Granulation: Endpoint Determination and Scale-Up
by Michael Levin, Ph.D.

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Encyclopedia of Pharmaceutical Technology (Third Edition)


Factors in Wet Granulation    Additional Factors    Active Forces    

Why Monitor a Mixer?    

Endpoint Determination    Benefits of Mixer instrumentation    Mixer Measurements

Power Consumption    Impeller Torque    Torque vs. Power    Frequency Analysis

Method of Binder Addition    End Point Optimization    End Point Scale-Up

Dimensional Analysis    Froude Numbers   

End Point Scale-Up using Dimensional Analysis

Equipment Used in References     List of Symbols    Literature References



In addition to active ingredients, formulations are complex mixtures of diluents, binders, disintegrants, surface active agents, glidants, lubricants, colorants, coating substances, surfactants and many other raw materials that impart different properties to the final solid dosage product. Granulation is often required to improve the flow of powder mixtures and mechanical properties of tablets.  Granules are usually obtained by adding liquids (binder or solvent solutions).  Larger quantities of granulating liquid produce a narrower particle size range and coarser and harder granules, i.e. the proportion of fine granulate particles decreases.  The optimal quantity of liquid needed to get a given particle size should be known in order to keep a batch-to-batch variations to a minimum. Wet granulation is used to improve flow, compressibility, bio-availability, homogeneity, electrostatic properties, and stability of solid dosage forms.          

The particle size of the granulate is determined by the quantity and feeding rate of granulating liquid. Wet granulation is used to improve flow, compressibility, bio-availability, and homogeneity of low dose blends, electrostatic properties of powders, and stability of dosage forms.

This review is limited to a wet granulation process in low and high shear mixing devices where a low viscosity liquid (usually water) is added to a powder blend containing binder that was dry mixed with the rest of the formulation.  Due to time constraints, the following subjects will be excluded: melt granulation, fluid bed granulation, dry mixing, liquid binder addition, and high viscosity binders.

Let me just mention in passing that wet massing in a high-shear mixing is frequently compared to fluid bed mixing and to roller compaction technique, for example [6], and the results seem to be formulation dependent. 

For the comparison of high and low shear granulator performance, see, e.g. [115].  Compared to high shear granulation, low shear or fluid bed process requires less fluid binder, resulting in a shorter drying time, but also in a less cohesive material.

The generally known facts about types of mixers and measurement instruments available in the field will be briefly summarized in the following slides.  For an excellent review of the wet granulation process, equipment and variables see Holm [47].

Factors in Wet Granulation include:

§       Agglomeration

§       Shearing and compressing action of the impeller

§       Mixing, granulation and wet massing

§       Possibility of overgranulation due to excessive wetting

§       Possibility of producing low porosity granules

§       Liquid bridges

§       Coalescence

§       Breakage of the bonds

Due to rapid densification and agglomeration that are caused by the shearing and compressing action of the impeller in a high-shear single pot system, mixing, granulation and wet massing can be done relatively quickly and efficiently.   The dangers lie in a possibility of overgranulation due to excessive wetting and producing low porosity granules thus affecting the mechanical properties of the tablets.

As the liquid bridges between the particles are formed, granules are subjected to coalescence alongside with some breakage of the bonds. 

Additional Factors in Wet Granulation:

§       Specific surface area

§       Moisture content

§       Liquid saturation

§       Intragranular porosity

§       Heating

§       Evaporation

§       Mean granule size

§       Apparent viscosity

It stands to reason that mean granule size is strongly dependent on the specific surface area of the excipients, as well as the moisture content and liquid saturation of the agglomerate.

During the wet massing stage, granules may increase in size to a certain degree while the intragranular porosity goes down.  However, some heating and evaporation may also take place leading to a subsequent decrease in the mean granule size, especially in small-scale mixers.

Load on the main impeller is indicative of granule apparent viscosity and wet mass consistency.

The following forces act on the particles:

§       acceleration (direct impact of the impeller),

§       centrifugal,

§       centripetal, and

§       friction

Why Monitor a Mixer?

·       Binder addition rate controls  granule density

·       Impeller speed control granule size and granulation rate

·       End point controls the mix consistency and reproducibility

These statements are substantiated in [18].  Other factors that affect the granule quality include spray position and spray nozzle type, and, of course, the product composition.

Such variables as mixing time and bowl or product temperature are not independent factors in the process but rather are responses of the primary factors listed above.

Endpoint Determination

The formulator can define endpoint as a target particle size mean or distribution, or in terms of granulate viscosity or density.  It has been shown [26] that once you have reached the desired endpoint, the granule properties and the subsequent tablet properties are very similar regardless of the granulation processing factors, such as impeller or chopper speed or binder addition rate.  This can be called “the principle of equifinality”.

The ultimate goal of any measurement in a granulation process is to estimate viscosity and density of the granules, and, perhaps, to obtain an indication of the particle size mean and distribution.  One of the ways to obtain this information is by measuring load on the main impeller.

Benefits of Mixer instrumentation:

·       Machine Troubleshooting

Ø     detect worn-out gears and pulleys

Ø     identify mixing and binder irregularities

·       Formulation Fingerprints

Ø     batch record becomes a batch and mix ID

·       Batch Reproducibility

Ø     use end point to achieve consistency

·       Process Optimization

Ø     raw material evaluation

Ø     ideal end point determination

·       Use of experimental design to minimize the effort

·       Process Scale-Up

Ø     move the end-point value along the scale-up path

Mixer Measurements:

Conductivity of the damp mass [118] measures uniformity of liquid distribution and packing density.

Probe vibration analysis [120, 121] requires a specially constructed probe that includes a target plate attached to an accelerometer (in-process monitoring).  This measurement is based on the theory that increasing granule size results in the increase of the acceleration of agglomerates striking the probe target.  The method has a potential for granulation monitoring and end-point control.

Boots Diosna Probe measures densification and increase of size of granules (changes in momentum of granules moving with constant velocity due to a mass change of the granules) [53].  Did not gain popularity because of its invasive nature.

Laser beam diffraction in free-flowing systems could be used in-process by creating a product loop similar to those available for the fluid bed granulators and measuring the reflection of the beam and losses due to diffusion [48].

Current  in DC motors can be used as some indication of the load on the main impeller because torque T is proportional to current in some intervals [19] and therefore a current meter (ammeter) can be used for small scale direct current (DC) motors.

