eg Sp) will become visible, showing the properties of the combined feed stream. 
ShowQOF  CheckBox  QOF and associated tab pages (eg Sp) will become visible, showing the properties of the overflow stream. 
ShowQUF  CheckBox  QUF and associated tab pages (eg Sp) will become visible, showing the properties of the underflow stream. 
SizeForPassingFracCalc  Input  Size fraction for % Passing calculation. The size fraction input here will be shown in the Stream Summary section. 
FracForPassingSizeCalc  Input  Fraction passing for Size calculation. The fraction input here will be shown in the Stream Summary section. 
Stream Summary  
MassFlow / Qm  Display  The total mass flow in each stream. 
SolidMassFlow / SQm  Display  The Solids mass flow in each stream. 
LiquidMassFlow / LQm  Display  The Liquid mass flow in each stream. 
VolFlow / Qv  Display  The total Volume flow in each stream. 
Temperature / T  Display  The Temperature of each stream. 
Density / Rho  Display  The Density of each stream. 
SolidFrac / Sf  Display  The Solid Fraction in each stream. 
LiquidFrac / Lf  Display  The Liquid Fraction in each stream. 
Passing  Display  The mass fraction passing the userspecified size (in the field SizeForPassingFracCalc) in each stream. 
Passes  Display  The userspecified (in the field FracForPassesSizeCalc) fraction of material in each stream will pass this size fraction. 
Classifier page
The Classifier page is used to specify the input parameters for the classifier model.
Partition page
The Partition page is used to specify or display the partition by species and size values.
Tag (Long/Short)  Input / Display  Description/Calculated Variables/Options 

Distribution  
Name  Display  Shows the name of the SysCAD Size Distribution (PSD) quality associated with the feed stream. 
IntervalCount  Display  Shows the number of size intervals in the SysCAD Size Distribution (PSD) quality associated with the feed stream. 
SpWithPSDCount  Display  Shows the number of species in the feed stream assigned with the SysCAD Size Distribution (PSD) quality. 
Partition  
Method  Model/User  Select modelcalculated or userdefined partition to separate each solids species type. 
Density  Display  Density of each solid species. 
Size  Display  Size of each interval in mesh series. 
MeanSize  Display  Geometric mean size of each interval in mesh series. 
All (All column)  Display 

Partition  Display 

All (All row, All column)  Display 

All (All row, per species)  Display 

About page
This page is provides product and licensing information about the Met Dynamics Models SysCAD AddOn.
Tag (Long/Short)  Input / Display  Description/Calculated Variables/Options 

About  
HelpLink  Opens a link to the Installation and Licensing page using the system default web browser. Note: Internet access is required.  
Information  Copies Product and License information to the Windows clipboard.  
Product  
Name  Display  Met Dynamics software product name 
Version  Display  Met Dynamics software product version number. 
BuildDate  Display  Build date and time of the Met Dynamics Models SysCAD AddOn. 
License  
File  This is used to locate a Met Dynamics software license file.  
Location  Display  Type of Met Dynamics software license or file name and path of license file. 
SiteCode  Display  Unique machine identifier for license authorisation. 
ReqdAuth  Display  Authorisation level required, MDSysCAD Full or MDSysCAD Runtime. 
Status  Display  License status, LICENSE_OK indicates a valid license, other messages report licensing errors. 
IssuedTo  Display  Only visible if Met Dynamics license file is used. Name of organisation/seat the license is authorised to. 
ExpiryDate  Display  Only visible if Met Dynamics license file is used. License expiry date. 
DaysLeft  Display  Only visible if Met Dynamics license file is used. Days left before the license expires. 
Additional notes
 Solid species that do not possess a particle size distribution property are split according to the overall mass split of the default particle size distribution species selected in the SysCAD Project Configuration.
 If the default particle size distribution species is not present in the unit feed, the overall split of all other species with particle size distributions combined is used, as determined by the model.
 Gas phase species report directly to the overflow stream without split.
See also
References
 ↑ ^{1.0} ^{1.1} ^{1.2} Plitt, L.R., and Flintoff, B.C., 1985. Unit Models of Ore and Coal Process Equipment: Classification and Coal Processing. In SPOC Manual. Edited by D. Laguitton. Ottawa, Canada: CANMET.
 ↑ Fuerstenau, M.C. and Han, K.N. eds., 2003. Principles of mineral processing. SME.
 ↑ Reid, K.J., 1971. Derivation of an equation for classifierreduced performance curves. Canadian Metallurgical Quarterly, 10(3), pp.253254.
 ↑ Plitt, L.R., 1971. The analysis of solidsolid separations in classifiers. CIM bulletin, 64(708), pp.4247.
 ↑ Krieger, I.M. and Dougherty, T.J., 1959. A mechanism for non‐Newtonian flow in suspensions of rigid spheres. Transactions of the Society of Rheology, 3(1), pp.137152.
 ↑ ^{6.0} ^{6.1} Gupta, A. and Yan, D.S., 2016. Mineral processing design and operations: an introduction. Elsevier.