8

CHAPTER-2

LITERATURE REVIEW

PREAMBLE

This chapter is the discussion of the previous work by other researchers. At the

beginning of the chapter earlier studies on the effects of solids concentration and wall

effects on the settling behaviour of suspensions are discussed. The drag- coefficient

particles Reynolds number relationships proposed by earlier workers are presented

and their recommendations are discussed.

Next part of the chapter includes discussion on rheological properties of the

suspensions, the rheological behaviours and different rheological models. Further

effects of system parameters like solids concentration, particle size and temperature

on suspension viscosity are discussed. Different dispersants are also discussed. The

chapter concludes with the discussion on applications of artificial neural networks in

various fields of chemical engineering.

2.1 Effect of Solids concentration on suspension settling

When the concentration of solids is high, the distance between particles becomes so

small that the particles come into contact with one another. As a result, the settling

process occurs differently and Stokes law fails to describe the settling of particles

beyond infinite dilution. Hindered settling is a term used to describe behavior at

higher concentrations where sedimentation rates are largely related to concentration

rather than to particle size [1]. In hindered settling particles are crowded and surrounding

particles interfere with the motion of individual particles, typically creating a slower-

moving mixture than would normally be expected. Upward displacement of the liquid is

also more prominent under hindered settling conditions. Settling rates in multiparticle

systems are influenced by particle interaction effects, which consist of collision

among particles and non-hydrodynamic interactions.

In the concentrated suspensions of significant solid volume fraction (f), as the

suspension settles, it replaces equivalent volume of liquid. If suspensions settle with

their settling velocity (um) under the action of gravity, the displaced liquid moves

9

upward. The liquid velocity (uw) depends on the settling velocity of solids. According

to continuity, the relative motion between solid particles and liquid can be presented

as follows (Equation 2.1):

m wu (1 ) u 0f f+ - = (2.1)

m wu u u= - (2.2)

Where, u is the relative velocity between solids particles and the dispersing medium

and is the pertinent settling velocity as given below in Equation 2.3:

mu 

(1 )u

f=

- (2.3)

For sedimentation phenomena, dimensional analysis suggests that,

u[(1 ), (Re )]

u pf f¥

= - (2.4)

Where, u∞ is the free falling velocity of the particle alone in the same fluid and the

container as the sedimentation of uniform spheres and Rep is the particle Reynolds

number. Richardson and Zaki [2] extensively studied sedimentation of solid-liquid

suspensions of spherical particles; they investigated the dependency of the settling

velocity on the solids volume fraction. Their results were summarized with the

relationship known worldwide as the Richardson-Zaki equation. Their relationship

(Equation 2.5) is a power law of the void ratio (1-f).

(1 )nu u f¥= - (2.5)

The parameter n was found to be a function of the flow regime, expressed by the

particle Reynolds number Rep, and of the particle to column diameter ratio.

Richardson and Zaki [2] have given the following relationships (Equations 2.6 to 2.9)

for the exponent; n as a function of particle diameter (dp) to cylinder diameter (D)

ratio and particle Reynolds number Rep:

4.65 19.5( ) Re 0.2pp

dn for

D= + < (2.6)

0.034.36 17.6( ) 0.2 Re 1pp

dn for

D-= + < < (2.7)

0.14.45 Re 1 Re 500p pn for-= + < < (2.8)

2.39 500 Re 7000pn = < < (2.9)

10

When the ratio of the particle to the container diameter is small, n has a value of about

4.6 [3], value of n between 4.65 and 5.1 was reported by Barnea and Mizrahi [4], Capes

[5] obtained the reduced values of n between 3 and 3.5. Turian et al [6] have suggested

the alternative scheme of maintaining the value of n to be near to 4.68. Recently Koo

[7] reported the value of n as 5.5 for settling of mono-dispersed suspensions. When

Particles of mixed sizes settle, inter-particle interactions are further compounded as

the faster settling, larger particle approach and overtake the slower, smaller particles

leaving then in their wake of trailing displaced liquid. Garside and Al Dibouni [8],

Cheng [9] and Baldock [10] confirmed the decreasing behaviour of n with the particle

Reynolds number.

2.2 Wall Effects on suspension settling

When particles settle in a quiescent liquid in a given container, the presence of the

container wall at a finite distance from the settling particle exerts retarding effect on

it. This phenomenon due to presence of solid boundary at a finite distance is known as

wall effect. Wall effect is commonly reported as a function of particle to container

diameter ratio (dp/D). The wall effect becomes significant at higher values of dp/D.

Garside and Al-Dibouni [8] and Selim et al [11] examined wall effects on sedimentation

particles. Settling of single spherical particle and multisized particle mixture in

Newtonian fluid was exhaustively investigated. It was found that the correction for

wall effects gives measurably better correlation of free falling velocity. For single

particle terminal velocity Garside and Al-Dibouni [8] recommended the following wall

effect correlations:

4u

1 0.475 1 Re 0.2 p pp

d dfor

u D D¥

é ùæ öæ ö= - - <ê úç ÷ç ÷

è øè øë û (2.10)

3u1 2.35 0.2 Re 10  p

p

dfor

u D¥ æ ö

= - < <ç ÷è ø

(2.11)

3 38/2

u 1   10 Re 3 10

1p

p

foru d

D

¥

é ùê úê ú= < < ´ê úæ öê ú- ç ÷ê úè øë û

(2.12)

11

Lali et al [12] studied settling of spherical particles of glass and stainless steel in

aqueous solution of CMC in the concentration range of 0.2 to 2 weight %, the settling

velocities were measured in nine different cylinders in the range of 9 - 200 mm

diameter. It was found that the wall effect factor is function of both the particle to

container diameter ratio and the particle Reynolds number. Di Felice and Parodi [13]

have demonstrated that the container wall diameter influences the falling velocity

only for dilute systems, which is in contrast with a widely used, established empirical

relationships. In creeping flow regime Francis [14] proposed the following relationship

for the wall effects:

4

1

0.4751

p

p

du D

du

D¥

é ù-ê ú

ê ú=ê ú-ê úë û

(2.13)

This relationship is simpler than those proposed by Clift et al [15]. Di Felis [16]

proposed the following equations (2.14) and (2.15) for wall effects correction for the

terminal settling velocity in viscous and inertial flow regimes respectively:

2.7

1

0.331

p

t

p

dV D

dU

D¥

é ù-ê ú

ê ú=ê ú-ê úë û

(2.14)

0.85

1

0.331

p

p

du D

du

D¥

é ù-ê ú

ê ú=ê ú-ê úë û

(2.15)

2.3 Drag coefficient particle Reynolds number relationship

The CD-Rep relationship (Equation 2.16) was first proposed by Stokes [18]; he obtained

the solution to a general equation of motion for a single sphere settling in a fluid by

assuming the total drag as viscous drag. The relationship is the well known Stokes

law, applicable for Rep < 1.

24ReD

p

C = (2.16)

12

Gilbert et al [19] proposed a three parameter equation (Equation 2.3.2) to correlate the

drag coefficient and the particle Reynolds number. They introduced a third parameter

in addition to the two parameters given by Stokes.

ReYD pC X Z= + (2.17)

A five parameter model (Equation 2.18) suggested by Clift and Gauvin [15]

incorporated the corrections to the Stokes law; these additional parameters were

obtained as a function of particle Reynolds number.

24

(1 Re )Re 1 Re

BD p E

p p

CC A

D= + +

+ (2.18)

Tourton and Levenspiel [20] introduced two equations (Equations 2.19 and 2.20) to

correlate the drag coefficient and particle Reynolds number for falling spheres. These

two equations are similar to the original three parameter model by Gilbert et al [19],

and five parameter model by Clift and Gauvin [15].

