MIXING. CHARACTERISTICS OF MIXTURES (1) ► Mixing is the dispersing of components, one throughout the other. ► Ideally, a mixing process begins with the

MIXINGMIXING

CHARACTERISTICS OF MIXTURES CHARACTERISTICS OF MIXTURES (1)(1)

►Mixing is the dispersing of components, one Mixing is the dispersing of components, one throughout the other. throughout the other.

► Ideally, a mixing process begins with the Ideally, a mixing process begins with the components, grouped together in some components, grouped together in some container, but still separate as pure container, but still separate as pure components. components.

► The frequency of occurrence of the The frequency of occurrence of the components is proportional to the fractions components is proportional to the fractions of these components in the whole container. of these components in the whole container.

CHARACTERISTICS OF MIXTURES CHARACTERISTICS OF MIXTURES (2)(2)

►As mixing then proceeds, samples will As mixing then proceeds, samples will increasingly contain more of the increasingly contain more of the components, in proportions approximating components, in proportions approximating to the overall proportions of the to the overall proportions of the components in the whole container. components in the whole container.

►Complete mixing could then be defined as Complete mixing could then be defined as that state in which all samples are found that state in which all samples are found to contain the components in the same to contain the components in the same proportions as in the whole mixture. proportions as in the whole mixture.

MEASUREMENT OF MIXING (1)MEASUREMENT OF MIXING (1)

►The assessment of mixed small The assessment of mixed small volumes, which can be taken or volumes, which can be taken or sampled, is what mixing measurement sampled, is what mixing measurement is all about. is all about.

►Sample compositions move from the Sample compositions move from the initial state to the mixed state, and initial state to the mixed state, and measurements of mixing must reflect measurements of mixing must reflect this. this.

MEASUREMENT OF MIXING (2)MEASUREMENT OF MIXING (2)

► If the sample is so large that it includes the If the sample is so large that it includes the whole mixture, then the sample composition whole mixture, then the sample composition is at once the mean composition and there is at once the mean composition and there remains no mixing to be done. remains no mixing to be done.

► If it were possible to take samples of If it were possible to take samples of molecular size, then every sample would molecular size, then every sample would contain only one or other of the components contain only one or other of the components in the pure state and no amount of mixing in the pure state and no amount of mixing would make any difference. would make any difference.

PARTICLE MIXING (1)PARTICLE MIXING (1)

► The mixing of particles varying substantially The mixing of particles varying substantially in size or in density presents special in size or in density presents special problems, as there will be gravitational problems, as there will be gravitational forces acting in the mixer which will tend to forces acting in the mixer which will tend to segregate the particles into size and density segregate the particles into size and density ranges.ranges.

► In such a case, initial mixing in a mixer may In such a case, initial mixing in a mixer may then be followed by a measure of (slow then be followed by a measure of (slow gravitational) un-mixing and so the time of gravitational) un-mixing and so the time of mixing may be quite critical. mixing may be quite critical.

PARTICLE MIXING (2)PARTICLE MIXING (2)

►Mixing is simplest when the quantities that Mixing is simplest when the quantities that are to be mixed are roughly in the same are to be mixed are roughly in the same proportions.proportions.

► In cases where very small quantities of one In cases where very small quantities of one component have to be blended uniformly into component have to be blended uniformly into much larger quantities of other components.much larger quantities of other components.

► In planning the mixing process it would be In planning the mixing process it would be wise to take analyses through each stage of wise to take analyses through each stage of mixing, but once mixing times had been mixing, but once mixing times had been established it should only be necessary to established it should only be necessary to make check analyses on the final product. make check analyses on the final product.

RATES OF MIXING (1)RATES OF MIXING (1)

►Once a suitable measure of mixing has been Once a suitable measure of mixing has been found, it becomes possible to discuss rates found, it becomes possible to discuss rates of accomplishing mixing. of accomplishing mixing.

► It has been assumed that the mixing index It has been assumed that the mixing index ought to be such that the rate of mixing at ought to be such that the rate of mixing at any time, under constant working conditions any time, under constant working conditions such as in a well-designed mixer working at such as in a well-designed mixer working at constant speed, ought to be proportional to constant speed, ought to be proportional to the extent of mixing remaining to be done the extent of mixing remaining to be done at that time. at that time.


►That is,That is, d dMM/d/dtt = = KK[(1- ([(1- (MM))] ))]

where (where (MM) is the mixing index and ) is the mixing index and KK is a is a constant, and on integrating from constant, and on integrating from tt = 0 to = 0 to t = tt = t during which ( during which (MM) goes from 0 to () goes from 0 to (MM),),

[(1 - ([(1 - (MM))] = e))] = e-Kt-Kt

or (M) = 1 - eor (M) = 1 - e-Kt-Kt


► This exponential relationship, using (This exponential relationship, using (MM) as ) as the mixing index, has been found to apply in the mixing index, has been found to apply in many experimental investigations at least many experimental investigations at least over two or three orders of magnitude of over two or three orders of magnitude of ((MM). ).

