综合考虑 合理选择――谈制粒工艺与药品生产的适应性
先进的工艺为药品的规模化生产打下了良好的基础。作为口服制剂制备过程中重要的单元操作――制粒正在多方位发展。但是，不同的制粒技术与生产规模、建筑物等多种因素密切相关，企业在选择制粒工艺时需要给予重视。
&&&&●生产规模
&&&&一步锅法制粒的生产规模可达3~1200升，高效制粒机/流化床组合系统的处理能力可达1800升，流化床顶喷制粒的处理能力为30克~2吨。但连续制粒工艺，如连续流化床制粒、流化床喷雾干燥制粒、微丸制备技术的情况是不同的。尽管这三种技术的处理能力没有上限(如奶粉颗粒通过喷雾干燥可以最高10吨/小时的速度生产)，但是它们不适合极小规模(包括实验室级别)的生产，原因是其达到平衡状态需要一定的处理时间。
&&&&●批的定义
&&&&必须重视的是，对于连续流化床制粒、流化床喷雾干燥制粒、微丸制备等连续生产工艺来说，如果没有经过称配和预混就连续进料，就需要在容器内收集干燥的颗粒，以确定每一批次每个容器所需的装载量。通常，容器的大小应与片剂包衣时一个批量的大小相符。
&&&&●放大能力
&&&&设备的开发通常都是从实验室开始的，因此，生产规模的扩大必须经过设计。对流化床顶喷制粒、高效制粒/流化床组合系统制粒等，其工艺过程通常会随规模的增大而运行愈好。但对一步锅法来说，只有在使用微波进行干燥时，才可能呈线性放大，否则就需增加干燥时间。对于连续生产工艺来说，由于运行时间是惟一需要改变的参数，因此放大也比较简单。但是，若短时运行，设备难以达到放大目的，情况就较为复杂。
&&&&●建筑物要求
&&&&大规模一步锅法制粒设备重量可达10吨。因此，生产间的地板必须具有足够强度，并且需考虑将设备安装到建筑物上所需的其他辅助装置的重量，特别是当设备安装位置不在底层时。
&&&&高效制粒机/流化床组合系统可以实现垂直和水平的生产流程。湿颗粒的输送是一个重要的步骤，将制粒机安装在较高位置，可以使颗粒输送更加简便和安全。因此，需要增加安装高度(一个平台或独立楼层)。
&&&&由于在连续生产工艺中对于物料的处理要求较为复杂，相关系统须与建筑物融合在一起，并对设备周围的建筑进行修整。例如，生产型流化床可能高达几米，没有必要将整个装置安装在生产间。若按“穿墙式设计”建造流化床，可将所有必要的工艺置于技术区域，并且流化床塔顶部也可被置于生产间上方的技术区域。
&&&&●成品率
&&&&一个工艺过程的成品率在很大程度上受处理时间和配方的影响。处理时间越长，成品率就越高。制粒过程越潮湿，原料损失就越大，原因是湿物料会黏在壁上。其他的影响因素还包括与产品接触的总表面积、产品的特性等。
&&&&●密闭性
&&&&在处理毒性或高活性物质时，系统的密闭性是非常重要的。在这种情况下，原料在进出设备时是否能保证系统密闭；系统是否能够自动清洁，至少达到打开时不会有任何危险的水平，都是必须考虑的问题。除制微丸工艺外，密闭的原料流动在以上提及的工艺中都是可以实现的。即使像从高效制粒机将湿颗粒经湿法整粒机整粒后输送到流化床这样的极度灵敏的工艺过程，通过先进的分离阀技术实现与中间周转容器的对接，也能实现全密闭。
&&&&影响密闭性的因素很多，例如排气滤器能否轻易的被更换而不会产生污染；设备在负压下能否完成连续操作等。并且，尽管类似于流化床、高效制粒机、一步锅、喷雾干燥器这样的单个机器都可以具备有效的自动清洁系统(WIP/CIP)。但是，随着越来越多的上、下游设备被整合在一起，全自动清洁变得越来越复杂，给密闭生产带来了较大的难度。
&&&&●有机溶媒
&&&&若使用有机溶媒，则必须保证设备的气密性。为消除爆炸的危险，必须确保有机物蒸气和氧气的混合物浓度在爆炸范围以外，或者使用氮气作为工艺气体?br>
此外，对类似于防爆、抑爆或卸爆的设计，都需要进行分选，但一步锅法除外。这是因为只有在干燥步骤中才会有爆炸危险，而一步锅法中的干燥过程是在真空状态下完成的。若排气中含有有机物蒸气，则需对其进行清除。可以通过在一个封闭的循环中进行冷却、吸收或催化燃烧，将有机物蒸气清除掉。
&&&&●热敏性原料
&&&&为成功地处理热敏性原料，需对其温度、暴露时间、湿度及含氧量进行仔细的控制。
&&&&一步锅法制粒提供了一种在真空下安全的干燥方法，特别是在使用有机溶媒进行制粒时。因为在这种情况下，相应的温度会更低。然而，在喷雾干燥器中，温度会相当高，不过出现的时间很短。流化床制粒则是在喷雾及干燥开始阶段使用较高的进气温度，随后会慢慢降低，并维持在一个较低的温度。
&&&&●处方限制
&&&&高效制粒机可针对各种处方进行制粒。在使用一步锅法制粒时，则必须考虑暴露在微波中的各成分的变化。特别是在使用新原料时，应该对其进行测试。因为，微波吸收情况取决于含湿量及实际温度，而新原料有可能出现意外过热的情况。
&&&&流化床具有分粒器的作用，经其处理的原料的粒度分布是相似的。但是，用其处理非常细的粉末时，细粉可能会聚集在过滤区域。这时，通过加入液体喷雾可以解决。若喷雾干燥器喷入的是悬浮液，则悬浮颗粒的大小应小于30微米，以便获得良好的雾化效果。若需运用挤出工艺，则需采用特定的配方，如包含大量微晶纤维素的配方等。
&&&&●黏合剂
&&&&在口服制剂的生产中，高速制粒机几乎取代了中、低速制粒机。因为通过增加机械能，只需用较少的黏合剂就能形成相似特性的颗粒，而且在制粒过程中添加的液体愈少，则干燥过程中的舴⒘烤陀?。?庋?嵊薪细叩拇?砹浚?⒓跣?br>制备活性药物的难度。
&&&&●细粉的数量
&&&&如果细粉(小于63微米)所占的百分比过大，则会出现颗粒流动性差、分层及片剂成型差等问题。若采用微丸制备工艺，由于所有的原料都被混合成挤出物，因此最终产品中不会有细粉产生。若采用流化床顶喷制粒、流化床喷雾干燥工艺，细粉不会被排出，而是被反吹至工作区，并可能黏结成颗粒。一步锅法制粒中的细粉数量之多，是所有真空干燥装置中最典型的。如果发现问题，可通过调节处方来减少细粉数量。
&&&&●均一性和流动性
&&&&现有的制粒工艺一般不存在产品均一性问题。所有成分在液体阶段被混合，随后通过制粒可以达到较好的均一性。
&&&&连续流化床制粒机中的原料生产环节很少会出现均一性问题。但如果对系统刚启动后和刚停止前的产品分开进行检查，并且没有与中间生产的产品进行混合，则可能出现均一性问题。
&&&&制粒的主要目的是得到能够自由流动的原料。因此，只有能达到该项要求的工艺，才是企业所关心的。高效制粒机可生产更稠密、强度更稳定的颗粒。但在真空干燥过程中，一部分颗粒会被破坏而产生大量的细粉。
&&&&●堆密度和溶解度
&&&&堆密度取决于原料的物理密度、黏合剂的类型和数量、所选择的工艺参数等。
&&&&颗粒溶解度的大小取决于颗粒表面及结构。由低剪切力的设备生产的颗粒是开放多孔的结构，因而，具有较好的速溶性，但其强度却不够稳定。
&&&&(祝华)
(文章出处：中国医药报&2005年第113期)
在寻医问药你还可以
大家都在搜：热门关键词
电话：传真：地址：江西省宜春经济技术开发区春风路28号国内业务部E-mail:&国际业务部E-mail:网址：www.wonsen.com.cnwww.ycwsyj.com
高效湿法制粒机中切刀的秘密
您的当前位置：
高效湿法制粒机中切刀的秘密
[01]原理说到的切刀，大家第一想到的是，切碎呗。实际上，切碎只是切刀的40%的功能。我们知道，当我们俯视一个工作状态中的湿法制粒机的时候，物料由于向心力在锅壁四周成环状分布，我们暂时叫这个“物料带&吧。那么，切刀，对于物料在锅内的导流起着至关重要的作用；我们仔细观察就会发现，物料带中的物料并不是平行做圆周运动，而是在切刀这个地方发生了翻滚！（不要告诉我你没有注意到找一个现象，如果不是设备设计有问题，那就是你实在是太粗心）。这个翻滚，我们来分析看的时候，包括两个方向：上下和内外（相对于物料带，侧观）。上下翻滚，保证了物料上层和下层充分混合，因为制粒主要发生在下层（主桨和锅壁、物料之间的糅合）。这主要是依靠物料在顺着锅壁被主桨带着平行做圆周运动的时候，遇到切刀的高速翻转后，和锅壁的弯曲配合实现（看到没，一个湿法制粒机的锅的形状，和切刀是有联系的！）。同样，内外翻滚，保证了同心圆锅壁一侧（制粒强度大）向物料内部翻滚，保证内部物料都实现和参与制粒；这是如何实现的呢？我们仔细观察就会发现，切刀大部分是类似花一样的结构，这种结构有利于对物料进行由外向内进行导流。但是我见过一些切刀设计的跟一个塔似的，不知道是处于何种目的。这种上下左右的翻滚效果，是切刀存在的核心价值，因为切碎，实际上可以通过后面的湿整粒实现；这种翻滚的效果，有一位丁香园战友称之为“爆流”，合适。[02]旋转方向对于我们广大的制剂研发工作者来说，什么顺时针逆时针，记起来实在有点复杂，记住一点，切刀的方向一定要和物料运行方向一致。[03]形状说实话，我看过的国产设备，十个供应商就有十个不同的设计，花样比主桨还多。我不是工程背景出身，真的没有办法告诉你，哪个设计是好的，除非挨个使用和测试。但是，从用户角度讲，形成爆流的效果是判断它是否优秀的最直接指标。&[04]尺寸（直径和深度），离锅底高度这一个参数，直接影响到不同装载量的时候，物料翻滚的效率；如何能把一个湿法制粒机的切刀设计到，尽可能涵盖30~70%这个装量体积范围，是一个优秀设备供应商需要努力的方向；一个好的切刀的设计，可以使得制粒机达到20~80%的装载量，这样一来，就给设备的使用和工艺批量的容忍范围，带来了非常大的灵活性，有时候，可以一个顶两；具体品牌，大家自己去调研。在使用同一个制粒锅进行不同装载量的时候，需要考量这个湿法制粒机的装载高位和低位在什么位置，这主要是由切刀的高度和直径来决定，当然，这通常是固定的，大部分设备中，高度的选择空间不大，直径也是同样。至于深度，当我们俯视制粒过的时候，我们知道制粒过程中的物料主要集中在同心圆的外侧，形成一个环形的“物料带”，这个物料带的宽度，切刀完全没有必要达到这个宽度；对于同一部设备来说，这些参数都是固定的，不过都没有关系，制药切刀的形状和锅的形状设计的足够好，我们完全可以通过调整切刀的转速来弥补上述不足。工艺放大过程中，理想状态是使用相同的装载量，此时你的切刀参数放大参照线性速度相同的原理进行放大，就已经足够；但是，当迫不得己需要使用不同的装载量的时候，就要考虑对切刀的转速进行适当的调整，来平衡物料的顺利流动和翻转；所以，当一个设备供应商告诉你，他的设备装载量可以覆盖多么宽的范围的时候，很简单，你就直接看看设备装载量在最高位和最低位的运行过程中的爆流效果，基本可以判断；看看下面这个图，你觉得这样的切刀设计好吗？
上一篇：下一篇：
最近浏览：
相关产品：
相关新闻：
扫描二维码本文作者其他最新文章
系统随机推荐文章赞助商链接
当前位置： >>
湿法制粒工艺放大与终点判断
Wet Granulation: End-Point Determination and Scale-UpBy Michael Levin, Ph. D. Metropolitan Computing Corporation East Hanover, New Jersey, USAKeywords: wet granulation, end-point determination, dimensional analysis, scaleup, instrumentation, torque, power consumption. Abstract: Both high-shear and planetary mixers-granulators are routinely instrumented to measure and record various process variables, most commonly, impeller torque and motor power consumption. These variables provide information for end-point determination, reproducibility, and scale-up. Illustrated by several case studies, this article shows how to scale-up scientifically, using a dimensional analysis approach, and offers practical considerations for practitioners in the field of wet granulation.ContentsList of Figures.............................................................................................................................. 2 List of Tables ............................................................................................................................... 3 INTRODUCTION ............................................................................................................................. 4 WHAT IS AN END-POINT? ............................................................................................................ 5 WHAT CAN BE MEASURED ON A MIXER-GRANULATOR?...................................................... 5 Current ........................................................................................................................................ 5 Voltage ........................................................................................................................................ 5 Capacitance ................................................................................................................................ 5 Conductivity................................................................................................................................. 6 Probe vibration ............................................................................................................................ 