However, for alternating current (AC) motors (most often used in modern mixers), there may be no significant change in current as motor load varies up to 50% of full scale.  At larger loads, current draw may increase but this increase is not linearly related to load, and, consequently, current is completely ineffective as a measurement of load.

Voltage measurement has no relation to load.

Capacitance sensor [20, 21, 32, 33, 122] responds to moisture distribution and granule formation. It provided similar endpoints (based on the total voltage change) under varying rates of agitation and liquid addition. Capacitance sensor can be threaded into an existing thermocouple port for in-process monitoring.

Chopper Speed has no significant effect on the mean granule size [40], [41].

Impeller or Shaft Speed could be used as some indication of the work being done on the material [5].

Motor Slip [124, 125, 5] is the difference between rotational speed of an idle motor and motor under load.  Motor slip measurements, although relatively inexpensive, do not offer advantages over the power consumption measurements and did not gain popularity, probably because the slip is not linearly related to load [30] despite some claims to the contrary.

Impeller Tip Speed corresponds to shear rate and has been used as a scale-up parameter in fluid mixing [84, 97].  For processing of lactose granulations in Gral mixers, however, it was shown by Horsthuis et al. [49] that the same tip speed did not result in the same end point (in terms of particle size distribution).  These findings were contradicted by other studies in Fielder mixers indicating that, for a constant tip speed, successful scale-up is possible when liquid volume is proportional to the batch size and wet massing time is related to the ratio of impeller speeds [97].

Relative Swept Volume, that is, the volume swept by the impeller (and chopper) per unit time, divided by the mixer volume, has been suggested as a scale-up factor [107, 106, 112].  This parameter is related to work done on the material and was studied extensively at various blade angles [46]. 

Higher swept volume leads to higher temperature and denser granules.

However, it was shown by Horsthuis et al. [49] that the same relative swept volume did not result in the same end point (in terms of particle size distribution).

Product and jacket temperature is usually measured by thermocouples.  These response variables are controlled by a variety of factors, notably, the speed of the main impeller and the rate of binder addition.

The most popular measurements are direct and reaction torque, and the power consumption of the main motor. In the following slides we will examine the benefits and relative disadvantages of the torque and power measurements.

Power  Consumption of the main mixer motor is a relatively inexpensive measurement.  It is done by a watt transducer or a power cell utilizing Hall effect.

Power  consumption of the impeller motor for endpoint determination and scale-up is widely used [69, 71, 72, 70, 66, 122, 131, 9, 20, 42, 43, 56, 100, 113, 119, 133] because the measurement is inexpensive, it does not require extensive mixer modifications and is well correlated with granule growth [100].  Mean granule size of a granulation does not vary linearly with the absolute value of the power consumption of the motor but intragranular porosity does show some correlation with power consumption [100].

Power is a product of

·       Current

·       Voltage

·       Power factor

Power is proportional to load and reflects system performance. The main problem with power consumption measurements is that this variable reflects the overall mixer performance and mixer motor efficiency, as well as the load on the main impeller. 

Up to 30% of the power consumption of a motor can be attributed to no-load losses due to windage (by cooling fan and air drag), friction in bearings, and core losses that comprise hysteresis and eddy current losses in the motor magnetic circuit.  Load losses include stator and rotor losses (resistance of materials used in the stator, rotor bars, magnetic steel circuit) and stray load losses (current losses in the windings) [39].

Attempts to use a no-load (empty bowl, or dry mix) values as a baseline may be confounded by a possible nonlinearity of friction losses with respect to load [25]. As the load increases, so does the current draw of the motor.  This results in heat generation that further impacts the power consumption [30].  A simple test might be to run an empty mixer for several hours and see the shift in the baseline.  Also, as the motor efficiency drops, the baseline most definitely shifts with time.

Motor power consumption is non-linearly related to the power that is transmitted to the shaft [47] and the degree of this non-linearity could only be “guestimated”.      

In the mixing process, changes in torque on the blades and power consumption occur as a result of change in the cohesive force or the tensile strength of the agglomerates in the moistened powder bed.

Direct Impeller Torque measurements require installation of strain gages on the impeller shaft or on the coupling between the motor and impeller shaft.  Since the shaft is rotating, a device called slip ring is used to transmit the signal to the stationary data acquisition system.

Impeller torque is an excellent in-line measure of the load on the main impeller [12, 20, 21, 35, 127, 100] and was shown to be more sensitive to high frequency oscillations than power consumption [20, 56].

Torque Rheometer is an off-line technique of measuring rheological properties of the granulation.  It has been extensively used for endpoint determination [38, 37, 63, 65, 87, 102, 114]

Reaction torque is a less expensive alternative and is recommended for mixers that have the motor and impeller shafts axially aligned (in this case it is equal to direct torque and opposite in sign). By the third law of Newton, for every force there is a counter-force, collinear, equal and opposite in direction. As the impeller shaft rotates, the motor tries to rotate in the opposite direction, but it does not because it is bolted in place.  The reaction torque transducer can measure the tensions in the stationary motor base.

Planetary mixer instrumentation for direct torque measurement does not substantially differ from that of a high shear mixer.  Engineering design should only take into account the planetary motion in addition to shaft rotation.

Other possibilities:

When the agglomeration process is progressing very rapidly, neither power consumption nor torque on the impeller may be sensitive enough to adequately reflect changes in the material.  Some investigators feel that other measurements, such as torque or force on the impeller blades may be better suited to monitor such events.

Torque vs. Power

Power consumption is easier to measure since wattmeters are inexpensive and can be installed with almost no downtime.

·       Power may not be sensitive enough for specific products or processing conditions.

·       Wear and tear of mixer and motor may cause power fluctuations.

·       Power baseline may shift with load.

·       Torque is sensing higher frequency events due to material impact on the impeller.

Although the motor power consumption is strongly correlated with the torque on the impeller [56], it is less sensitive to high frequency oscillations caused by direct impact of particles on the impeller as evidenced by FFT technique [20].

Impeller power consumption (as opposed to motor power consumption) is directly proportional to torque multiplied by the rotational speed of the impeller. The power consumption of the mixer motor differs from that of the impeller by the variable amount of power draw imposed by various sources (mixer condition, transmission, gears, couplings, motor condition, etc.).










These are the classical power and torque profiles that start with a dry mixing stage, rise steeply with binder solution addition, level off into a plateau, and then exhibit overgranulation stage. The power and torque signals have similar shape and are strongly correlated. The pattern shows a plateau region where power consumption or torque is relatively stable.