0.827 527.2Re 0.427 Re 2 10D p pC for= + < ´ (2.19)

0.6571.09

24 0.413(1 0.173Re )

Re 1 16300ReD pp p

C -= + ++

6Re 2.6 10pfor < ´ (2.20)

Another five parameter equation obtained by Khan and Richardson [21] is as given

below:

( )3.450.31 0.06 52.25Re 0.36Re Re 3 10D p p pC for- -= + < ´ (2.21)

Turton and Levenspiel [20] tested their experimental data with three parameter

equation (Equation 2.19) and five parameter equation (Equation 2.20), as shown in

the following Figures 2.1 and 2.2. The results show that the three parameter equation

predict the drag coefficients value well for low particle Reynolds number where as the

predictions show significant error for the higher value of particle Reynolds number.

The five-parameter equation, on the other hand, is capable of showing a minimum CD

value, and it can be seen from Figure 2.2 that this equation correlates the data

extremely well throughout the whole particle Reynolds number range. Equation 2.20

has the added advantage of converging to the Stokes equation at low particle

Reynolds number; it is a better correlation for prediction of the drag coefficient values

in the sub critical regime (Rep < 2 x 105).

13

Figure 2.1: Comparison between experimental and predicted values of

drag coefficient of spheres using three parameter model [20]

A four parameter general drag coefficient-Reynolds number relationship proposed by

Haider and Levenspiel [22] is given below (Equation 2.22)

24( Re )

Re 1Re

BD p

p

p

CC A

D= + +

+ (2.22)

The experimental data used to find the best values of the four parameters was same as

used by Turton and Levenspiel [20]. The final equation obtained for the drag

coefficient is as given below (Equation 2.23):

0.645924 0.4251(0.1806 Re )

6880.95Re 1Re

D pp

p

C = + ++

(2.23)

The drag coefficient values predicted by this equation were compared with the

experimental values and earlier predictions by Turton and Levenspiel [20] with the

three parameter equation (Equation 2.21) and five parameter equation (Equation 2.22)

as discussed earlier. The drag coefficient values calculated by four parameter model

as depicted in Figure 2.3 were found more accurate.

14

Figure 2.2: Comparison between experimental and predicted values of

drag coefficient of spheres using five parameter model [20]

An explicit equation for particle settling velocities in solid-liquid systems was

presented by Zigrang and Sylvester [23]. This equation can be used to predict the

settling velocity of particles in liquid-solid suspensions; this correlation gives the

terminal velocity of a single spherical particle in a liquid as given below (Equation

2.24):

3/2 2

**

*

( 14.51 1.83 3.81)du

d

+ -= (2.24)

Where, d* and u* are dimensionless diameter and dimensionless terminal velocity of

sphere respectively.

13

2*

3Re

4 D pd Cæ ö= ç ÷è ø

(2.25)

13

*

Re43

p

D

uC

æ ö= ç ÷

è ø (2.26)

15

Figure 2.3: Comparison between experimental and predicted values of drag coefficient of spheres using four parameter model [22]

Turton and Clark [24] proposed the following correlation (Equation 2.27) to represent a

very simple and accurate way to evaluate the terminal velocity of a sphere of known

dimensions and density in a known fluid.

1.214

* 0.824 1.214

2* *

1

18 0.321u

d d

é ùê úê ú= ê úæ ö æ öê ú+ç ÷ ç ÷ê úè ø è øë û

(2.27)

This correlation cannot predict the velocity of a particle driven through a fluid by a

force other than its own weight without further manipulation. There are number

relationships available in the literature for the drag coefficient as a function of particle

Reynolds number; some of them are reported in the following Table 2.1

16

Table 2. 1: Drag coefficient- Reynolds number relationships

Author(s) Equation Range of Applicability

24ReD

p

C = Rep < 0.3

0.6

18.5ReD

p

C = 0.3 < Rep < <1000

Perry and Chilton [25]

0.44DC = 1000 < Rep < 20000

Cheng [9] ( )0.43 0.38241 0.27 Re 0.47(1 exp( 0.04Re )

ReD p pp

C = + + - - Rep < 100

Flemmer and Banks [26]

2410

ReE

Dp

C =

Where, 0.369 0.431

210

0.1240.261Re 0.105Re

1 (log Re )p pp

E = - -+

Rep < 3 x 105

Saha et al [27] 0.75

18.5ReD

p

C = 1 < Rep < 1000

Choncha and Almendra [28]

2

0.5

9.060.28 1

ReDp

Cæ ö

= +ç ÷ç ÷è ø

1 < Rep < 1000

Madhav and Chhabra [29]

( )0.529241 0.0604Re

ReD pp

C = + 0.095 < Rep < 400

Brown and Lawler [30]

( )0.681

1

24 0.4071 0.15Re )

Re 1 8710ReD pp p

C -= + ++

Rep < 2 x 105

2.4 Flow curve modeling

In order to describe the flow curves mathematically, several rheological models have

been developed. Mechanistic approaches are, however, difficult to apply because of

the diversity of the properties responsible for the rheological behaviour. More

commonly, empirical models have been used to describe the characteristics of the

flow behaviour. Several empirical equations relating shear stress to the shear rate have

been developed to model the basic flow curve shapes. The criteria for the suitability

of the model are:

i. It should be simple with minimum number of independent constants

17

ii. Its’ constants should be easily determined and

iii. The constants should have some physical significance

Regression methods can be used to fit the equations to the rheological data. The fit of

these equations can be then compared using statistical methods. Models with smallest

number of coefficients are preferred because they are usually simple to use. The

following sections describe some of the models commonly used to represent the

rheological properties of the suspensions. Included are Newton’s law of viscosity,

three models can be used to describe the shear thinning behaviour and three models

that describe plastic behaviour. The shear thinning properties are often characterized

by the power law model, the Cross model and the Cerreau model. Models that

describe plastic flow properties must have yield stress term such as the Bingham

plastic model, the Herschel Bulkley model and the Casson Model.

2.4.1 Newton’s law of viscosity

The flow behaviour of Newtonian fluids can be described by Newton’s Law of

Viscosity (Equation 2.28)

dudr

t m æ ö= ç ÷è ø

(2.28)

Where, m is the Newtonian viscosity of the fluid. It has been used to describe the

rheology of non-interacting spheres in Newtonian liquids [18, 31]. Above a critical

solids concentration, suspensions exhibit non-Newtonian properties.

2.4.2 The power law model

ndu

kdr

t æ ö= ç ÷è ø

(2.29)

This model (Equation 2.29) is also referred as Ostwld-De Waele model. This equation

can be used to model all three basic viscous flow behaviours. The coefficients k and n

are referred to as the fluid consistency index and flow index, respectively [32]. A high

k value implies that the suspensions have a high viscosity. The deviation of n from

unity is a measure of the non-Newtonian behaviour. Clearly, at n equal to unity, the

equation becomes Newton’s law of viscosity and k becomes m. For n is less than

unity, the model describes pseudoplastic flow and, for n greater than one it describes

the dilatant flow. This model has been used to describe many solid-liquid suspensions [6].

18

2.4.3 The Cross model

The Cross model (Equation 2.30) was developed base on the assumption that the

pseudoplastic flow is due to the process of formation and rupture of linkages in chains

of particles. This process is believed to occur in aggregated systems where links

between particles result in the formation of chain-like aggregates which rupture due to

Brownian motion and shearing [33-34].

mdudr

m m a-

¥æ ö= + ç ÷è ø

(2.30)

Where, m¥ is the apparent viscosity at infinite shear rate. A value of m equal to 2/3

was found to be suitable for many pseudoplastic systems which reduce the number of

coefficients in the equation to 2 [33]. The Cross model has been applied to suspensions

that exhibit pseudoplastic behaviour [35].