6 Boots Diosna Probe .................................................................................................................... 6 Chopper Speed ........................................................................................................................... 6 Impeller or Motor Shaft Speed .................................................................................................... 6 Motor Slip and Motor Load Analyzer........................................................................................... 6 Impeller Tip Speed ...................................................................................................................... 7 Relative Swept Volume ............................................................................................................... 7 Temperature................................................................................................................................ 7Page 1 of 40Binder Addition Rate ................................................................................................................... 7 Power Consumption................................................................................................................... 8 Impeller Torque ........................................................................................................................... 9 Torque Rheometer ...................................................................................................................... 9 Reaction Torque........................................................................................................................ 10 Other possibilities...................................................................................................................... 10 Emerging Technology: Acoustic ................................................................................................ 10 Emerging Technology: Near Infra-Red (NIR) ............................................................................. 11 Emerging Technology: FBRM ................................................................................................... 11 END-POINT DETERMINATION.................................................................................................... 11 Torque vs. Power ...................................................................................................................... 12 Torque and Power Profiles........................................................................................................ 13 End-Point Optimization ............................................................................................................. 14 End-Point Reproducibility.......................................................................................................... 15 END-POINT SCALE-UP ............................................................................................................... 15 Scale-Up Attempts .................................................................................................................... 15 Dimensional Analysis ................................................................................................................ 16 Principle of Similitude................................................................................................................ 16 Dimensionless Numbers ........................................................................................................... 17 Comparison of attainable Froude Numbers .............................................................................. 18 Π-theorem (Buckingham).......................................................................................................... 18 Scientific scale-up procedure: ................................................................................................... 19 Relevance List........................................................................................................................... 19 Dimensional Matrix.................................................................................................................... 19 Case Study I: Leuenberger ()................................................................................... 20 Case Study II: Landin et al. (1996) ........................................................................................... 23 Case Study III: Faure et al. (1998) ............................................................................................ 26 Case Study IV: Landin et al. (1999) .......................................................................................... 27 Case Study V: Faure et al. (1999) ............................................................................................ 28 Case Study VI: Hutin et al. (2004) ............................................................................................ 29 PRACTICAL CONSIDERATIONS FOR END-POINT DETERMINATION AND SCALE-UP ....... 30 LIST OF SYMBOLS AND DIMENSIONS ..................................................................................... 32 ARTICLES OF RELATED INTEREST.......................................................................................... 33 LITERATURE REFERENCE......................................................................................................... 33List of FiguresFig. 1. Voltage, current, and power consumption of a typical mixer motor Fig. 2. Schematic of a direct impeller torque transducer Fig. 3. Impeller torque and motor power consumption for a small high shear mixer Fig. 4. A torque profile in a typical production batch Fig. 5. Another batch by the same operator (power consumption profile)Page 2 of 40Fig. 6. A batch by a novice operator (power consumption profile) Fig. 7. Another batch by inexperienced operator (torque profile) Fig. 8. Wet granulation end-point as a factor in tableting optimization Fig. 9. The range of Froude numbers for Collette Gral high-shear mixers. Fig. 10. The range of Froude numbers for Fielder PMA high-shear mixers. Fig. 11. Newton Power Number as a function of the Specific Amount of Graqnulating Liquid (adapted from , Leuenberger and Sucker, 1979). Fig. 12. Regression lines of the Newton Power Number on the product of Reynolds number, Froude Number, and the length ratio for 3 different Fielder mixers (from Landin et al., 1996). Fig. 13. Regression graph of Case Study III. Fig. 14. Regression graph of Case Study IV. Fig. 15. Regression graph of Case Study V.List of TablesTable I. The Relevance List used by Leuenberger (1983) Table II. The Dimensional Matrix for Case Study I Table III. The Transformed Dimensional Matrix for Case Study I Table IV: Dimensionless Π groups formed from the matrix in Table III Table V. Relevance List for Case Study II (Landin et al., 1996) Table VI. The Dimensional Matrix for Case Study II Table VII. The Transformed Dimensional Matrix for Case Study II Table VIII: Dimensionless Π groups formed from the matrix in Table VII Table IX. Relevance list for Hutin et al. (2004)Page 3 of 40IntroductionWet granulation is used mainly to improve flow and compressibility of powders, and to prevent segregation of the blend components. Particle size of the granulate is affected by the quantity and feeding rate of granulating liquid. Wet massing in a high-shear mixing is frequently compared to fluid bed mixing and to roller compaction technique (1), and the results seem to be formulation dependent. 