Based on the theory by Leuenberger [9, 69-72], useable granulates can be obtained in the region that starts from the peak of the signal derivative with respect to time and extends well into the plateau area. The peak of the derivative indicates the inflection point of the signal.  Prior to this point, a continuous binder solution addition may require variable quantities of liquid.  After that point, the process is well defined and the amount of binder solution required to reach a desired endpoint may be more or less constant.

It seems that monitoring torque or power can fingerprint not only the product, but the process and the operators as well. A number of publications relate to practical experience of operators on the production floor ([126], [133],[78], [95] ).

Power Consumption or Torque –  Frequency Analysis

Power consumption or torque fluctuations are influenced by granule properties (particle size distribution, shape index, apparent density) and the granulation time. Fluctuation of torque / power consumption and intensity of spectrum obtained by FFT analysis can be used for end point determination [131, 123].

Another interesting fact was reported recently by Terashita et al. [123] who observed that when the end point region of a granulation is reached, the frequency distribution of a signal reaches a steady state.

It should be repeated here that torque shows more susceptibility to high frequency oscillations.

Torque or power consumption pattern of a mixer is a function of the viscosity of the granulate and binder. With the increasing viscosity, the plateau is shortened and sometimes vanishes completely thereby increasing the need to stop the mixer at the exact end point.  At low impeller speeds or high liquid addition rates, the classic S-shape of the power consumption curve may become distorted with a steep rise leading into overgranulation [43]. 

The area under the torque-time curve is related to the energy of mixing and can be used as an endpoint parameter [38]. Area under power consumption curve divided by the load gives the specific energy consumed by the granulation process.  This quantity is well correlated with the relative swept volume [46, 107, 106].  The consumed energy is completely converted into heat of the wet mass [42], so that the temperature rise during mixing shows some correlation with relative swept volume and Froude number [49] that relates the inertial stress to the gravitational force per unit area acting on the material.

Method of Binder Addition

There are conflicting reports on the preferred method of adding the binder.  For example, Holm [47] does not generally recommend adding dry binder to the mix in order to avoid preparation of a binder solution because a homogeneity of binder distribution can not be assured.   Others recommend just the opposite [133, 75, 61].

Slow continuous addition of water (in case the water-soluble binder is dry mixed) or a binder solution to the mix is a granulation method of choice [40, 41, 42, 45, 43, 51, 58, 75, 106, 107, 135, 136, 66 and many others].  The granulating fluid should be added at a slow rate to avoid local overwetting [133].

If the binder solution is added continuously, then the method of addition (pneumatic or binary nozzle, atomization by pressure nozzle) should be considered in any endpoint determination and scale-up.

An alternative to a continuous binder addition method is to add binder all at once [49] to assure ease of processing and reproducibility, reduce processing time and to avoid wet mass densification that may occur during the liquid addition.  This latter phenomenon may obscure the scale-up effect of any parameter under investigation.

End Point Optimization

Mixing and agglomeration of particles in wet granulation have been studied extensively ([60], [3]).  The optimal endpoint can be thought of as the factor affecting a number of granule properties.

With so many variables involved in a granulation process, it is no wonder that more and more researchers throw in a number of factors together in an attempt to arrive at an optimum response.  Examples of the experimental design references that include processing factors are: [128, 74, 97, 1, 132, 130, 129, 83, 82].

The final goal of any granulation process is a solid dosage form, such as tablets.  Therefore, when optimizing a granulation process, it stands to reason to include, alongside the end-point factor, the tableting processing parameters, such as compression force or tablet press speed. 

Searching through literature I could find but one reference [1] that applied this idea using the tablet hardness, friability and disintegration as response variables. 

This study has also investigated the possibility of adjusting the tableting parameters in order to account for an inherent variability of a wet granulation process.

End Point Scale-Up

Granulation and mixing scale-up was specifically addressed in numerous recent publications [29, 17, 49, 83, 84, 97, 130].

A rational approach to scale-up using dimensional analysis has been in use in chemical engineering for quite some time.  This approach, based on the use of process similarities between different scales, is being applied to pharmaceutical granulation since the early work of Hans Leuenberger in 1982 [69, 72

Scale-up - Example

In this seminal and elegant work published in 1993, Horsthuis and his colleagues from Organon in The Netherlands have studied granulation process in Gral mixers of 10, 75, and 300 liter size. 


• relative swept volume

• blade tip speed

• Froude number

with respect to end point determination (as expressed by the time after which there is no detectable change in particle size), they have concluded that only constant Froude numbers results in a comparable end point.

Scale-up - Example

In this work, the University of Maryland group under the direction of Dr. Larry Augsburger has applied the ideas of Leuenberger and Horsthuis to show that, for a specific material, end point can be expressed in terms of wet massing time. 

In a scale-up study, for a constant ratio of a binder volume to a batch size, this factor was found to be inversely proportional to impeller speed when the impeller tip speed was held constant for all batches. However, this result was not corroborated by other studies or other materials.

Dimensional Analysis

Dimensionless analysis is a method for producing dimensionless numbers and it can be applied when the equations governing the process are not known. Dimensional analytical procedure was first proposed by Lord Rayleigh in 1915 [93].

p-theorem (or Buckingham theorem) [72, 139, 138, 11] states:

Every physical relationship between n dimensional variables and constants can be reduced to a relationship between m=n-r mutually independent dimensionless groups, where r = number of dimensional units, i.e. fundamental units (rank of the dimensional matrix).

Imaging that you have successfully scaled up from a 10 liter batch to 300 liter batch.  What exactly happened?  You may say: “I got lucky”.  Apart from luck, there had to be similarity in the processing of the two batches

According to the modeling theory, two processes may be considered similar if there is a geometrical, kinematic and dynamic similarity [580, 72]. 

Two systems are geometrically similar if they have the same ratio of linear dimensions.  Two geometrically similar systems are kinematically similar if they have the same ratio of velocities between corresponding points.  Two kinematically similar systems are dynamically similar when they have the same ratio of forces between corresponding points.

For any two dynamically similar systems, all the dimensionless numbers necessary to describe the process have the same numerical value [139].

It was shown, for example, that Collette Gral 10, 75 and 300 are not geometrically similar [49].

Dimensionless representation of the process is scale-invariant and thus can be easily scaled up. For notation, formulas and units, see the one of the appendices.

Dimensionless Reynolds numbers that relate the inertial force to the viscous force are frequently used to describe mixing processes [99], especially in chemical engineering. For example, for problems of water-air mixing in vessels equipped with turbine stirrers where scale-up can range from 2.5 l to 906 l (scale-up factor of 1:71) – see, e.g. Zlokarnik [139].