2.4.4 The Carreau model

The Carreau model (Equation 2.31) was developed to describe the pseudoplastic

properties of polymer solutions and melts.

2

1

s

duA

drm m

-

¥

æ öæ ö= +ç ÷ç ÷ç ÷è øè ø (2.31)

It is based on molecular network theory which describes the non-Newtonian flow with

respect to the creation and loss of segments. The rate of creation and loss of these

segments is function of shear rate which results in the non-Newtonian response to

shear [36-38].

2.4.5 The Bingham plastic model

The Bingham plastic model (Equation 2.32) describes the simplest type of

viscoplastic flow. The model characterizes the ideal case in which a complete

structure breakdown occurs once a yield stress has been exceeded. Once the yield

stress is exceeded a linear relationship exists between the shear stress and shear rate [39].

0

dudr

t t h æ ö= + ç ÷è ø

(2.32)

Where, t0 is the yield stress and h is the plastic viscosity. The Bingham model is

widely used because of its simplicity. Many suspensions including red mud, kaolinite,

clays, drilling mud and yeast suspensions have been modeled with equation [6, 35, 40-41].

19

2.4.6 The Herschel Bulkley Model

The Herschel Bulkley model (Equation 2.33) is the combination of the Oswald-De

Waele power law model and the Bingham plastic model. As the yield stress becomes

small the equation takes form of the power law model and as the index, n, approaches

unity, it becomes Bingham plastic model.

0

ndu

kdr

t t æ ö= + ç ÷è ø

(2.33)

This simple, versatile and practical model has been widely used to characterize both

dilute and concentrated suspensions [6, 35].

2.4.7 The Casson model

1/21/2o

dudr

t t hæ ö= + ç ÷è ø

(2.34)

The Casson model (Equation 2.34) is a simple two parameter model that has a

physical basis and is derived from structural arguments. This model is capable of

fitting low shear rate curvature and therefore it estimates the yield stress compare well

to the values obtained experimentally [6].

2.5 Effect of Solids Concentration on Suspension Viscosity Several studies have shown that the viscosity of suspensions increase in an

exponential manner with solids concentration and becomes infinite at the maximum

packing fraction. It is well known that the earliest theoretical work on the effective

viscosity was due to Einstein [18] whose derivation led to the effective viscosity to be

linearly related to the particle concentration as follows (Equation 2.35):

1 2.5rh f= + (2.35)

Where,

hr = µm/µf = relative viscosity of the suspension

µm = effective viscosity of the particle-fluid mixture

µf = viscosity of fluid, and

f = solid volume fraction of the suspension

This expression is exact when the viscous effect is dominant so that the creeping flow

equations can be applied at the particle level. This equation is based on the viscous

20

energy dissipated by the flow around the sphere, relating the relative viscosity of the

solids content. With increasing solids concentration, there are a greater number of

particle interactions: these are responsible for the exponential increase in viscosity.

These interactions result in energy dissipation that can be described in terms

hydrodynamic, and aggregation effects. These effects are also responsible for the

increase in non-Newtonian nature of the suspensions that is found at higher

concentrations.

Following Einstein’s work, numerous expressions have been proposed to extend the

range of validity to higher concentrations. They are either theoretical expansions of

Einstein formula to higher order in f, or empirical expressions that were obtained

based on experimental data [42-44]. The theoretical expansions are usually expressed in

the form of a power series as given below (Equation 2.36):

2 31 2 31 .....r k k kh f f f= + + + + (2.36)

Where k1, k2, k3 are the coefficients. Evaluation of these coefficients other than k1

requires the formulation of particle interactions, which is rather difficult. This is one

of the reasons that only the theoretical values of the coefficients related to lower order

in f, like k2 and k3, can be found in the literature so far. Even for these lower order

coefficients, the calculations are available only for idealized cases when the particle

arrangement or its statistic properties are simple.

An example for determining the k2-value was presented by Batchelor and Green [45]

who reported that the coefficient k2 was equal to 7.6 for a suspension undergoing a

pure straining motion. It should be noted however that Batchelor and Green

introduced a rough interpolation in their derivation, which led to an inaccuracy in the

k2-value obtained. A re-calculation under the same condition was conducted by Kim

and Karrila [46], leading to the k2-value to be changed to 6.95. Other k2-values have

been reviewed by Elic and Phan-Thien [47]. Furthermore, Thomas and Muthukumar [48]

found the third order coefficient, k3, to be 6.40 by applying the multiple scattering

theories to the evaluation of the hydrodynamic interaction of three spheres.

Following these theoretical attempts, it can be expected that more complicated

configurations of the particle arrangements will lead to further difficulties in the

mathematical formulation. On the other hand, particles suspended in fluid should in

fact be distributed in a random manner so that their arrangement cannot be fitted to a

21

simple configuration or described by a simple distribution function. Therefore,

although an idealized particle arrangement may enable a theoretical evaluation of the

k-coefficients in higher order, the applicability of the effective viscosity so derived is

limited in practice.

When aggregation effects exist, the aggregates may be considered to be the suspended

units in the suspension. This result in an increase in effective solids content as the

aggregate will trap liquid [49]. The size of aggregates depends on the type of attractive

forces, the shearing conditions and solids concentration in the suspensions [50]. Many

of these effects have been considered in the evaluation of the coefficients of the

general power formula [51]. This model, which is extension of the Einstein’s equation

applies only to moderately concentrated suspensions and does not cover the entire

solids concentration range [43, 51].

In addition to the theoretical expressions, various empirical relationships have been

proposed to evaluate the effective viscosity of a suspension with higher concentration.

An early survey of such relationships made by Rutgers [51] showed that large

discrepancies exist among the different relationships. Table 2.2 shows some typical

examples of the existing empirical formulas, where fm is the maximum particle

concentration and h is the intrinsic viscosity. It is noted that for those relationships

where the so-called maximum concentration is included as a parameter, the effective

viscosity approaches infinity when the concentration is equal to the maximum value.

This may not be physically reasonable. Strictly speaking, there are only two extreme

conditions that are meaningful for the effective viscosity. The first condition is a

suspension without particles, implying that the effective viscosity is the same as the

fluid viscosity. The other is a suspension without fluid, which would then

theoretically behave as a solid with infinite viscosity. On the other hand, only for

particles with regular shapes can the maximum concentration be mathematically

determined for a given packing arrangement. For example, the maximum

concentration can reach 1.0 for cubes packed face-to-face and 0.74 for spheres with

the closest hexagonal packing arrangement. With irregular particles, the maximum

value varies markedly even though the particle size is uniform. As a matter of fact, the

maximum concentration and intrinsic viscosity were often used as two empirical

parameters in fitting experimental data to an empirical formula [52-53].

22

Eilers [18] used the maximum solids content as an upper limit in relating relative

viscosity to the solids fraction for bitumen emulsions. Chong et al [54] modified Eiler’s

equation to correlate the relative viscosity to the solids content for poly-disperse

suspensions. Mooney [55] considered the crowding effects of mono-disperse sphere to

obtain his equation. He also showed how his approach could be extended to bimodal

and poly-disperse suspensions. Krieger and Dougherty [56] also used particle

crowding, in similar manner to derive their equation. Ting and Luebber [57] considered

the effects of liquid-solid density ratio, particle size distribution and particle shape on

packing arrangement to derive an empirical relation between the relative viscosity and

some function of these parameters for varying solids contents.