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 (see, for example, 2, 3, or 4). For excellent classical review of the wet granulation process, equipment and variables, and measurement instruments available in the field, see papers by P. Holm and his group (5-12). These papers have become a standard reference for numerous subsequent publications. 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. 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. It can be seen as an interplay of acceleration (direct impact of the impeller), centrifugal, centripetal, and friction forces that act on the particles. According to Cliff (13-14), binder addition rate controls granule density, while impeller and chopper speed control granule size and granulation rate. The endpoint controls the mix consistency and reproducibility. 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.Page 4 of 40What is an end-point?End-point can be defined by the formulator as a target particle size mean or distribution. Alternatively, the end-point can be defined in rheological terms. It has been shown (15) that once you have reached the desired end-point, 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. I would call this “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. Mixer instrumentation, in general, has numerous benefits. In addition to a possible end-point determination, it can be used to troubleshoot the machine performance (for example, help detect worn-out gears and pulleys or identify mixing and binder irregularities). Instrumentation can serve as a tool for formulation fingerprinting, assure batch reproducibility, aid in raw material evaluation, process optimization and scale-up.What Can Be Measured on a MixerGranulator?CurrentCurrent in DC motors can be used as some indication of the load on the main impeller because impeller torque is proportional to current in some intervals (13) 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. Moreover, current baseline may shift with time.VoltageVoltage measurement generally has no relation to load.CapacitancePage 5 of 40Capacitive sensor responds to moisture distribution and granule formation (1620). It provided similar end-points (based on the total voltage change) under varying rates of agitation and liquid addition. Capacitive sensor can be threaded into an existing thermocouple port for in-process monitoring.ConductivityConductivity of the damp mass (21) makes it possible to quantify uniformity of liquid distribution and packing density during wet massing time.Probe vibrationProbe vibration analysis (22-23) require a specially constructed probe that includes a target plate attached to an accelerometer (for 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 ProbeThis probe (23) measured densification and increase of size of granules (changes in momentum of granules moving with constant velocity due to a mass change of the granules). The method did not gain popularity because of its invasive nature.Chopper SpeedChopper speed has no significant effect on the mean granule size (5,6).Impeller or Motor Shaft SpeedRate of impeller rotation could be used as some indication of the work being done on the material (24). Since the motor or impeller power consumption is proportional to the product of torque and speed, the latter is an important factor in evaluating the corresponding load.Motor Slip and Motor Load AnalyzerMotor slip is the difference between rotational speed of an idle motor and motor under load (25-26). Motor slip measurements, although relatively inexpensive, do not offer advantages over the power consumption measurements. The method did not gain popularity, probably because the slip is not linearly related to load (27) despite some claims to the contrary.Page 6 of 40Impeller Tip SpeedImpeller tip speed corresponds to shear rate and has been used as a scale-up parameter in fluid mixing (28). For processing of lactose granulations in Gral mixers, however, it was shown by Horsthuis et al. (29) 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 with 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 (30).Relative Swept VolumeRelative 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 (11, 12, 31). This parameter is related to work done on the material and was studied extensively at various blade angles (32). Higher swept volume leads to higher temperature and denser granules. However, it was shown by Horsthuis et al. (29) that the same relative swept volume did not result in the same endpoint (in terms of particle size distribution).TemperatureProduct and jacket temperature are 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.Binder Addition RateThere are conflicting reports on the preferred method of adding the binder. For example, Holm (33) does not generally recommend adding dry binder to the mix (as commonly done in order to avoid preparation of a binder solution) because a homogeneity of binder distribution can not be assured. Others recommend just the opposite (34-36). 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 (5, 6, 10-12, 37-40 and many others). The granulating fluid should be added at a slow rate to avoid local overwetting (34). 