Froude Numbers [31] has been described for powder blending [84] and was suggested as a criterion for dynamic similarity and a scale-up parameter in wet granulation [49].  The mechanics of the phenomenon was described as an interplay of the centrifugal force (pushing the particles against the mixer wall) and the centripetal force produced by the wall, creating a “compaction zone”.

We have seen that there exists sort of a “principle of equifinality” that states: “An endpoint is an endpoint is and endpoint, no matter how it was obtained”.  The rheological and dimensional properties of the granules are similar [26].  That means that the density and dynamic viscosity are constant, and the only two variables that are left are impeller diameter and speed.

It is therefore seem appropriate to characterize and compare different mixers by the range of the Froude numbers they can produce.  A matching range of the Froude numbers would indicate the possibility of a scale-up even for the mixers that are not geometrically similar [49].

We have attempted to compute Froude numbers for mixers of different popular brands and the results are presented on the following slides. Such representation is akin to tablet press characterization using dwell time ranges. It allows some measure of comparison between otherwise incomparable devices.  I realize, of course, that this measure should not be used in absolute terms.  Rather, its use and relative usefulness will be evident during scale-up and technology transfer between various stages of product development.

Collette-Gral Mixers.  Looking at the chart, we can notice, that both the minimum and the maximum Froude numbers tend to decrease with mixer scale.  This essentially is a restatement of the fact that laboratory scale mixers tend to produce higher shear and intensity of agglomeration having relatively more powerful motors.

As was shown by Horsthuis et al. [49], it is possible to match dynamic conditions of Gral 10 and 75, or Gral 75 and 300, but not between Gral 10 and 300.

The Fielder PMA mixers exhibit essentially the same pattern of Froude number distribution as the Grals.  Again, we notice a tendency of larger mixers to have smaller Froude numbers - both extremes and ranges.

It is then understandable why scaling up the process quantified on a 10 liter mixer is sometimes so difficult to apply to PMA 600 - it is virtually impossible to match Froude numbers for a comparable dynamic conditions.

The impeller speed is the governing factor in Froude representation because it is squared.  The geometrical dimensions of the blades are of a secondary significance.


The popular Diosna mixers show a distribution pattern of Froude numbers similar to those of other brands.

It can be seen that one may expect to scale-up easily from P10 mixer to P100 but not to P600.

A word of caution: in addition to matching Froude numbers, certain corrections may be needed to account for geometric dissimilarity of vessels in the machines of different size.

Powrex mixers, distributed by Glatt, show a better distribution of Froude numbers than Grals or Fielders. 

Despite the fact that mixers with 100 liter capacity and above have only one shaft speed available, the ranges of the laboratory scale mixers seem to be wide enough to create a possibility of a match.

Once again, formulators should be encouraged to experiment with low speeds in an attempt to simulate dynamic conditions that exist in production mixers.

When a number of selected mixers from the preceding charts are placed on the same chart for comparison, an interesting conclusion can be made:  One may expect to scale up successfully from Gral 10 to Fielder PMA 65 but not to Gral 300, while PMA 65 can be matched with Diosna P250 but not with P600.  Powrex VG-10, on the other hand, covers the whole range rather nicely.

The rationale for using Froude numbers to compare different mixers may be found in the fact that at any desired endpoint (as defined by identical particle size mean and distribution), viscosity and density of the wet mass are similar in any mixer regardless of its brand and model, and the Newton Power Number Ne will depend solely on the diameter d and speed n of the impeller.  In this case any assumed relationship between Re and Fr can be reduced to Ga = Re 2 /Fr.

End Point Scale-Up using Dimensional Analysis

To set up a relevance list for mixing-granulation process, one needs to compile a complete set of all dimensional relevant and mutually independent variables and constants that affect the process.  The word “complete” is crucial here.  All entries in the list can be subdivided into geometric, physical and operational.  Each relevance list should include only one target (dependent “response”) variable.

Many pitfalls of dimensional analysis are associated with the selection of the reference list, target variable, or measurement errors (e.g. when friction losses are of the same order of magnitude as the power consumption of the motor). The larger the scale-up factor, the more precise the measurements of the smaller scale have to be [139]

In  Power number calculations, the power of the load (blades), not the idle motor should be taken into account!  Before attempting to use dimensional analysis, one has to measure / estimate power losses for empty bowl mixing. However, this baseline does not stay constant and changes significantly with load.  This may present inherent difficulties in using power meters instead of torque.  Torque, of course, is directly proportional to power drawn by the impeller so that the power number can be calculated from the torque measurements

Based on certain simplifying assumptions, Hans Leuenberger [72] suggested the following relevance list for the wet granulation process (in its final dimensionless form):








Ne  =  P / (r n3 d5)

Newton (power) number, which relates the drag force acting on a unit area of the impeller and the inertial stress.


m t / (V r)

Specific amount of granulating liquid       


V / C

Fraction of volume loaded with particles 


Fr   =  n2 d / g

Froude number, which relates the centrifugal and gravitational energy.       


d / l

Geometric number (ratio of characteristic lengths)

One of the assumptions implied that viscosity is not a system property (i.e. there is only a short range particle interaction), thus effectively excluding Reynolds number from the list.

It was then postulated that the target variable p0 is a function of the other four dimensionless numbers, i.e.  p0 = f(p1, p2, p3, p4), and p0 = f(p1) when  p2, p3, p4  ”were essentially kept constant” [72].  This was shown for planetary mixers (Dominici, Glen, Molteni) ranging from 5.75 to 60 kg.

According to Leuenberger’s school, the correct amount of granulating liquid per batch is a scale-up invariable, provided that the binder is mixed in as a dry powder and then water is added at a constant rate.  This was shown for non-viscous binders.

The ratio of quantity of granulating liquid to batch size at the inflection point S3 is constant irrespective of batch size and type of machine.

Moreover, for a constant rate of low viscosity binder addition proportional to the batch size, the rate of change (slope or time derivative) of torque or power consumption curve is linearly related to the batch size for a wide spectrum of high shear and planetary mixers.  In other words, the process end point, as determined in a certain region of the curve, is a practically proven scale-up parameter for moving the product from laboratory to production mixers of different sizes and manufacturers.

Different vessel and blade geometry will contribute to differences in absolute values of the signals but the signal profile of a given granulate composition in a high shear mixer is very similar to one obtained in a planetary mixer.