► In such cases, the constant In such cases, the constant KK can be related can be related to the mixing machine and to the conditions to the mixing machine and to the conditions and it can be used to predict, for example, and it can be used to predict, for example, the the times required to attain a given times required to attain a given degree of mixingdegree of mixing. .

ENERGY INPUT IN MIXINGENERGY INPUT IN MIXING

►There is no necessary connection There is no necessary connection between energy consumed and the between energy consumed and the progress of mixing.progress of mixing.

► In well-designed mixers energy input In well-designed mixers energy input does relate to mixing progress, though does relate to mixing progress, though the actual relationship has normally to the actual relationship has normally to be determined experimentally. be determined experimentally.

LIQUID MIXING (1)LIQUID MIXING (1)

►Most of the information that is Most of the information that is available concerns the power available concerns the power requirements for the most commonly requirements for the most commonly used liquid mixer - some form of used liquid mixer - some form of paddle or propeller stirrerpaddle or propeller stirrer. .

►Measurements have been made in Measurements have been made in terms of dimensionless ratios involving terms of dimensionless ratios involving all of the physical factors that all of the physical factors that influence influence power consumptionpower consumption. .


► The results have been correlated in an The results have been correlated in an equation of the form equation of the form

(Po) = (Po) = KK(Re)(Re)nn(Fr)(Fr)mm

where where (Re) = ((Re) = (DD22NN//µµ) )

(Po) = ((Po) = (PP//DD55NN33) ) the the Power numberPower number (relating drag forces to inertial (relating drag forces to inertial

forces) forces)


(Fr) = ((Fr) = (DNDN22//gg) ) the the Froude numberFroude number (relating inertial forces to those of gravity)(relating inertial forces to those of gravity)

DD the diameter of the propeller, the diameter of the propeller, NN the rotational frequency of the the rotational frequency of the propeller propeller (rev/sec), (rev/sec), r r the density of the liquid, the density of the liquid, m m the viscosity of the liquid and the viscosity of the liquid and PP the power consumed by the propeller. the power consumed by the propeller.


►The Froude number correlates the The Froude number correlates the effects of gravitational forces and it effects of gravitational forces and it only becomes significant when the only becomes significant when the propeller disturbs the liquid surface. propeller disturbs the liquid surface.

►Below Reynolds numbers of about 300, Below Reynolds numbers of about 300, the Froude number is found to have the Froude number is found to have little or no effect, so that little or no effect, so that

(Po) = (Po) = KK(Re)(Re)nn


► Experimental results from the work of Experimental results from the work of Rushton are shown plotted in Rushton are shown plotted in Fig. 2.1.Fig. 2.1.

Figure 2.1 Performance of propeller mixersFigure 2.1 Performance of propeller mixersAdapted from Rushton (1950)Adapted from Rushton (1950)


► Unfortunately, general formulae have not Unfortunately, general formulae have not been obtained, so that the results are been obtained, so that the results are confined to the particular experimental confined to the particular experimental propeller configurations that were used. propeller configurations that were used.

► In cases in which experimental results are not In cases in which experimental results are not already available, the best approach to the already available, the best approach to the prediction of power consumption in propeller prediction of power consumption in propeller mixers is to use physical models, measure the mixers is to use physical models, measure the factors, and then use the equation for scaling factors, and then use the equation for scaling up the experimental results. up the experimental results.


EXAMPLE Blending vitamin concentrate into EXAMPLE Blending vitamin concentrate into molassesmolassesVitamin concentrate is being blended into molasses and Vitamin concentrate is being blended into molasses and it has been found that satisfactory mixing rates can be it has been found that satisfactory mixing rates can be obtained in a small tank 0.67 m diameter, height 0.75 obtained in a small tank 0.67 m diameter, height 0.75 m,with a propeller 0.33 m diameter rotating at 450 rev m,with a propeller 0.33 m diameter rotating at 450 rev minmin-1-1. If a large-scale plant is to be designed which will . If a large-scale plant is to be designed which will require a tank 2 m diameter, what will be suitable require a tank 2 m diameter, what will be suitable values to choose for tank depth, propeller diameter and values to choose for tank depth, propeller diameter and rotational speed, if it is desired to preserve the same rotational speed, if it is desired to preserve the same mixing conditions as in the smaller plant? What would mixing conditions as in the smaller plant? What would be the power requirement for the motor driving the be the power requirement for the motor driving the propeller? Assume that the viscosity of molasses is 6.6 propeller? Assume that the viscosity of molasses is 6.6 N s mN s m-2-2 and its density is 1520 kg m and its density is 1520 kg m-3-3. .

MIXING EQUIPMENT (1)MIXING EQUIPMENT (1)

►Possibly the easiest way in which to Possibly the easiest way in which to classify mixers is to divide them classify mixers is to divide them according to whether they mix liquids, according to whether they mix liquids, dry powders, or thick pastes. dry powders, or thick pastes.