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 liquid addition method is to add binder liquid all at once (29) to assure ease of processing and reproducibility, reduce processing time and to avoid wet mass densification that may occur during the liquid addition. ThisPage 7 of 40latter phenomenon may obscure the scale-up effect of any parameter under investigation.Power ConsumptionOne of the most popular and relatively inexpensive measurements is the power consumption of the main mixer motor. It is measured by a watt transducer or a power cell utilizing Hall effect (a measurable transversive voltage between the two radial sides of a current conductor in a magnetic field, an effect discovered by E.H. Hall in 1879). Power consumption of the mixer motor for end-point determination and scale-up is widely used [Leuenberger (40) and subsequent work, Holm (5) Landin et al. (41-44); Faure et al., (46-49); and many others (16, 17, 20, 34, 36-40, 50-51)] because the measurement is economical, does not require extensive mixer modifications and is well correlated with granule growth. Power consumption correlates with mean granule size of a granulation (8), although the correlation is not always linear in the entire range. Intragranular porosity also shows some correlation with power consumption (52). Normalized work of granulation (power profile integrated over time) can accurately determine end-points and is correlated well with properties granulates (53). The main problem with power consumption measurements is that this variable reflects load on the motor rather than load on the impeller. It relates to the overall mixer performance, depends on motor efficiency and can change with time regardless of the load.Fig. 1. Voltage, current, and power consumption of a typical mixer motor Motor power consumption is a product of current, voltage, and the so-called power factor. In the range of interest, motor power consumption is generally proportional to load on the motor and, to some degree, can reflect the load on the impeller (Fig.1). However, 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 motorPage 8 of 40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 such as current losses in the windings (54). 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 (55). As the load increases, so does the current draw of the motor. This results in heat generation that further impacts the power consumption (27). A simple test might be to run an empty mixer for several hours and see if there is any the shift in the baseline. Also, as the motor efficiency drops with age, the baseline most definitely shifts over time. Motor power consumption is non-linearly related to the power transmitted to the shaft (56) and the degree of this non-linearity could only be “guestimated”.Impeller TorqueIn a mixing process, changes in torque on the blades and power consumption of the impeller occur as a result of change in the cohesive force or the tensile strength of the agglomerates in the moistened powder bed.Fig. 2. Schematic of a direct impeller torque transducer Direct torque measurement requires installation of strain gages on the impeller shaft or on the coupling between the motor and impeller shaft (Fig.2). Since the shaft is rotating, a device called slip ring is used to transmit the signal to the stationary data acquisition system. 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 (57). Impeller torque is an excellent in-line measure of the load on the main impeller (52, 58).Torque RheometerA torque rheometer is a device that provides an off-line measurement of torque required to rotate the blades of the device and this torque can be used to assess rheological properties of the granulation. It has been extensively used for endpoint determination (41, 59-61). The torque values thus obtained were termed a “measure of wet mass consistency” (46, 47, 62).Page 9 of 40One of the main concerns is that using the torque value that the unit is reporting instead of the dynamic viscosity for calculation of Reynolds numbers renders the latter to become dimensional. Therefore, the Reynolds number calculated from torque rheometer data is referred to as “pseudo-Reynolds” dimensional number. Due to the fact that torque was shown to be proportional to a kinematic (rather than dynamic) viscosity (63), it can have a conditional use in the dimensional analysis of the process, as will be shown below.Reaction TorqueBy 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 tensions in the stationary motor base can be measured by a reaction torque transducer. Reaction torque is a less expensive alternative to direct impeller torque and is recommended for mixers that have the motor and impeller shafts axially aligned (in this case, the reaction torque is equal to direct torque and is opposite in sign).Other possibilitiesWhen 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. There are other ideas floating around, for example, use of neural network to describe and predict the behavior of the wet granulation (64) or control the endpoint by rapid image processing system (65). A technique for measuring tensile strength of granules, in addition to power consumption measurement, to facilitate optimal end-point determination was recently described by Betz, Bürgin and Leuenberger (50). Powder flow patterns in wet granulation can be studied using positron emission particle tracking (66). Eventually, this and similar techniques can be used to validate various mathematical and statistical models of the process.Emerging Technology: AcousticApplicability of piezo-electric acoustic emission sensors to end-point determination have been studied since the beginning of this century (67). The technique is very promising, especially since it is non-invasive, sensitive and relatively inexpensive. Granulation process signatures obtained with acoustic transducer can be used to monitor changes in particle size, flow and compression properties (68, 69).Page 10 of 40Emerging Technology: Near Infra-Red (NIR)Use of a refractive NIR moisture sensor for end-point determination of wet granulation was described by several authors (70, 71). There are technological challenges associated with this approach, as the sensor can only measure the amount of water at the powder surface. Near infra-red monitoring of granulation process was attempted by researchers at many major pharmaceutical corporations with a modest success. In particular, yet unpublished work by David Rudd of GlaxoSmithKline in England should be mentioned as a part of the global effort in the field of Process Analytical Technology (PAT).Emerging Technology: FBRMFocused Beam Reflectance Measurement (FBRM) is a particle size determination technique based on a laser beam focusing in the vicinity of a sapphire window of a probe. The beam follows a circular path at speeds of up to 6 m/s. When it intersects with the edge of a particle passing by a window surface, an optical collector records a backscatter signal. The time interval of the signal multiplied by the beam speed represents a chord length between two points on the edge of a particle. The chord length distribution (CLD) can be