Another approach

Scale-up in fixed bowl mixer-granulators has been studied by Ray Rowe and Mike Cliff’s group using the classical dimensionless numbers of Newton (Power), Reynolds and Froude to predict end-point in geometrically similar high-shear Fielder PMA25, 100, and 600 liter machines [64].

The relevance list included power consumption of the impeller (as a response) and six factor quantities: impeller diameter, impeller speed, vessel height, specific density and dynamic viscosity of the wet mass, and the gravitational constant.

Note: Why do we have to include the gravitational constant?  Well, imagine the same process to be done on the moon - would you expect any difference?

In a subsequent communication [62] it was stated that, in order to maintain the geometric similarity between mixers, it is important to keep the batch size in proportion to the overall shape of the mixer and especially its bowl height.

The problem with using torque values from mixer torque rheometer for the viscosity of wet granulation is that it is proportional to kinematic viscosity

n  =  h / r rather than dynamic viscosity h required to calculate the Reynolds numbers.

Most recently, the same approach was applied to planetary Hobart AE240 mixer with two interchangeable bowls [29, 28].  Assuming the absence of chemical reaction and heat transfer, the following relevance list for the wet granulation process was suggested:

Dimensional quantity




net impeller power consumption (motor power consumption minus the dry blending baseline level)


impeller diameter (or radius)


impeller speed


height of granulation bed in the bowl


granulation bulk or specific density


granulation dynamic viscosity

Dimensional analysis and application of the Buckingham theorem indicates that there are 4 dimensionless quantities that adequately describe the process: Ne, Re, Fr, and h/d (the latter corresponds to Leuenberger’s dimensionless group p2). 

Again, a relationship of the form Ne = k [Re * Fr * (h/d)]-r  was postulated and the constants k and r were found empirically with a good correlation (>0.92) between the observed and predicted numbers.

The proposed quantification of mixer performance using the dimensionless Froude numbers may be utilized in a variety of scale-up paths. As a possible variation on the dimensional analysis techniques, one may want to investigate the usefulness of the Galileo dimensionless number Ga = Re 2 /Fr  for identification of an endpoint.

List of Symbols


vessel capacity (m3) – dimensional units [L3]


impeller diameter (m) – dimensional units [L]


the gravitational constant (m / s2) – dimensional units [LT-2]


height of granulation bed in the bowl


characteristic length (or height) of the vessel (m) – dimensional units [L]


amount of granulating liquid added per unit time (kg) – dimensional units [M]


impeller speed  (revolutions / s) – dimensional units [T-1]


power required by the impeller (W = J / s) – dimensional units [ML2T-5], equal to motor power consumption assuming no losses due to eddy currents, friction in couplings, etc.


total mixing time (s) – dimensional units [T]


particle volume (m3) – dimensional units [L3]


specific density of particles (kg / m3) – dimensional units [M L-5]

n  =  h/ r

kinematic viscosity (m2 / s) = – dimensional units [L2T]


dynamic viscosity (Pa*s) = – dimensional units  [M L-1 T-1]



Fr   =  n2 d / g

Froude number.  It relates the inertial stress to the gravitational force per unit area acting on the material.  It is a ratio of the centrifugal force to the gravitational force.

Ne  =  P / (r n3 d5)

Newton (power) number.  It relates the drag force acting on a unit area of the impeller and the inertial stress.

Re  =  d2 n r / h

Reynolds number.  It relates the inertial force to the viscous force.

Ga = Re2 / Fr

Galileo number


Equipment Used in References






10 l

[22], [109], [110]


[112], [71], [72]

Gral 10

[326], [49]

Gral 75

[56], [69], [49]

Gral 300

[133], [49]

Gral 400



[112], [52], [69] , [71]


[61], [8]


[5], [74], [75], [110]






[137], [95]


[19], [95]


[112], [71], [121], [24]

PMA 10

[97], [137]

PMA 25

[23], [46], [100], [80], [57], [42], [110]

PMA 65

[62], [52], [97], [137]

PMA 100

[18], [19], [23]

PMA 150


PMA 250


PMA 300


PMA 600


Fukae Powtec

[65], [131]

Key 5 liter


Littleford Lodige

[112], [69], [71], [72], [17]






[49], [33]





Morton M4E



[125], [124]




[82], [83], [115]


[12], [83], [26]





Roto J

[128], [129], [130]

Roto P


Planetary mixers

[9], [50], [71], [66], [119], [120]


[12], [52], [118], [29], [34], [35], [50], [28]

Literature References




Achanta AS, Adusumilli P, James KW. Endpoint determination and its relevance to physicochemical characteristics of solid dosage forms. Drug Dev Ind Pharm 23(6):539-546, 1997


Akbuga J. Studies on granulation properties of furosemide: effects of process and product variables on size and properties of granules. Pharmazie 45:50, 1990


Alderborn G. Granule properties of importance to tableting. Acta Pharm Seuc 25:229-238, 1988


Alkan MH, Yuksel A. Granulation in a fluidized bed II.  Effect of binder amount on the final granule. Drug Dev Ind Pharm 12:1529, 1986


Andersson J, Lindberg NO. Diosna P25 high-speed mixer equipped with instruments for measuring the rate of rotation of the main impeller motor shaft. Drug Dev Ind Pharm 9:1495-1505, 1983


Arnaud P, Brossard D, Chaumeil J. Effect of the granulation process on nitrofurantoin granule characteristics. Drug Dev Ind Pharm 23(1):57-66, 1998


Bakker A, Fasano JB, Leng DE. Pinpoint mixing problems with lasers and simulation software. Chem Eng Sci 94-100, January, 1994


Becker D, Rigassi T, Bauer-Brandl A. Effectiveness of binders in wet granulation: a comparison using model formulations of different tabletability. Drug Dev Ind Pharm 23(8):791-808, 1997


Bier HP, Leuenberger H, Sucker H. Determination of the uncritical quantity of granulating liquid by power measurements on planetary mixers. Pharm Ind 4:375-380, 1979


Bouckaert S, et al. Optimization of a granulation procedure for a hydrophilic matrix tablet using experimental design. Drug Dev Ind Pharm 22(4):321-327, 1996


Buckingham E. On physically similar systems; Illustrations of the use of dimensional equations. Phys Rev NY 4:345-376, 1914


Cabelka TD, et al. Comparison of high-shear, low-shear, and fluid bed granulation of vitamin C a strain gaged torque sensor. AAPS Meeting Poster, 1992