23

Table 2.2: Formulas for effective viscosity

Einstein’s Equation [18]

Eiler Equation [18]

2

rm

1fhf

-æ ö

= -ç ÷è ø

Leighton and Acrivos’s Equation [52]

2

r

m

0.5 1

1

hfhff

æ öç ÷ç ÷= +ç ÷-ç ÷è ø

Chong et al’s Equation [54]

2

1 0.751

mr

m

ff

hff

æ öç ÷ç ÷= +ç ÷-ç ÷è ø

Mooney’s Equation [55]

r

m

2.5 exp

1

fhff

æ öç ÷ç ÷=ç ÷-ç ÷è ø

Krieger Dowarty’s Equation [56] m

rm

[1- ] hffhf

-=

Liu’s Equation [58]

nr m [a( )]h f f= -

Metzner’s Equation [59]

2

1 1.251

r

m

fhff

æ öç ÷ç ÷= +ç ÷-ç ÷è ø

Quemada’s Equation [60]

m2r

m

[1- ] ffhf

-=

2.6 Effect of Temperature on Suspension Viscosity

Liquid viscosity decreases with the increase in temperature. The trend of decreasing

viscosity at elevated temperatures occurs due to increased kinetic energy of the

particles promoting the breakage of intermolecular bond between adjacent layers

which results in decrease in viscosity of the suspension. For the limestone slurry of 70

weight % solids concentration, He et al [61] investigated influence of temperature on

the viscosity. They found that, the slurry viscosity decreases with increase in the

temperature from 13 to 55 0C. Reduction in the viscosity from the range of 0.0215 to

(1 2.5 )rh f= +

24

0.0365 Pas to the range of 0.01 to 0.019 Pas as for the increase in temperature from 13

to 55 0C was reported.

Mikulasek et al [62] shown the decrease in viscosity of the titanium oxide suspensions

of 10 to 30 volume % concentration over the range of temperature from 20 to 50 0C.

Similar results were observed by Roh et al [63] for coal water suspensions for the

temperature range of 15 to 50 0C and Senapati et al [64] for limestone suspensions in

the temperature range of 30 to 60 0C. The decrease in the suspension viscosity may be

the result of decrease in the interparticle forces between particles with temperature.

The decreased value of the viscosity with increased temperature confirms to

fundamental properties of any viscous materials as for all normal liquids [65]. Work of

different researchers [66-69] shown that the suspension viscosity also decreases with the

increase in temperature.

Senapati et al [64] presented a simple Arhenious type equation for the temperature

dependence of suspension viscosity. An identical relationship was confirmed by Li et

al [70] for temperature dependence of silicon carbide suspensions, they observed

increase in viscosity as temperature of the slurries increased from 20 to 60 0C. The

increase in the viscosity was observed because the suspensions induce flocculation

trend, which might be enhanced at higher temperature.

2.7 Effect of Particle Size on Suspension Viscosity

It is expected that the effects of particle size on suspension viscosity varies depending

on the range of particle size where these effects are studied because the actual inter-

particle forces will vary with the size of particles. Renehan et al [71] found that

suspensions of coal particles in a non-Newtonian suspension of bentonite clay

exhibited both increase and decrease in viscosity with increasing particle size.

Experimental results from Hasan et al [72] show that for high concentrations there is a

decrease in viscosity with increasing particle size, whereas at lower concentrations

there is an increase with increasing particle size. The size of particles in a suspension

has been shown strong influence on its rheological properties. In particular it has been

shown that suspensions with very large (higher than 100 mm) or very small (less than

10 mm) particles have a higher viscosity than suspension containing immediately

sized particles i.e.-100+10 mm [71]. These differences in the viscosities can be

25

explained by contributions of the hydrodynamic and aggregation effects. These

effects contribute to the viscosity to a greater or lesser degree depending on the size of

the particles.

It is difficult to determine the effect of particle size on the viscosity of suspensions

since parameters like shape and charge, which characterize the system may vary with

particle size. Most authors do not specify precisely the accuracy of the size

distribution, or provide much detail as to experimental conditions. Therefore the

disparity in observed results is not unexpected.

Some investigators have reported an increase in viscosity with the decrease in the

particle size [73-76]. This increase in viscosity has been attributed to the aggregation

effects that dominate fine particle behaviour [43, 70, 76-79]. Inter-particle forces of

attraction and repulsion are responsible for these effects which dominate the

movement of colloidal size particles [43, 71]. The magnitude of these factors may be

large enough to influence the movement of course particles. Rehenan et al [71] showed

that the movement of coal particles as course as 200 mm were influenced by surface

charge related effects, that were large enough to contribute to the rheological

properties. Sweeney and Geckler [74] suggested that the contribution from

electroviscous effects to the rheological properties of fine particle suspension can be

very significant. They showed that the viscosity of a suspension of glass spheres in

anionic suspending fluid, where electroviscous effects should be large, was greater

than the viscosity of the same sphere suspension in non-ionic fluid, in which

electroviscous effects should be small.

For suspensions of glass and polystyrene spheres, Parkinson et al [73] Saunders [78]

explained the increase in non-Newtonian behaviour with decreasing particle size, by

contribution of aggregation effects. Inter-particle forces of attraction dominate over

inertial forces for small particles which make them more susceptible to aggregation

than course ones. With increasing shear rate the attachments break resulting in more

dispersed suspension. As the particle becomes dispersed the apparent viscosity

decreased resulting in the shear thinning behaviour [75]. Since this dispersion with

shearing is not instantaneous, at a given shear rate the apparent viscosity will decay

with time resulting in the thixotropic characteristics of such suspensions. The

structure that forms as a result of the aggregation of the fine particle contributes to the

yield stress. Below a critical solids concentration the structure may not be continuous

26

and therefore no yield stress may be present [80]. The effects of particle size are more

pronounced at high solids concentrations than at low ones.

The magnitude of the hydrodynamic effects is proportional to specific surface area of

the particles. Since the specific surface area increases with decreasing particle size,

the contribution of the hydrodynamic effects also increases. Therefore the increase in

viscosity of suspensions resulting from decreasing particle sizes can be explained by

the greater amount of hydrodynamic energy dissipation [78]. According to Hasan et al. [72] increased particle interaction for smaller particles leads to increase in the

suspension viscosity. The formation of aggregates or flocks with decreasing particle

size due to the increasing significance of inter-particle forces at smaller particle sizes

increases the suspension viscosity. Kawatra and Eisele [81] observed an increase in

viscosity with reduction in particle size for constant solids concentration. This is due

to increased surface area, which binds up water molecules and thus increases the

effective solids concentration.

The results of several investigations [71, 75, 77] have shown that the increase in viscosity

occurs as particle size increases. This result has been explained by the energy

dissipated due to physical particle interactions. Since coarse particles have greater

inertia than fine ones they will collide rather than slip past each other. The physical

collisions dissipate energy through friction and loss of translational and rotational

momentum. Thomas [43] and Hasan et al [72] suggest that at low concentrations particle

interactions are minimal and viscosity may increase with particle size. Mangesana at

al [82] shown that viscosity increases with particle size at a fixed concentration for any

given shear rate. The reason suggested for this increase was that particles of greater

size possess greater inertia such that on interaction, the particles are momentarily

retarded and then accelerated. In both these stages their inertia affects the amount of

energy required. This dissipation of energy is what may appear as extra viscosity. The

contributions of the hydrodynamic, aggregation and electroviscous effects clearly

depend on the size of the particles. In order to minimize the viscosity, it seems that an

optimum particle size exists that is not too large and not too small.

27

2.8 Dispersing Agents

Dispersing agent can be classified into: (i) Inorganic compounds, and (ii) polymeric

dispersants [83]. While inorganic dispersants are primarily to control the charge density

at the solid/liquid interface, the polymeric compounds also provide steric hindrance.