recalculated to represent either a number or volume weighted particle size distribution. in many cases, where precision is more important than accuracy, CLD measurements are adequate to monitor dynamic changes in process parameters related to particle size and shape, concentration, and rheology of fluid suspensions Several attempts were made to evaluate the use of FBRM particle size analyzer as a potential tool for granulation end-point determination (72). Dilworth et al. (73) have compared power consumption, FBRM and acoustic signals in a study of a wet granulation process in Fielder PMA 200 mixer. It was found that these techniques were complimentary, with FBRM probe capable to follow median granule size growth even when the power consumption curve showed a plateau. A major disadvantage of the FBRM method is that measured CLD does not directly represent a particle size distribution (PSD). Conversion of CLD to PSD is not straightforward and requires sophisticated mathematical software that is not easy to validate. Moreover, CLD depends on optical properties and shape of the particles, as well as the focal point position. The total number of counts measured is a function both of solids concentration and probe location.End-Point DeterminationPage 11 of 40End-point detection in wet granulation has become a major scientific and technological challenge (74). Monitoring granulation is most commonly achieved by collecting either power or torque signals, or both. In what follows, we will compare both methods.Torque vs. PowerWhen we say “power consumption”, we usually refer to the main motor. It reflects the load on the motor due to useful work, as well as the power needed to run the motor itself (losses due to eddy currents, friction in couplings, etc.). It is quite possible (and, indeed, quite pertinent) to talk about the power consumption of the impeller, which is, obviously, quantitatively less than the power consumption of the motor and relates directly to the load on the impeller. Power ~ Torque * Speed Impeller power consumption can be calculated as a product of the direct torque, rotational impeller speed, and a coefficient (usually equal to 2π times a unit conversion factor, if required). 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.) Compared to impeller torque, motor power consumption
watt meters are inexpensive and can be installed with almost no downtime. However, motor power signal may not be sensitive enough for specific products or processing conditions. Wear and tear of mixer and motor may cause power fluctuations. Moreover, power baseline may shift with load. Impeller torque, on the other hand, is closer to where the action is, and is directly related to the load on the impeller. Torque is not affected by mixer condition. Although the motor power consumption is strongly correlated with the torque on the impeller (38), it is less sensitive to high frequency oscillations caused by direct impact of particles on the blades as evidenced by FFT technique (16). 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 (37). It was observed that when the end-point region of a granulation is reached, the frequency distribution of a power consumption signal reaches a steady state (75). It should be repeated here that torque shows more sensitivity to high frequency oscillations.Page 12 of 40Torque and Power ProfilesFig. 3. Impeller torque and motor power consumption for a small high shear mixer (Fielder PMA 10). Fig. 3 illustrates 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. The peak of the derivative indicates the inflection point of the signal. Based on the theory by Leuenberger (1979 and subsequent work), 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 (40). Prior to the inflection 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 end-point may be more or less constant. Torque or power consumption pattern of a mixer is a function of the viscosity of both 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 (9). The area under the torque-time curve is related to the energy of mixing and can be used as an end-point parameter. 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 (11, 12, 32). The consumed energy is completely converted into heat of the wet mass (7), so that the temperature rise during mixing shows some correlation with relative swept volume and Froude number (29) that relates the inertial stress to the gravitational force per unit area acting on the material. Fig. 4. A torque profile in a typical production batch Fig. 4 represents a record of a typical granulation batch done by an experienced operator on large Hobart mixer. You can see that the batch was stopped on the downslope of the derivative. Fig. 5. Another batch by the same operator (power consumption profile)Page 13 of 40On a Fig. 5 you can see another batch made by the same operator. This time it is a power consumption trace, but again it extends beyond the peak of the derivative and the end-point thus can be deemed reproducible. Fig.6. A batch by a novice operator (power consumption profile) In the batch represented in Fig. 6, a novice operator trainee has stopped the batch well before the peak of the derivative. This required a major adjustment of the tableting operation (force and speed) to produce tablets in an acceptable range of material properties (hardness and friability). Fig. 7. Another batch by inexperienced operator (torque profile) In this batch (Fig. 7), the same novice operator has stopped the granulation process, opened the lid, took a sample, and decided to granulate for another 10 seconds. You can see that there is no indication that the peak of the derivative was reached at the end-point. Thus, 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 (34, 76-78).End-Point OptimizationFig. 8. Wet granulation end-point as a factor in tableting optimization Agglomeration of particles in wet granulation have been studied extensively (24, 79). The optimal end-point can be thought of as the factor affecting a number of agglomerate properties (Fig.8). 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 (30, 35, 80-88). The final goal of any granulation process is a solid dosage form, such as tablets. Therefore, when optimizing a granulation process, the list of factors affecting tablet properties may include both the granulation end-point and the tableting processing parameters, such as compression force or tablet press speed. Page 14 of 40In one of the most interesting works based on the experimental design approach, an attempt was made to find a statistical relationship between the major factors affecting both granulation and compaction, namely, granulation end-point, press speed (dwell time), and compression force (88). The resulting equation allowed optimization of such standard response parameters as tablet hardness, friability and disintegration time. 