Carstensen JT. Theory of wet granulation. TechSource Conf , 1988


Chalmers AA, Elworthy PH. Oxytetracycline tablet formulations: the effect of wet mixing time, particle size and batch variation on granule and tablet properties. J Pharm Pharmacol 82:239, 1976


Chirkot T, Propst CW. Low shear granulators. In: Parikh DM (ed.). Handbook of Pharmaceutical Granulation Technology. Marcel Dekker, Inc.  New York, 1997


Choi W. Fundamental study on agglomeration of powdered crude drugs in high speed test granulator. Pusan Bull Pharm Sci 24(1):46-53, 1990


Chowhan ZT. Aspects of granulation scale up in high-shear mixers. Pharm Tech 26-42, February, 1988


Cliff MJ. Granulation end point and automated process control of mixer-granulators: Part 1. Pharm Tech 4:112-132, 1990


Cliff MJ. Granulation end point and automated process control of mixer-granulators: Part 2. Pharm Tech 5:38-44, 1990


Corvari V, et al. Instrumentation of a high-shear mixer:  Evaluation and comparison of a new capacitive sensor, a watt meter, and a strain-gage torque sensor for wet granulation. Pharm Res 9(12):1525-1533, 1992


Corvari V, Fry W C, Seibert WL. Wet granulation endpoint detection in a high shear mixer instrumented with a capacitive sensor and a strain gaged torque sensor. AAPS Meeting , 1992


D'Alonzo GD, O'Connor RE, Schwartz JB. Effect of binder concentration and method of addition on granule growth in a high intensity mixer. Drug Dev Ind Pharm 16:1931-1944, 1990


Daniel J, Jan S, Goodhart F. Process characterization of a wet granulation in a high intensity mixer. AAPS Meeting Poster, 1993


Diorio CR, Vendola TA, Hausberger AG. Development of a high shear mixing method for prediction of powder blend sensitivity to overlubrication. AAPS Meeting November, 1997


Elliott T. Efficiency, reliability of drive systems continue to improve. Power February:33-41, 1993


Emori H, et al. Prospective validation of high-shear wet granulation process by wet granule sieving method. II. Utility of wet granule sieving method. Drug Dev Ind Pharm 23(2):203-215, 1997


Ertel KD, et al. Physical aspects of wet granulation. IV - Effect of kneading time on dissolution rate and tablet properties. Drug Dev Ind Pharm 16:963, 1990


Faure A, et al. A methodology for the optimization of wet granulation in a model planetary mixer. Pharm Dev Tech 3(3):413-422, 1998


Faure A, et al. Scale-up of a pharmaceutical granulation in a laboratory scale planetary mixer. AAPS Meeting November, 1997


Fink DG, Beaty HW. Standard Handbook for Electrical Engineers.  13th edition. McGraw-Hill, New York 2-17, 3-26:27, 20-13, 20-40, 1993


Froude W, see Merrifield CW. The experiments recently proposed on the resistance of ships. Trans Inst Naval Arch (London) 11:80-93, 1870


Fry WC, et al. Computer-interfaced capacitive sensor for monitoring the granulation process 1: Granulation monitor design and application. J Pharm Sci 73:420-421, 1984


Fry WC, et al. Computer-interfaced capacitive sensor for monitoring the granulation process 2: System response to process variables. Pharm Tech 30-41, Oct, 1987


Ghanta SR, Srinivas R, Rhodes CT. Some studies of the affect of processing variables on the properties of granules and tablets made by wet granulation. Pharm Acta Helv 61(7):191-197, 1986


Ghanta SR, Srinivas R, Rhodes CT. Use of mixer-torque measurements as an aid to optimizing wet granulation process. Drug Dev Ind Pharm 10(2):305-311, 1984


Habib YS, et al. An investigation of the effect of granulating fluid level on the physical-mechanical properties of microcrystalline cellulose (MCC) and silicified microcrystalline cellulose (SMCC). AAPS Meeting November, 1997


Hancock BC, York P, Rowe RC. Characterization of wet masses using a mixer torque rheometer: 1:  Effect of instrument geometry. Int J Pharm 76:239-245, 1991


Hirzel J. Understanding premium-efficiency motor economics. Plant Eng May 7:75-78, 1992


Holm P, et al. Granulation in high speed mixers.  Part I: Effect of process variables during kneading. Pharm Ind 45:806-811, 1983


Holm P, et al. Granulation in high speed mixers.  Part II: Effect of process variables during kneading. Pharm Ind 46:97-101, 1984


Holm P, Schaefer T, Kristensen HG. Granulation in high speed mixers.  Part V: Power consumption and temperature changes during granulation. Powder Technol 43:213-223, 1985


Holm P, Schaefer T, Kristensen HG. Granulation in high speed mixers.  Part VI: Effects of process conditions on power consumption and granule growth. Powder Technol 3:286, 1993


Holm P, Schaefer T, Kristensen HG. Granulation in high-speed mixers.  Part IV.  Effects of process conditions on power consumption and granule growth. Powder Technol 43:225, 1985


Holm P, Schaefer T, Kristensen HG. Pelletization by controlled wet granulation in a high-shear mixer. STP Pharm Sci 3:286, 1993


Holm P. Effect of impeller and chopper design on granulation in a high speed mixer. Drug Dev Ind Pharm 13:1675, 1987


Holm P. High shear mixer granulators. In: Parikh DM (ed.). Handbook of Pharmaceutical Granulation Technology. Marcel Dekker, Inc.  New York, 1997


Holve DJ, Harvil TL. In-process particle size distribution measurements. Cegram Ind XX:19, 1995


Horsthuis GJB, et al. Studies on upscaling parameters of the Gral high shear granulation process. Int J Pharm 92:143, 1993


Hunter BM, Ganderton D. The influence on pharmaceutical granulation of the type and capacity of mixers. J Pharm Pharmacol 255:71P-78P, 1973


Jaegerskou A, et al. Granulation in high speed mixers.  Part III: effects of process variables on intergranular porosity. Pharm Ind 46:310-314, 1984


Jawadekar MS, Srinivas R. Evaluation of new granulation equipment:  High intensity mixing equipment vs. conventional planetary mixer. PharmTech Conf , 1983


Kay D, Record PC. Automatic wet granulation end-point control system. Manuf Chem Aerosol News 9:45-46, 1978


Kaye BH. A new approach to powder rheology. Pharm Tech 116-124, March, 1994


Kaye BH. Using an expert system to monitor mixer performance. Powder Bulk Eng 36-40, January, 1991