Suspensions of aggregated particles can exhibit yield stress and typically have shear

thinning flow properties [84]. Dispersing the particles results in more Newtonian flow

behaviour and reduced apparent viscosity. It should be noted, however, that by

increasing electrostatic repulsion, electroviscous forces can also become important

resulting in greater apparent viscosities. Organic reagents typically used in iron ore

processing are polysaccharides such as starch, guar gum and carboxyl methyl

cellulose which are used to flocculate iron ore [85-86].

The effectiveness of these regents depends on the nature of the reagents, the particle

surface chemistry, the type of dissolved ions and the pH. Typical inorganic dispersing

agents are sodium polyphosphates and sodium silicates [84]. These dispersing agents

are widely used in processing of iron ores.

2.9 Artificial Neural Networks (ANN)

ANNs are massively connected parallel distributed processor made up of simple

processing units, which has a ability for storing experimental knowledge and making

it available for use. ANNs are well known for their utility as universal approximator

of complex nonlinear relationships between process variables and product quality

properties. ANNs have the ability to learn from input data and are very useful for the

prediction of complex high-dimensional data. ANN methods have a broad range of

applications in agriculture [87], weather forecasting [88], water resources engineering [89-

90] finance, medicine, robotics, etc. As in other fields of science, ANN methods have

become popular in chemical engineering too, soon after their development.

Artificial neural networks have been successfully used for dynamic modeling and

control of chemical processes and fault diagnosis [91], in the catalytic reactor modeling

and design of solid catalysts [92] and for modeling the kinetics of a chemical reaction [93]. The applicability of ANN modeling in emulsion liquid membranes [94] and in the

prediction/estimation of the vapor–liquid equilibrium data [95-96] has also been

investigated. Melkon Tatlier et al [97] used ANN model for the prediction of the molar

28

composition of the zeolitess. They estimated the quantities of Si and H2O in the

zeolites by using ANN. They reported the amounts of deviation from the experimental

results for the Si and H2O contents to be equal to about 10 and 20%, respectively.

Bhat and McAvoy [98] applied ANN to dynamic modelling for a pH-controlled CSTR.

The predicted pH values when compared to two other approaches demonstrated that

ANN could predict more accurately than conventional method. Willis et al [99]

discussed the application of ANN as both inferential estimator and predictive

controller. The results demonstrated that ANN could accurately predict the process

output and significantly improved the control scheme. Pollard et al [100] utilized

backpropagation trained ANN for process identification. They concluded that ANN

was particularly useful when the input-output mapping was unknown since ANN was

able to accurately represent nonlinear behaviour in a black box manner. Rajasimman

et al [101] used ANN for modeling of an inverse fluidized bed bioreactor. Initial

substrate concentration and the chemical oxygen demand (COD) values for a given

retention time were predicted by using ANN. Predictions of these parameters were

obtained with desired accuracy.

Shaikh and Al-Dahhan [102] compared the selected literature correlation and the ANN

model for the prediction of gas holdup in bubble column reactor. The standard

deviation of the ANN results for different column parameters was within 14% which

was still less than the other models. They further suggested the use of ANN for scale

up of he bubble column reactors. Sablani et al [103] developed ANN model capable of

explicitly calculating the friction factor for a non Newtonian fluid over a wide range

of Reynolds number. Among different architectures studies they found the maximum

average mean error to be about 3% for the laminar and turbulent regions. Fadare and

Ofidhe [104] developed artificial neural network for the prediction of friction factor in

pipe flow. The proposed model found accurate for prediction of factor using relative

roughness and Reynolds number as input parameters.

ANNs are good at pattern recognition, trend prediction, modeling, control, signal

filtering, noise reduction, image analysis, classification, and evaluation. In fact, the

uses for neural networks are so numerous and diverse that these applications may

seem to have nothing in common. However, they all share the ability to make

associations between known inputs and outputs by observing a large number of

examples. ANNs have been successfully applied in various fields of chemical

29

engineering which include, modeling of multiphase reactors [105], Process control [91,

106-109], Catalysis [110], Estimation of concentration of components in a mixture [108-113],

calculation of heat transfer coefficient [114], modeling of pump-mixer characteristics [114], Membrane separations [110], Reactor modeling [105, 116], waste water treatment [117].

The success of the ANN depends on the selection of the process variables, the quality

of the data and the type of algorithm used. The backpropagation [118-120] is the most

well known and widely among all types of ANN algorithms. The back propagation is

the multilayer feed forward network with different transfer functions in an artificial

neuron and a powerful learning rule. The learning rule is known as backpropagation,

which is kind of error minimization technique with backward error propagation.

ANN is attractive due to its information processing characteristic such as nonlinearity,

high parallelism, fault tolerance as well as capability to generalize and handle

imprecise information [118, 120]. These characteristics have made ANN suitable for

solving a variety of problems.

2.10 Critical Appraisal

The two phase systems of solid-liquid suspensions are inherently unstable. Sufficient

amount of literature is available on settling behaviours of different types of

suspensions for different ranges of particle Reynolds numbers. Among the

relationships for the single particle terminal settling velocity in concentrated

suspensions, Richardson and Zaki’s equation is confirmed and recommended by

several theoretical and experimental studies. From the available literature it is well

understood that, the hindered settling coefficient ‘n’ varies from suspension to

suspension. No unique value of ‘n’ is available for all suspensions. It varies from 3 to

5.1 for the suspensions of different types of solids. In the literature various drag

coefficient- particle Reynolds number (CD-Rep) relationships are available. The

available relationships contain two to five constants.

No settling data for the hindered settling coefficient ‘n’ of magnetite ore suspensions

is available in the literature. Because of the unstable nature of these two phase

systems the, available CD-Rep relationships are erroneous if applied to all types of

suspensions. Hence there is good scope for studying settling behaviour of magnetite

ore suspensions and to obtain the useful data on the ‘n’ values. From the experimental

30

data it would be possible to develop experimental CD-Rep relationship for magnetite

ore suspensions.

Rheological characteristics of the suspensions depend on various parameters. Particle

size and concentration of solids significantly influence the shear stress-shear rate

relationship and the relative viscosity of the suspensions. The effect of solids

concentration on the suspension rheology is not the same for all types of suspensions.

It depends on the nature and type of the solid particles and their surface

characteristics. Studies by Some suspensions show the increase in non Newtonian

behaviour with the increase in solids concentration, whereas the decrease in non

Newtonian behaviour of the suspensions also has been presented in some studies.

Same suspension also can show different rheological behaviours at different solids

concentrations and shear rates. Particle size effect on suspension rheology and relative

viscosity was studies by many workers. The earlier studies show increase in non

Newtonian behaviour and relative viscosity with the increase in particle size of the

solids in suspensions as well as decrease in non Newtonian behaviour and relative

viscosity with increased particle size.

Well established empirical equations are available in the literature to describe the flow

curves of the suspensions, but the suspensions of different types of solids particles can

not be presented by a same equation. Even for same suspensions different equations

were suggested by a few workers. For magnetite ore suspensions, to describe the

shear stress- shear rate relationship, equations such as power law, Bingham plastic

and Casson equation were proposed by earlier workers. For very dilute suspensions,

the relative viscosity can be predicted by Einstein’s formula. For concentrated

suspensions, numbers of equation are available in literature, but any of these

equations is not suitable for all types of suspensions. Different equations are suitable

for different type of suspensions. No such relationship for magnetite ore suspensions

was found in the literature.

Hence there is good scope studying rheological behaviour of the magnetite ore

suspensions, to investigate the effects of particle size and solids concentration on the

suspensions rheology and to find out a suitable equation to describe the flow curves. It

would be worth to know the effect of particle size on relative viscosity of magnetite

ore suspensions and to find out a suitable better fitting equation for the dependence of

relative viscosity on the solids concentration in the suspension. Further there is good

31

potential to develop artificial neural network models to describe the flow curves for

magnetite ore suspensions and the relative viscosity-solids volume fraction

relationships for the same.