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. Multivariate optimization of wet granulation may include hardness, disintegration and ejection as response variables (89). Compressibility property of granulations is extremely sensitive to various processing parameters of wet granulation (90). Recently, the experimental design procedure was applied to low shear wet granulation (91) with a factorial design used to evaluate the influence of such factors as binder strength and agitator speed.End-Point ReproducibilityAs will be shown in the next section, for every blend and a fixed set of values for processing factors (such as mixer geometry, blade speed, powder volume, amount and method of addition of granulating liquid), a wet granulation process state (end-point) is completely characterized by rheological properties of the wet mass (density, viscosity), which are, in turn, a function of particle size, shape and other properties. The process can be quantified with the help of dimensionless Newton Power Number Np that will assume a certain numerical value for every state (condition) of the granulate. Under fixed processing conditions, Np will be proportional to Net Power Consumption ΔP for any end-point (defined, in part, by wet mass density). Thus, in order to reproduce an end-point, it is sometimes sufficient to monitor power of the impeller (or the motor) and stop when a predefined net level of the signal is reached. If, however, any of the processing variables or the rheological definition of the end-point has changed, a more sophisticated approach is required, as described below.End-Point Scale-UpScale-Up AttemptsNumerous studies were undertaken in an attempt to determine empirically (and, lately, with a solid theoretical foundation) useful scale-up parameters of the wet granulation process (e.g., 46, 87, 92). In a 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 (29). Comparing relative swept volume, blade tip speed and Froude numbers with respect to end-point determination (as expressed by the time Page 15 of 40after which there is no detectable change in particle size), they have concluded that only constant Froude numbers result in a comparable end-point. In another attempt to determine good scale-up parameters, the University of Maryland group under the direction of Dr. Larry Augsburger (30) 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. 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. Yet another example of semi-empirical scale-up effort (93) was based on the fact that normalized power profiles are very similar and allow for direct comparison of different size granulators, at least for the equipment and materials used in the study. Normalized power curve rose at a relatively constant rate in the region where the ratio of water to dry mass is 0.1 - 0.2 (“slope plateau”). Despite a rapid increase in the slope of the power curve, the desired end-point was still detectable at a moment when the slope of power consumption signal exceeded the plateau level by a factor of 5 (empirical observation). Using this approach, an acceptable end-point (target particle size of 135 microns) was first established on a 10 liter Fielder and then scaled to 65 liter Fielder and 250 liter Diosna.Dimensional AnalysisA 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, was being applied to pharmaceutical granulation since the early work of Hans Leuenberger in 1979 (40). Dimensional analysis is a method for producing dimensionless numbers that completely describe the process. The analysis should be carried out before the measurements are made because dimensionless numbers essentially condense the frame in which the measurements are performed and evaluated. The method can be applied even when the equations governing the process are not known. Dimensional analytical procedure was first proposed by Lord Rayleigh in 1915 (94).Principle of SimilitudeImagine 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 and the end-point conditions of the wet mass of the two batches. According to the modeling theory, two processes may be considered similar if there is a geometrical, kinematic and dynamic similarity (95). Two systems are called geometrically similar if they have the same ratio of characteristic linear dimensions. For example, two cylindrical mixing vessels are geometrically similar if they have the same ratio of height to diameter. Page 16 of 40Two geometrically similar systems are called kinematically similar if they have the same ratio of velocities between corresponding system points. Two kinematically similar systems are dynamically similar when they have the same ratio of forces between corresponding points. Dynamic similitude for wet granulation would imply that the wet mass flow patterns in the bowl are similar. The gist of dimensionless analysis is as follows: For any two dynamically similar systems, all the dimensionless numbers necessary to describe the process have the same numerical value (96). Once a process is expressed in terms of dimensionless variables, we are magically transferred in a world where there is no space and no time. Therefore, there is no scale and, consequently, there are no scale-up problems. The process is characterized solely by numerical values of the dimensionless variables (numbers). In other words, dimensionless representation of the process is scale-invariant. Lack of geometrical similarity often is the main obstacle in applying the Dimensional Analysis to solving the scale-up problems. It was shown, for example, that Collette Gral 10, 75 and 300 are not geometrically similar (29). In such cases, a proper correction to the resulting equations is required.Dimensionless NumbersDimensionless numbers most commonly used to describe wet granulation process are Newton, Froude and Reynolds: Np = ΔP / (ρ n3 d5) Newton (power) Fr = n2 d / g Re = d2 n ρ / η Froude Reynolds(for list of symbols, notation and dimensions, see Appendix). Newton (power) number, which relates the drag force acting on a unit area of the impeller and the inertial stress, represents a measure of power requirement to overcome friction in fluid flow in a stirred reactor. In mixer-granulation applications, this number can be calculated from the power consumption of the impeller or estimated from the power consumption of the motor. Froude Number (96) has been described for powder blending and was suggested as a