Kopcha M, et al. Monitoring the granulation process in a high shear mixer/granulator: an evaluation of three approaches to instrumentation. Drug Dev Ind Pharm 18(18):1945-1968, 1992


Kornchankul W, Parikh NH, Sakr A. The effect of process variables on the content uniformity of a low dose drug in a high shear mixer. AAPS Meeting November, 1997


Kristensen HG, et al. Granulation in high speed mixers.  Part IV: effect of liquid saturation on the agglomeration. Pharm Ind 46:763-767, 1984


Kristensen HG, Schaefer T. Granulation: a review on pharmaceutical wet-granulation. Drug Dev Ind Pharm 13:803, 1987


Kristensen HG. Agglomeration of powders. Acta Pharm Seuc 25:187-204, 1988


Laicher A, et al. A modified signal analysis system for end-point control during granulation. Eur J Pharm Sci 5:7-14, 1997


Landin M, et al. The effect of batch size on scale-up of pharmaceutical granulation in a fixed bowl mixer-granulator. Int J Pharm 134:243-246, 1996


Landin M, Rowe RC, York P. Characterization of wet powder masses with a mixer torque rheometer.

3. Nonlinear effects of shaft speed and sample weight. J Pharm Sci 84/5:557-560, 1995


Landin M, York P, Cliff MJ. Scale-up of a pharmaceutical granulation in fixed bowl mixer granulators. Int J Pharm 133:127-131, 1996


Lang BA, et al. Use of the mixer torque rheometer to evaluate effect of drug substance morphology on the wet granulation process. AAPS Meeting November, 1997


Leuenberger H, Bier HP, Sucker HB. Theory of the granulating-liquid requirement in the conventional granulation process. Pharm Tech 6:61-68, 1979


Leuenberger H, Luy B, Studer J. New development in the control of a moist agglomeration and pelletization process. STP Pharm Sci 6:303, 1990


Leuenberger H. Design and Optimization approaches in the field of granulation drying and coating. In: Crommelin BJS, Midha KK, Nagai T (eds.).  Proceedings, 53rd International Congress of Pharm. Sci. of FIP.  Topics in Pharm. Sci., 1993 Medpharm. Scientific Publ., Stuttgart 1994


Leuenberger H. Granulation, new technique. Pharm Acta Helv 57(3):72-80, 1982


Leuenberger H. Monitoring granulation, Part 2. Manuf Chem Aerosol News, June, 1983


Leuenberger H. Monitoring granulation. Manuf Chem Aerosol News 67-71, May, 1983


Leuenberger H. Scale-up of granulation processes with reference to process monitoring. Acta Pharm Technol 29(4), 274-280, 1983


Lindberg N-O, Hansson E, Holmquist B. The granulation of a tablet formulation in a high-speed mixer, Diosna P25.  Influence of intragranular porosity and liquid saturation. Drug Dev Ind Pharm 13:1067, 1987


Lindberg N-O, Jonsson C, Holmquist B. The granulation of a tablet formulation in a high-speed mixer, Diosna P25. Drug Dev Ind Pharm 11:917-930, 1985


Lindberg N-O, Jonsson C. The granulation of lactose and starch in a recording high speed mixer, Diosna P25. Drug Dev Ind Pharm 11(2&3), 387-403, 1985


Lindberg N-O, Leander L, Wenngren L. Studies on granulation in a change can mixer. Acta Pharm Seuc 11:603-620, 1974


Lindberg N-O, Leander L. Studies on granulation in a small planetary mixer 1:  Instrumentation. Acta Pharm Seuc 14:191-196, 1977


Lindberg N-O. Some experience of continuous granulation Acta Pharm Seuc 25:239-246, 1988


Lloyd PJ, Yeung PCM, Freshwater DC. The mixing and blending of powders. J Soc Cosmet Chem 21:205-220, 1970


Mackaplow MB, Rosen LA, Michaels JN. Effect of primary particle size on granule growth and endpoint determination in high shear granulators. AAPS Meeting November, 1997


Mendes R. Wet granulation principles. TechSource Conf , 1991


Miyamoto Y, et al. An evaluation of process variables in wet granulation. Drug Dev Ind Pharm 21:2213, 1995


Ogawa S, et al. A new attempt to solve the scale-up problem for granulation using response surface methodology. J Pharm Sci 83(3):439-443, 1994


Oldshue JY. Mixing processes. In: Bisio A, Kabel RL (eds). Scale-up of Chemical Processes: Conversion from Laboratory Scale Tests to Successful Commercial Size Design.  Wiley, New York, 1985


Ormos Z, Pataki K, Csukas B. Studies on granulation in a fluidized bed II.  the effects of the amount of the binder on the physical properties of granules formed in a fluidized bed. Hung J Ind Chem 1:307, 1973


Ormos Z, Pataki K, Csukas B. Studies on granulation in a fluidized bed III.  calculation of the feed rate of granulating liquid. Hung J Ind Chem 1:463, 1973


Parker MD, Rowe RC, Upjohn NG. Mixer torque rheometry: A method for quantifying the consistency of wet granulation's. Pharm Tech Int 2:50-64, 1990


Parker MD, Rowe RC. Rheological characterization of wet powder masses. J Pharm Pharmacol 41:31P, 1989


Parker MD, York P, Rowe RC. Use of granulation theology in identifying interactions between microcrystalline cellulose and typical polymer binders. J Pharm Pharmacol 39:89P, 1987


Peck G. Principles of wet granulation. TechSource Conf , 1990


Pendharkar CM, et al. Influence of the specific surface area of selected raw materials on the granulation process using an instrumented mixer. Pharm Tech 44-53, April, 1990


Railkar AM, Schwartz JB. Evaluation and comparison of a moist granulation technique with conventional wet granulation. AAPS Meeting November, 1997


Rayleigh Lord. The principle of similitude. Nature 95(2368, March 18):66-68, 1915


Record PC. A review of pharmaceutical granulation technology. J Powder Bulk Solids Technol 4:33, 1980


Record PC. Practical experience with high-speed pharmaceutical mixer/granulators. Manuf Chem Aerosol News 11:65, 1979


Reier GE, Oliver JE, Wheatley TA. The compressibility of wet-granulated formulations containing microcrystalline cellulose. AAPS Meeting November, 1997


Rekhi GS, Caricofe RB, Parikh DM. A new approach to scale-up of a high-shear granulation process. Pharm Tech Suppl - TabGran Yearbook 58-67, 1996