References

1. Rushton, A. S. Ward and R. G. Holdich, “Solid-Liquid Filtration and Separation Technology”, Wiley-VCH Verlag GmbH, Weinheim, Germany, (1996)

2. J F Richardson and W N Zaki., “The Sedimentation of a Suspension of Uniform Spheres under Condition of Viscous Flow”, Chemical Engineering Science, 3, (1954), 66-73

3. S Mirza and J F Richardson, “Sedimentation of Suspensions of Particles of Two or More Sizes”, Chemical Engineering Science, 34, (1979), 447-454

4. E. Barnea, J. Mizrahi, “Generalized Approach to the Fluid Dynamics of Particulate Systems Part 1: General Correlation for Fluidization and Sedimentation in Solid Multiparticle Systems”, The Chemical Engineering Journal, 5, (1973), 171-189

5. E. Capes, “Particle Agglomeration and the Value of the Exponent n in the Richardson-Zaki Equation”, Powder Technology, 10, (1074), 303-306

6. R. M. Turian, T. W. Ma, F. L. G. Hsu and D. J. Sung, “Characterization, settling and rheology of concentrated fine particulate mineral slurries” Powder Technology, 93, (1997), 219-233

7 Sangkyun Koo, “Estimation of hindered settling velocity of suspensions”, Journal of Industrial and Engineering Chemistry, 15, (2009), 45–49

8 Garside and M.R. Al-Dibouni, “Velocity-voidage relationships for fluidization and sedimentation in solid-liquid systems”, Industrial and Engineering Chemistry Process Design and Development, 16, (1977), 206–214

9. Nian-Sheng Cheng , “Comparison of formulas for drag coefficient and settling velocity of spherical particles”, Powder Technology, 189, (2009), 395–398

10. T.E. Baldock,, M.R. Tomkinsa, P. Nielsena and M.G. Hughes, “Settling velocity of sediments at high concentrations”, Coastal Engineering, 51, (2004), 91–100

11. M.S. Selim, A.C. Kothari and R.M. Turian, “Sedimentation of multi-sized particles in concentrated suspensions”, A.I.Ch.E.Journal, 29, (1983), 1029–1038

32

12. M. Lali, A. S. Khare and J. B. Joshi, “Behaviour of Solid Particles in Viscous Non-Newtonian Solutions: Settling Velocity, Wall Effects and Bed Expansion in Solid-Liquid Fluidized Beds”, Powder Technology, 57, (1989), 39 – 50

13. Di Felice, R. and Parodi, E., “Wall effects on the sedimentation velocity of suspensions in viscous flow”, AIChE Journal, 42, (1996),. 927–931

14. Alfred W Francis, “Wall Effects in Falling Ball Method for Viscosity”, Journal of Applied Physics, 4, (1933),.403-406

15. Clift R, Grace J. R. and Weber M. E., “Bubbles, Drops and Particles”, Academic Press New York (1978)

16. R Di Felice, “A Relationship for the Wall Effect on the Settling Velocity of a Sphere at Any Flow Regime”, International Journal of Multiphase Flow, 22 (3), (1996), 527-533

17. Edward J. Wasp, John P Kenny and Ramesh Gandhi, “Solid-liquid Flow Slurry Pipeline Transportation-Bulk Materials Handling”, Trans Tech Publications¸ Cranfield, UK (1977)

18. Sumer M. Peker Serife S. Helvaci, “Solid–Liquid Two Phase Flow”, Elsevier Amsterdam, The Netherlands (2008)

19. M. Gilbert, L. Davis and D. “Altman, Velocity lag of particles in linearly accelerated combustion gases”, Jet Propulsion 25, (1955), 26-31

20. R. Turton and 0. Levenspiel, “A Short Note on the Drag Correlation for Spheres”, Powder Technology, 47, (1986), 83 – 86

21. A.R. Khan and J.F. Richardson, “The Resistance to Motion of a Solid Sphere in a Fluid” , Chemical Engineering Communications, 62(1– 6), pp.135 – 150 (1987)

22. Haider and 0. Levenspiel, “Drag Coefficient and Terminal Velocity of Spherical and Nonspherical Particles” Powder Technology, 58, (1989), 63 – 70

23. J. Zigrang and N. D. Sylvester , “An explicit equation for particle settling velocities in solid-liquid systems”, AIChE Journal, 27(6), (1981), 1043–1044

24. R. Turton and N. N. Clark, “An explicit relationship to predict spherical particle terminal velocity”, Powder Technology, 53, (1987), 127 – 129

25. R. H. Perry and C. H. Chilton, “Chemical engineers' handbook”, McGraw-Hill, New York, USA (1973)

26. R.L.C. Flemmer and C.L. Banks, “On the drag coefficient of a sphere”, Powder Technology, 48(3), (1986), 217-221

33

27. G. Saha, N.K. Purohit and A.K. Mitra, “Spherical particle terminal settling velocity and drag in Bingham liquids”, International Journal of Mineral Processing, 36 (3-4), (1992), 273-281

28. F. Concha and E. R. Almendra, “Settling velocities of particulate systems, 1. Settling velocities of individual spherical particles”, International Journal of Mineral Processing, 5 (4), (1979), 349-367

29. G. Venu Madhav and R. P. Chhabra, “Drag on non-spherical particles in viscous fluids”, International Journal of Mineral Processing, 43 (1-2), (1995), 15-29

30. P.P. Brown and D.F. Lawler, “Sphere drag and settling velocity revisited”, Journal of Environmental Engineering, 129 (3), (2003), 222–231

31. Harris J., “Rheology and non-Newtonian flow”, Longman, New York, USA (1977)

32. Bird, R.B., Stewart, W.E. and Lightfoot, E.N., “Transport Phenomena”, John Wiley & Sons, New York, USA (2001)

33. Malcom M Cross, “Rheology of non-Newtonian fluids: a new flow equation for pseudoplastic systems”, Journal of Colloid Science, 20, (1965), 417-437,

34. Malcom M Cross, “Rheology of viscoelastic fluids: elasticity determination from tangential stress management”, Journal of Colloid and Interface Science, 21, (1968), 84-90

35. Mewis J and Spaull A J B, “Rheology of concentrated dispersions”, Advances in Colloid l Interface Science, 6, (1976), 173-200

36. Carreau P. J., “Rheological equations from molecular network theories”, Transactions of Society of Rheology , 16(1), (1972), 99-127

37. Carreau P. J. and De Kee D., “ Review of some useful rheological equations”, Canadian Journal of Chemical Engineering, 57, (1979a), 3-15

38. Carreau P. J. and De Kee D., “Analysis of viscous behaviour of polymeric solutions”, Canadian Journal of Chemical Engineering, 57, (1979b), 135-140

39. Howard A Barnes, “A Handbook of Elementary Rheology”, Cambrian Printers, Llanbadarn Road, Aberystwyth, UK (2000)

40. Q.D. Nguyen and D.V. Boger, “Application of rheology to solving tailings disposal problems”, International Journal of Mineral Processing, 54, (1998), 217–233

41. S K Nicol and R J Hunter, “Some Rheological and electrokinetic properties of kaolinite suspensions”, Australian Journal of Chemistry, 23(11), (1970),

34

2177 – 2186

42. Cheng, N. S., and Law, A. W. K., “Exponential formula for computing effective viscosity”, Powder Technology, 129(1-3), (2003), 156– 160

43. Thomas D. G. "Transport characteristics of suspension: VIII. A note on the viscosity of Newtonian suspensions of uniform spherical particles." Journal of Colloid Science., 20, (1965), 267-277

44. G. S. Khodakov, “On suspension rheology”, Theoretical Foundations of Chemical Engineering, 38(4), (2004), 430–439

45. Batchelor, G. K., and Green, J. T., “The determination of the bulk stress in a suspension of spherical particles to order c2”, Journal of Fluid Mechanics., 56, (1972), 401-472

46. Kim, S., and Karrila, S. J., “Microhydrodynamics: principles and selected applications”, Butterworth-Heinemann, Boston, USA (1991)

47. V Ilic and N Phan-Thien, “Viscosity of concentrated suspensions of spheres, Rheological acta., 33, (1994), 283-281

48. Thomas, C. U., and Muthukumar, M., “Convergence of multiple scattering series for two-body hydrodynamic effects on shear viscosity of suspensions of spheres”, Journal of Chemical Physics, 94(6), (1991), 4557-4567.