criterion for dynamic similarity and a scale-up parameter in wet granulation (29). The mechanics of the phenomenon was described as interplay of the centrifugal force (pushing the particles against the mixer wall) and the centripetal force produced by the wall, creating a “compaction zone”. Reynolds numbers relate the inertial force to the viscous force (97). They are frequently used to describe mixing processes and viscous flow, especially in chemical engineering (98).Page 17 of 40We have seen that there exists sort of a “principle of equifinality” that states: “An endpoint is an end-point is and end-point, no matter how it was obtained”. Different processing pathways can lead to different end-points, each with its own set of granulation properties. However, once an end-point is reached, it is characterized by certain numerical values of the dimensionless variables describing the process, and these values will be independent of scale. At the same end-point, no matter how defined, the rheological and dimensional properties of the granules are similar. As we will see from the examples described below, that means that the density and dynamic viscosity of the wet mass are constant, and the only variables that are left are the process variables, namely batch mass, impeller diameter and speed, and the geometry of the vessel.Comparison of attainable Froude NumbersHorsthuis et al. (29) showed that an end-point can be reproduced and scaled up in Gral mixers by keeping the Froude numbers constant. For the same end-point, in dynamically similar mixers (same geometrical ratios, same flow patterns), all dimensionless numbers describing the system should have the same numerical value, but Froude numbers for any mixer are easiest to compute. Fig. 9. The range of Froude numbers for Collette Gral high-shear mixers. Each mixer has a range of attainable Froude numbers, and an end-point transfer between mixers can only be achieved when such ranges overlap. Fig. 9 represents such a range for Collette Gral mixers. It can be seen that Gral 10 and Gral 150 has no overlap of Froude number ranges, and therefore a direct scale-up is not possible (in addition, Gral mixers are not exactly similar geometrically, as was stated elsewhere). The range of Froude numbers for Fielder PMA series mixers is shown on Fig. 10. The 10 liter laboratory scale mixer at its lowest speed settings can reach the Froude numbers of all other mixers, except one. These considerations can be useful for planning a scale-up or technology transfer operation. Fig. 10. The range of Froude numbers for Fielder PMA high-shear mixers.Π-theorem (Buckingham)The so-called π-theorem (or Buckingham theorem (99) states: Every physical relationship between n dimensional variables and constants ?(x0, x1, x2, … , xn) =0 Page 18 of 40can be reduced to a relationship? (Π0 ,Π1, … , Πm) = 0between m = n - r mutually independent dimensionless groups, where r = number of dimensional units, i.e. fundamental units (rank of the dimensional matrix).Scientific scale-up procedure:1. Describe the process using a complete set of dimensionless numbers, and 2. Match these numbers at different scales. The dimensionless space in which the measurements are presented or measured will make the process “scale invariant”.Relevance ListThe dimensional analysis starts with a list of all variables thought to be important for the process being analyzed (the so-called “relevance list”). To set up a relevance list for any process, one needs to compile a complete set of all 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 (96).Dimensional MatrixDimensional analysis can be simplified by arranging all relevant variables from the relevance list in a matrix form, with a subsequent transformation yielding the required dimensionless numbers. The dimensional matrix consists of a square core matrix and a residual matrix (you will see examples in the Case Studies below). The rows of the matrix consist of the basic dimensions, while the columns represent the physical quantities from the relevance list. The most important physical properties and process-related parameters, as well as the “target” variable (that is, the one we would like to predict on the basis of other variables) are placed in one of the columns of the residual matrix. The core matrix is then linearly transformed into a matrix of unity where the main diagonal consists only of ones and the remaining elements are all zero. ThePage 19 of 40dimensionless numbers are then created as a ratio of the residual matrix and the core matrix with the exponents indicated in the residual matrix. This rather simple process will be illustrated below in the examples.Case Study I: Leuenberger ()This example is based on the ground-breaking studies conducted by Hans Leuenberger at the University of Basel and Sandoz AG (40, 100-103). Table I. The Relevance List used by Leuenberger [1983] Quantity 1 Power consumption 2 3 4 5 6 7 8 Specific density Blade diameter Blade velocity Binder amount Bowl volume Gravitational constant Bowl height Symbol P ρ d n s Vb g H Units Watt kg / m3 m rev / s kg m3 m / s2 m Dimensions M L2 T-3 M L-3 L T-1 M L3 L T-2 LThe Relevance List in Table I reflects certain assumptions used to simplify the model, namely, that there are short range interactions only and no viscosity factor (and therefore, no Reynolds number). Why do we have to consider the gravitational constant? Well, imagine the same process to be done on the moon - would you expect any difference? One target variable (Power consumption) and 7 process variables / constants thus represent the number n=8 of the Π-theorem. The number of basic dimensions r = 3 (M, L, and T). According to the theorem, the process can be reduced to relationship between m = n - r = 8 C 3 = 5 mutually independent dimensionless groups. Table II. The Dimensional Matrix for Case Study I Core matrix ρ Mass [M] 1 d 0 1 n 0 0 P 1 2 Residual Matrix s 1 0 Vb 0 3 g 0 1 H 0 1Length [L] C3Page 20 of 40Time [T]00C1C300-20The Dimensional Matrix in Table II was constructed as described above, with the rows listing the basic dimensions and the columns indicating the physical quantities from the relevance list. Table III. The Transformed Dimensional Matrix for Case Study I Unity matrix ρ M 3M + L -T 1 0 0 d 0 1 0 n 0 0 1 P 1 5 3 Residual Matrix s 1 3 0 Vb 0 3 0 g 0 1 2 H 0 1 0Transformation of the Dimensional Matrix (Table III) into a unity matrix is straightforward. To transform -3 in L-row / ρ -column into zero, one linear transformation is required. The subsequent multiplication of the T-row by C1 transfers the -1 of the n-column to +1. The 5 dimensionless groups