MIXING EQUIPMENT (2)MIXING EQUIPMENT (2)LIQUID MIXERSLIQUID MIXERS

► For the deliberate mixing of liquids, the For the deliberate mixing of liquids, the propeller mixer is probably the most propeller mixer is probably the most common and the most satisfactory. In using common and the most satisfactory. In using propeller mixers, it is important to avoid propeller mixers, it is important to avoid regular flow patterns such as an even swirl regular flow patterns such as an even swirl round a cylindrical tank, which may round a cylindrical tank, which may accomplish very little mixing. accomplish very little mixing.

► To break up these streamline patterns, To break up these streamline patterns, baffles are often fitted, or the propeller may baffles are often fitted, or the propeller may be mounted asymmetrically. be mounted asymmetrically.

MIXING EQUIPMENT (3)MIXING EQUIPMENT (3)LIQUID MIXERSLIQUID MIXERS

► Various baffles can be used and the placing Various baffles can be used and the placing of these can make very considerable of these can make very considerable differences to the mixing performances. differences to the mixing performances.

► It is tempting to relate the amount of power It is tempting to relate the amount of power consumed by a mixer to the amount of consumed by a mixer to the amount of mixing produced, but there is no necessary mixing produced, but there is no necessary connection and very inefficient mixers can connection and very inefficient mixers can consume large amounts of power. consume large amounts of power.

MIXING EQUIPMENT (4)MIXING EQUIPMENT (4)POWDER&PARTICLE MIXERSPOWDER&PARTICLE MIXERS

►The essential feature in these mixers The essential feature in these mixers is to displace parts of the mixture with is to displace parts of the mixture with respect to other parts. respect to other parts.

►The ribbon blender, for example, The ribbon blender, for example, consists of a trough in which rotates a consists of a trough in which rotates a shaft with two open helical screws shaft with two open helical screws attached to it, one screw being right-attached to it, one screw being right-handed and the other left-handed. handed and the other left-handed.

MIXING EQUIPMENT (5)MIXING EQUIPMENT (5)POWDER&PARTICLE MIXERSPOWDER&PARTICLE MIXERS

►As the shaft rotates sections of the As the shaft rotates sections of the powder move in opposite directions powder move in opposite directions and so particles are vigorously and so particles are vigorously displaced relative to each other. displaced relative to each other.

►A commonly used blender for powders A commonly used blender for powders is the double-cone blender in which is the double-cone blender in which two cones are mounted with their two cones are mounted with their open ends fastened together and they open ends fastened together and they are rotated about an axis through their are rotated about an axis through their common base. common base.

MIXING EQUIPMENT (6)MIXING EQUIPMENT (6)DOUGH & PASTE MIXERSDOUGH & PASTE MIXERS

►Dough and pastes are mixed in machines Dough and pastes are mixed in machines that have, of necessity, to be heavy and that have, of necessity, to be heavy and powerful. powerful.

► Because of the large power requirements, it Because of the large power requirements, it is particularly desirable that these machines is particularly desirable that these machines mix with reasonable efficiency, as the power mix with reasonable efficiency, as the power is dissipated in the form of heat, which may is dissipated in the form of heat, which may cause substantial heating of the product. cause substantial heating of the product.

► Such machines may require jacketing of the Such machines may require jacketing of the mixer to remove as much heat as possible mixer to remove as much heat as possible with cooling water.with cooling water.

MIXING EQUIPMENT (7)MIXING EQUIPMENT (7)DOUGH & PASTE MIXERSDOUGH & PASTE MIXERS

► Another type of machine employs very Another type of machine employs very heavy contra-rotating paddles, whilst a heavy contra-rotating paddles, whilst a modern continuous mixer consists of an modern continuous mixer consists of an interrupted screw which oscillates with both interrupted screw which oscillates with both rotary and reciprocating motion between rotary and reciprocating motion between pegs in an enclosing cylinder. pegs in an enclosing cylinder.

► The important principle in these machines is The important principle in these machines is that the material has to be divided and that the material has to be divided and folded and also displaced, so that fresh folded and also displaced, so that fresh surfaces recombine as often as possible.surfaces recombine as often as possible.

COAGULATION/COAGULATION/FLOCCULATIONFLOCCULATION

► In coagulation operations, a chemical In coagulation operations, a chemical substance is added to an organic substance is added to an organic colloidal suspension to cause its colloidal suspension to cause its destabilization by the reduction of destabilization by the reduction of forces that keep them apart. forces that keep them apart.

► It involves the reduction of surface It involves the reduction of surface charges responsible for particle charges responsible for particle repulsions. repulsions.

►This reduction in charge causes This reduction in charge causes flocculation (agglomeration). flocculation (agglomeration).


►Particles of larger size are then settled Particles of larger size are then settled and clarified effluent is obtained. and clarified effluent is obtained.

►A diagram of a coagulation-flocculation A diagram of a coagulation-flocculation and settling of a wastewater is shown and settling of a wastewater is shown in Figure 2.2. in Figure 2.2.


POWER CURVESPOWER CURVES

Documents

MIXING. CHARACTERISTICS OF MIXTURES (1) ► Mixing is the dispersing of components, one throughout the other. ► Ideally, a mixing process begins with the