49. T. B. Lewis and L. E. Nielsen, “Viscosity of dispersed and aggregated Suspensions of spheres”, Journal of Rheology, 12, (1968), 421-442

50. Bruce A. Firth and Robert J. Hunter, “Flow properties of coagulated colloidal suspensions : I. Energy dissipation in the flow units”, Journal of Colloid and Interface Science, 57(2), (1976), 248-256

51. Rutgers, J. “Relative viscosity of suspensions of rigid spheres in Newtonian Liqiud”, Reologica Acta, 2, (1962), 202-212

52. David Leightont and Andreas Acrivos, “Viscous resuspension”, Chemical Engineering Science, 41(6), (1986), 1377-1384

53. Barnes, H. A., “Shear-Thickening (``Dilatancy'') in suspensions of non-aggregating solid particles dispersed in Newtonian liquids”, Journal of Rheology, 33(2), (1989), 329-366

54. Chong, J.S., Christiansen, E.B. & Baer, A.D., “Rheology of concentrated suspensions”, Journal of Applied Polymer Science, 15, (1971), 2007-2021

55. Mooney, M, “The viscosity of concentrated suspension of spherical particles”, Journal of Colloid Science, 6, (1951), 162-170

56. Irvin M. Krieger and Thomas J. Dougherty, “A mechanism for non-

35

Newtonian flow in suspensions of rigid spheres”, Transactions of the Society of Rheology, 3, (1959), 137-152

57. Andrew Pusheng Ting and Ralph H. Luebbers, “Viscosity of suspensions of spherical and other isodimensional particles in liquids”, AIChE Journal, l3, (1957), 111–116

58. Dean Mo Liu, “Particle packing and rheological property of highly-concentrated ceramic suspensions: An determination and viscosity prediction”, Journal of Material Science, 35, (2000), 5503 – 5507

59. Metzner, A. B., “Rheology of suspensions in polymeric liquids.” Journal of Rheology, 29, (1985), 729-735

60. Quemada, D., “Rheology of concentrated disperse systems and minimum energy dissipation principle”, Rheologica Acta, 16, (1977), 82-94

61. Mingzhao He , Yanmin Wang and Eric Forssberg, “Parameter studies on the rheology of limestone slurries”, International Journal of Mineral Processing, 78 (2006) 63– 77

62. Mikulasek, P., Wakeman, R.J., Marchant, J.Q., 1997. The influence of pH and temperature on the rheology and stability of aqueous titanium dioxide dispersions. Chem. Eng. J. 67, 97–102

63. Nam-Sun Roh, Dae-Hyun Shin, Dong-Chan Kim and Jong-Duk Kim, “Rheological behaviour of coal-water Mixtures- 2. Effect of surfactants and temperature”, Fuel, 74, (1995) 1313-1318

64. Pradipta Kumar Senapati, Dibakar Panda and Ashutosh Parida, “Predicting Viscosity of Limestone–Water Slurry”, Journal of Minerals & Materials Characterization & Engineering, 8(3), (2009), 203-221

65. Shenoy A. V., “Drag reduction with surfactants at elevated temperatures”, Rheologica Acta, 15(11-12), (1976), 658-664

66. Lu-Cun Guo, Yao Zhang, Nozomi Uchida and Keizo Uematsu, “Influence of temperature on stability of aqueous alumina slurry containing polyelectrolyte dispersant”, Journal of the European Ceramic Society, 17(2-3), (1997), 345-350

67. Mishra S. K., Senapati P. K. and D. Panda, “Rheological Behavior of Coal-Water Slurry” Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 24(2), (2002), 159 – 167

68. Naik H.K, Mishra M. K, and Rao Karanamet, “The effect of drag reducing additives on the Rheological properties of fly-ash water suspensions at varying temperature environment”, Coal Combustion and Gasification Products, 1 (2009), 25-31

69. Lu-Cun Guo, Yao Zhang, Nozomi Uchida and Keizo Uematsu, “Influence

36

of temperature on stability of aqueous alumina slurry containing polyelectrolyte dispersant”, Journal of the European Ceramic Society, 17(2-3), (1997), 345-350

70. Yang Hua-Gui Li, Chun-Zhong, Gu, Hong-chen, Fang, Tu-Nan, “Rheological behavior of titanium dioxide suspensions” Journal of Colloid and Interface Science 236, (2001)96– 103

71. Renehan M.J., Pullum L., Lambrianidis J. and Bhattacharya S.N., “Effects of coarse particle size fractions on rheology of coal suspensions containing fine particles”, Tenth International Congress on Rheology, 2, (1988), 207-213

72. Hasan, A.R., Baria, D.N. and Rao, A.V., , “Rheological behaviour of Low-rank coal-water slurries”, Chemical Engineering Communications, 46(4-6), (1986), 227-240

73. Parkinson, C., S. Matsumoto, and P. Sherman, “The influence of particle-size distribution on the apparent of non-Newtonian dispersed systems”, Journal of Colloid and Interface Science, 33, (1970), 150–160

74. Keith H. Sweeny and Richard D. Geckler, “The Rheology of Suspensions”, Journal of Applied Physics, 25( 9), (1954), 1135-1144

75. D. N. Saraf and S. D. Khullar, “Some studies on the viscosity of settling suspensions”, The Canadian Journal of Chemical Engineering, 53(4), (1975), 449–452

76. F. W. A. M. Schreuder, A. J. G. Van Diemen and H. N. Stein, “Viscoelastic properties of concentrated suspensions”, Journal of Colloid and Interface Science, 111(1), (1986), 35-43

77. Eveson G F, "Rheology of disperse systems”, Pergamon Press, London, UK, (1959)

78. Frank L. Saunders, “Rheological properties of monodisperse latex systems: Flow curves of thickened latexes”, Journal of Colloid and Interface Science, 23(2), (1967), 230-236

79. Irvin M.Krieger, “Rheology of monodisperse latices”, Advances in Colloid and Interface Science, 3(2), (1972), 111-136

80. Heikki R. Laapas and Ulla-Riitta Lahtinen, “Thedetermination of particle size distribution using combined gravitational and centrifugal sedimentation analysis”, Particle & Particle Systems Characterization, 1(1-4), (1984), 127–131

81. Kawatra and Т. C. Eisele, “Proceedings of the Sixteenth International Mineral Processing Congress”, Elsevier Science Publishers BV, Amsterdam, (1988), 195-207

37

82. N. Mangesana, R.S. Chikuku, A.N. Mainza, I. Govender, A.P. van der

Westhuizen, and M. Narashima, “The effect of particle sizes and solids concentration on the rheology of silica sand based suspensions”, The Journal of The Southern African Institute of Mining and Metallurgy, 108, (2008), 237-243