are formed from the 5 columns of the residual matrix by dividing each element of the residual matrix by the column headers of the unity matrix, with the exponents indicated in the residual matrix. The residual matrix c therefore five dimensionless Π groups (numbers) will be formed (Table IV). Table IV: Dimensionless Π groups formed from the matrix in Table III. Π group Π0 = Π1 = Expression P / (ρ1 * d5 * n3) s / (ρ1 * d3 * n0) = Np ~ q t / (ρVp) Definition Newton (Power) number Specific Amount of Liquid Vp ≡ Volume of particles q = binder addition rate t = binder addition time Π2 = Π3 = Π4 = Vb / (ρ0 * d3 * n0) g / (ρ0 * d1 * n2) H / (ρ0 * d1 * n0) ~ (Vp / Vb)-1 = Fr-1 =H/d Fractional Particle Volume Froude Number Ratio of LengthsPage 21 of 40The end result of the dimensional analysis is an expression of the form Π0 = f (Π1, Π2, Π3, Π4). Assuming that the groups Π2, Π3, Π4 are “essentially constant”, the Π-space can be reduced to a simple relationship Π0 = f (Π1), that is, the value of Newton number Np at any point in the process is a function of the specific amount of granulating liquid. Up to this point, all the considerations were rather theoretical. From the theory of modeling, we know that the above dimensional groups are functionally related. The form of this functional relationship f, however, can be established only through experiments. Leuenberger and his group have empirically established that the characteristic (that is, relative to the batch size) amount of binder liquid required to reach a desired endpoint (as expressed by the absolute value of Np and, by proxy, in terms of Net Power Consumption ΔP) is “scale-up invariable”, that is, independent of the batch size (Fig. 11), thus specifying the functional dependence f and establishing rational basis for granulation scale-up.Fig. 11. Newton Power Number as a function of the Characteristic Liquid Quantity (adapted from Bier, Leuenberger and Sucker, 1979, ref. 40). Experiments with 5 different planetary mixers with batch sizes ranging from 3.75 kg up to 60 kg showed that, if the binder is mixed in as a dry powder and then liquid is added at a constant rate proportional to the batch size, the ratio of granulation liquid quantity to a batch size is constant. This was shown for non-viscous binders. The ratio of quantity of granulating liquid to batch size at the inflection point of power vs. time curve 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. As we have indicated before, for any desired end-point, the power consumption will be proportional to the Newton power number, at a constant mixer speed. The Leuenberger’s ideas relating to the use of power consumption for wet granulation end-point determination were tested and implemented by numerous researchers [e.g., (9, 20, 34, 39, 40). In 2001, Holm, Schaefer and Larsen (74) have applied the Leuenberger method to study various processing factors and their effect on the correlation betweenPage 22 of 40power consumption and granule growth. They have found that such a correlation did indeed exist but was dependent, as expected, on the impeller design, the impeller speed, and the type of binder. The conclusion was that it was possible to control the liquid addition by the level detection method whereby the liquid addition is stopped at a predetermined level of power consumption. An alternative approach involves an inflection point (peak of signal derivative with respect to time). Different vessel and blade geometry will contribute to the differences in absolute values of the signals. However, the signal profile of a given granulate composition in a high shear mixer is very similar to one obtained in a planetary mixer. For accuracy, in power number Np calculations, the power of the load on the impeller rather than the mixer motor should be used. Before attempting to use dimensional analysis, one has to measure / estimate power losses for empty bowl or dry stage mixing. Unlike power consumption of the impeller (based on torque measurements), the baseline for motor power consumption does not stay constant and changes significantly with load on the impeller, mixer condition or motor efficiency. This may present inherent difficulties in using power meters instead of torque. Torque, of course, is directly proportional to power drawn by the impeller (the power number can be determined from the torque and speed measurements) and has a relatively constant baseline.Case Study II: Landin et al. (1996)Scale-up in fixed bowl mixer-granulators has been studied by Ray Rowe and Mike Cliff’s group (42) using the classical dimensionless numbers of Newton (Power), Reynolds and Froude to predict end-point in geometrically similar high-shear Fielder PMA 25, 100, and 600 liter machines. Table V. Relevance List for Case Study II (Landin et al., 1996) Quantity 1 Power consumption 2 3 4 5 6 7 Specific density Blade diameter Blade speed Dynamic viscosity Gravitational constant Bowl height Symbol P ρ D n η g H Units Watt kg / m3 m rev / s Pa * s m / s2 m Dimensions M L2 T-3 M L-3 L T-1 M L-1 T-1 L T-2 LPage 23 of 40The relevance list (Table V) 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 that dynamic viscosity has replaced the binder amount and bowl volume of the Leuenberger’s relevance list, thus making it applicable to viscous binders and allowing long range particle interactions responsible for friction. Table VI. The Dimensional Matrix for Case Study II Core matrix ρ Mass M Length L Time T 1 C3 0 d 0 1 0 n 0 0 C1 Residual Matrix P 1 2 C3 η 1 -1 -1 g 0 1 -2 H 0 1 0The dimensional matrix for Case Study II (Table VI) is different from Table II: the columns for mass [M] and bowl volume [L3] are replaced by a viscosity [ML-1T-1] column. Evidently, it was assumed that the mass and volume can be adequately represented in the Relevance List by the density and powder height in a semicylindrical vessel of a known diameter. Unity matrix ρ M 3M + L -T 1 0 0 d 0 1 0 n 0 0 1 Residual Matrix P 1 5 3 η 1 2 1 g 0 1 2 H 0 1 0Table VII. The Transformed Dimensional Matrix for Case Study II. The residual matrix (Table VII) contains four columns, therefore four dimensionless Π groups (numbers) will be formed, in accordance with the Π-theorem (7 variables C 3 dimensions = 4 dimensionless groups). Table VIII: Dimensionless Π groups formed from the matrix in Table VIIPage 24 of 40Π group Π0 = Π1 = Π2 = Π3 =Expression P / (r1 * d5 * n3) η / (r1 * d2 * n1) g / (r0 * d1 * n2) H / (r0 * d1 * n0) = Np = Re-1 = Fr-1 =H/dDefinition Newton (Power) number Reynolds number Froude number Geometric number (Ratio of Characteristic Lengths)Table VIII lists
they correspond to Newton pow