Rekhi GS, et al. Evaluation of critical formulation and processing variables for Metoprolol Tartrate tablets using high-shear granulation - I. Pharm Res 10(10):S134, 1993


Reynolds O. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinusous, and of the law of resistance in parallel channels. Philos Trans R Soc London 174:935-982, 1883


Ritala M, et al. Influence of liquid bonding strength on power consumption during granulation in a high shear mixer. Drug Dev Ind Pharm 14:1041, 1988


Ritala M, Virtanen S. The effect of binder solution quantity and lactose particle size on granule properties. Acta Pharm Nord 3:229, 1991


Rowe RC, Parker MD. Mixer torque rheometry: An update. Pharm Tech 74-82, March, 1994


Rowe RC, Sadeghnejad GR. The rheological properties of microcrystalline cellulose powder/water mixes - measurement using a mixer torque rheometer. Int J Pharm 38:227-229, 1987


Royce A, et al. Alternative granulation technique: melt granulation. Drug Dev Ind Pharm 22(9&10):917-924, 1996


Scarpone AJ, Dalvi UG, De Lorimer AE. Preparing tablet granulators in a 100 cu ft. solids processor. Pharm Tech 44-52, September, 1986


Schaefer T, et al. Granulation in different types of high speed mixers. Part 1: Effects of process variables and up-scaling. Pharm Ind 48:1083, 1986


Schaefer T, et al. Granulation in different types of high speed mixers. Part 2: Comparison between mixers. Pharm Ind 49:297-304, 1987


Schaefer T, et al. Melt pelletization in a high shear mixer. V. Effect of apparatus variables. Acta Pharm Nord 1:133, 1993


Schaefer T, Holm P, Kristensen HG. Melt granulation in a laboratory scale high shear mixer. Drug Dev Ind Pharm 16:1249, 1990


Schaefer T, Holm P, Kristensen HG. Melt pelletization in a high shear mixer. I. Effects of process variables and binder. Acta Pharm Nord 4:133, 1992


Schaefer T, Holm P, Kristensen HG. Wet granulation in a laboratory scale high shear mixer. Pharm Ind 52:1147, 1990


Schaefer T. Equipment for wet granulation. Acta Pharm Seuc 25:205, 1988


Schwartz JB, Szymczak CE. Power consumption measurements and the mechanism of granule growth in a wet granulation study. AAPS Meeting November, 1997


Sellappan P, et al. Mixer torque rheometry improvements: studies of mixer blade geometry and mode of binder addition. AAPS Meeting November, 1997


Sheskey PJ, Williams DM. Comparison of low-shear and high-shear wet granulation techniques and the Influence of percent water addition in the preparation of a controlled-release matrix tablet containing HPMC and a high-dose, highly water-soluble drug. Pharm Tech 3:80-92, 1996


Sinko CM. Granulation characterization: Methods and significance. In: Parikh DM (ed.). Handbook of Pharmaceutical Granulation Technology. Marcel Dekker, Inc.  New York, 1997


Smart I. Single pot processing and its integration within an automated production plant. Pharm Eng 5-6:76, 1993


Spring MS. The conductivity of the damp mass during the massing stage of the granulation process. Drug Dev Ind Pharm 9(8), 1507-1512, 1983


Stamm A, Paris L. Influence of technological factors on the optimal granulation liquid requirement measured by power consumption. Drug Dev Ind Pharm 11(2&3), 330-360, 1985


Staniforth JN, Quincey SM. Granulation monitoring in a planetary mixer using a probe vibration analysis technique. Int J Pharm 32, 177-185, 1986


Staniforth JN, Walker S, Flander P. Granulation monitoring in a high speed mixer/processor using a probe vibration analysis technique. Int J Pharm 31, 277-280, 1986


Terashita K, Kato M, Ohike A. Analysis of end-point with power consumption in high speed mixer. Chem Pharm Bull 38(7):1977-1982, 1990


Terashita K, Watano S, Miyanami K. Determination of end-point by frequency analysis of power consumption in agitation granulation. Chem Pharm Bull 38(11):3120-3123, 1990


Timko RJ, et al. Instrumentation of a vertical high shear mixer with a motor slip monitoring device. Drug Dev Ind Pharm 12(10):1375-1393, 1986


Timko RJ, et al. Use of a motor load analyzer to monitor the granulation process in a high intensity mixers. Drug Dev Ind Pharm 13(3):405-435, 1987


Titley PC. Agglomeration and granulation of powders, processing and manufacturing practice. Acta Pharm Seuc 25:267-280, 1988


Travers DN, Rogerson AG, Jones TM. A torque arm mixer for studying wet massing. N/A N/A, 1975


Vojnovic D, et al. Wet granulation in a small scale high shear mixer. Drug Dev Ind Pharm 18:961, 1992


Vojnovic D, Moneghini M, Rubessa F. Optimization of granulates in a high shear mixer by mixture design. Drug Dev Ind Pharm 20:1035, 1994


Vojnovic D, Moneghini M, Rubessa F. Simultaneous optimization of several response variables in a granulation process. Drug Dev Ind Pharm 19:1479, 1993


Watano S, Terashita K, Miyanami K. Frequency analysis of power consumption in agitation granulation of powder materials with sparingly soluble acetaminophen. Chem Pharm Bull 40(1):269-271, 1992


Wehrle P, et al. Response surface methodology: an interesting statistical tool for process optimization and validation: example of wet granulation in a high-shear mixer. Drug Dev Ind Pharm 19:1637, 1993


Werani J. Production experience with end point control. Acta Pharm Seuc 25:247-266, 1988


Wikberg M, Alderborn G. Compression characteristics of granulated materials. IV. The effect of granule porosity on the fragmentation propensity and the compactibility of some granulation's. Int J Pharm 69:239, 1991


Yliruusi J, Tihtonen R. High-speed granulation.  Part I: Effect of some process parameters of granulation on the properties of unsieved and wet-sieved granules. Acta Pharm Fen 98:39, 1989


Yliruusi J, Tihtonen R. High-speed granulation.  Part II: Effect of some process parameters on the properties of wet- and dry-sieved granules. Acta Pharm Fen 98:53, 1989


Zega J, et al. Scale-up of the wet granulation process for a dicalcium phosphate formulation using impeller power consumption. AAPS Meeting November, 1995


Zlokarnik M. Dimensional analysis and scale-up in chemical engineering. Springer , 1991


Zlokarnik M. Problems in the application of dimensional analysis and scale-up of mixing operations. Chem Eng Sci 53(17):3023-3030, 1998