83. J.S. Laskowski and J. Ralston, “Colloid chemistry in mineral processing”, Elsiever Science, Amsterdam, The Netherlands (1992)

84. H. D. Chandler; R. L. Jones, “Flow kinetics in concentrated suspensions of silica-iron (III) oxide-water”, Philosophical Magazine A, 59(3), (1989), 645–660

85. S. A. Ravishankar, Pradip, and N. K. Khosla, “Selective flocculation of iron oxide from its synthetic mixtures with clays: a comparison of polyacrylic acid and starch polymers”, International Journal of Mineral Processing, 43(3-4), (1995), 235-247

86. Pawlik, M. and Laskowski J.S., “Stabilization of Mineral Suspensions by Guar Gum in Potash Ore Flotation Systems” Canadian Journal of Chemical Engineering, 84, (2006), 532-538

87. Ray, C .and Klindworth, K. K., “Neural networks for agrichemical vulnerability assessment of rural private wells”, Journal of Hydrologic Engineering, 5, (2000), pp.162-172

88. Silverman, D., & Dracup, J. A., “Artificial neural networks and long-range precipitation prediction in California”, Journal of Applied Meteorology, 39, (2000), 57-63

89. Cigizoglu, H. K., “Incorporation of ARMA models into flow forecasting by artificial neural networks”, Environmetrics, 14, pp.417-421 (2003)

90. Cigizoglu, H. K., “Estimation, forecasting and extrapolation of flow data by artificial neural networks”, Hydrological Sciences Journal, 48, (2003), 349-359

91. Hussain, M. A., “Review of the applications of neural networks in chemical process control-simulation and online implementation”, Artificial Intelligence in Engineering, 13, (1999), 55-63

92. Huang, K., Chen, F. and Lu, D., “Artificial neural network-aided design of a multi-component catalyst for methane oxidative coupling”, Applied Catalysis A, 219, (2001), 61-67

93. Serra, J. M., Corma, A., Chica, A., Argente, E. and Botti, V., “Can artificial neural networks help the experimentation in catalysis?”, Catalysis Today, 81, (2003), 393-399

38

94. Chakraborty, M., Bhattacharya, C. and Dutta, S., “Studies on the applicability of artificial neural network (ANN) in emulsion liquid membranes”, Journal of Membrane Science, 220, (2003), 155-161

95. Sharma, R., Singhal, D., Ghosh, R., and Dwivedi, A., “Potential applications of artificial neural networks to thermodynamics: Vapor–liquid equilibrium predictions”, Computers and Chemical Engineering, 23, (1999), 385-391

96. Mehmet B., “The use of neural networks on VLE data prediction” Journal of Scientific and Industrial Research, 63 (4), (2004), 203-312

97. Melkon Tatlier, H. Kerem Cigizoglu, and Ays¸Erdem-Senatalar, “Artificial neural network methods for the estimation of zeolite molar compositions that form different reaction mixtures”, Computers and Chemical Engineering, 30, (2005), 137–146

98. Bhat N and McAvoy T.J., “Use of neural nets for dynamic modelling and control of chemical process systems”, Computers and Chemical Engineering, 14(4-5), (1990), 573-583

99. Willis, M., Montague, G.A., Massimo, C.D., Tham, M.T. and Morris, A.J., “Artificial Neural Networks in Process Estimation and Control”, Automatica, 28(6), (1992), 1181-1187

100. Pollard J.F., Broussard M.R., Garrison D.B. and San K.Y., “Process Identification Using Neural Networks”, Computers and Chemical Engineering, 16(4), (1992), 253- 270

101. Rajasimman, M., Govindarajan, L. and Karthikeyan, C., “Artificial Neural Network Modeling of an Inverse Fluidized Bed Bioreactor”, International Journal of Environment Research, 3(4), (2009), 575-580

102. Ashfaq Shaikh and Muthanna Al-Dahhan, “A new methodology for hydrodynamic similarity in bubble columns”, The Canadian Journal of Chemical Engineering, 88(4), (2010), 503–517

103. Sablani S. S., “A neural network approach for non-iterative calculation of heat transfer coefficient in fluid-particle system”, Chemical Engineering and Processing, 40, (2001), 363-371

104. D.A. Fadare and U.I. Ofidhe, “Artificial Neural Network Model for Prediction of Friction Factor in Pipe Flow”, Journal of Applied Sciences Research, 5(6), (2009), 662- 670

105. Laurentiu A. Tarca, Bernard P.A. Grandjean and Faıcal Larachi, “Reinforcing the phenomenological consistency in artificial neural network modeling of multiphase reactors”, Chemical Engineering and Processing, 42, (2003), 653-676

39

106. Soundar Ramchandran and R Russel Rhinhart, “A very simple structure for neural network control of distillation”, Journal of Process Control, 5(2), (1995), 115-128

107. J. Fernandez de Canete, S. Gonzalez-Perez, and P. del Saz-Orozco, “Artificial Neural Networks for Identification and Control of a Lab-Scale Distillation Column using LABVIEW”, World Academy of Science, Engineering and Technology, 47, (2008), 64-69

108. Zeybek Z., Yuce S., Hapoglu H. and Alpbaz M., “Adaptive heuristic temperature control of a batch polymerization reactor”, Chemical Engineering and Processing, 43, (2004), 911-918

109. Ngu C. W. and Hussain M. A., “Hybrid neural network- prior knowledge model in temperature control of a semi batch polymerization process”, Chemical Engineering and Processing, 43, (2004), 559-567

110. Yan Liu Yang Liu Dazhuang Liu Tao Cao, Sen Han and Genhui Xu, “Design of CO2 hydrogenation catalyst by an artificial neural network”, Computers and Chemical Engineering, 25, (2001), 1711–1714

111. Robert R. Jensen, Shankar Karki, Hossein Salehfar, “Artificial neural network based estimation of mercury speciation in combustion flue gases”, Fuel Processing Technology, 85, (2004), 451– 462

112. Tzu-Ming Yeh, Ming-Chieh Huang, Chi-Tsung Huang , “Estimate of process composition and plant wide control from multiple secondary measurements using artificial neural networks”, Computers and Chemical Engineering, 27, (2003), 55-72

113. Obodeh O and Ajuwa, C. I., “Evaluation of artificial neural network performance in predicting diesel engine NOx emissions”, European Journal of Scientific Research, 43(4), (2009) , 642-653

114. Sing K. K., Shenoy K. T., Mahendra A. K. and Ghosh S. K., “Artificial neural network based modeling of head and power characteristics of pump-mixer”, Chemical Engineering Science, 59, (2004), 2937-2944

115. Bowen W.R., Jones W. R. and Yusef H. N., “Prediction of the rate of cross flow membrane ultrafiltration of colloids: a neural network approach”, Chemical Engineering Science, 53(22), (1998), 3793-3799

116. Saxen B. J. and Saxen H., “A neural network based model of bio-reaction kinetics”, Canadian Journal of Chemical Engineering, 74, (1996), 124-129

117. Gontaraski C. A., Rodrigues D. R., Mori M. and Prenem L. F., “Simulation of an industrial waste water treatment plant using artificial neural networks”, Computers and Chemical Engineering, 24, (2000), 1719-1728

40

118. Boughman D. R. and Liu Y. A., “Neural networks in bioprocessing and chemical engineering”, Academic Press, London, UK (1995)

119. Tambe S. S., Kulkarni B. D. and Deshpande P. B., “Elements of artificial neural network with selected applications in chemical engineering and chemical and biological sciences”, Simulation and Advanced control Inc. USA. (1996)

120. Lumin Fu, “Neural networks in computer intelligence”, McGraw Hill Inc. New York, USA (1996)