Highlighting reproducibility & Comparison vs Flodex

再现性&Flodex的比较

1. Introduction

介绍

1. Theoretical Framework

理论概况

Granular materials and fine powders are widely used in industrial applications. To control and to optimize processing methods, these materials have to be precisely characterized. The characterization methods are related either to the properties of the grains (granulometry, morphology, chemical composition, …) and to the behaviour of the bulk powder (flowability, density, blend stability, electrostatic properties, …). However, concerning the physical behaviour of bulk powder, most of the techniques used in R&D or quality control laboratories are based on old measurement techniques. During the last decade, we have updated these techniques to meet the present requirements of R&D laboratories and production departments. In particular, the measurement processes have been automatized and rigorous initialization methods have been developed to obtain reproducible and interpretable results. Moreover, the use of image analysis techniques improves the measurements precision.

颗粒状材料和精细粉体在工业上有着广泛的应用。为了控制和优化加工方法，必须对这些材料进行的表征。表征方法既与颗粒的性质(粒度、形态、化学成分等)有关，也与粉体的行为(流动性、密度、共混稳定性、静电性能等)有关。然而，关于散装粉末的物理性能，大多数在研发或质量控制实验室使用的技术是基于旧的测量技术。在过去的十年中，我们更新了这些技术，以满足研发实验室和生产部门目前的要求。特别是，测量过程已经自动化，并开发了严格的初始化方法，以获得可重复和可解释的结果。利用图像分析技术提高了测量精度。

A range of measurement methods has been developed to cover all the needs of industries processing powders and granular materials. However, in this application note, we will be focused on the GranuFlow instrument.

一系列的测量方法已经发展，以涵盖所有的需要，工业加工粉末和颗粒材料。但是，在这个应用说明中，我们将主要关注GranuFlow仪器。

1. GranuFlow

粉体流动性分析仪

GranuFlow is an improved laboratory silo compared to the ancient Hall Flow Meter (ASTM B213, ISO4490) and compared to the “Flow Through An Orifice” method described in the Pharmacopeia (USP1174).

与古老的霍尔流量计(ASTM B213, ISO4490) 或者与药典(USP1174)中描述的“通过孔口的流动”方法相比，GranuFlow是一个先进的流速计。

GranuFlow is a straightforward powder flowability measurement device composed of a silo with different apertures associated with a dedicated electronic balance to measure the flowrate. This flowrate is computed automatically from the slope of the mass temporal evolution measured with the balance. The aperture size is modified quickly and easily with an original rotating system. The measurement and the result analysis are assisted by software. The flowrate is measured for a set of aperture sizes to obtain a flow curve. Finally, the whole flow curve is fitted with the well-known Beverloo theoretical model to obtain a flowability index (Cb, related to the powder flowability) and the minimum aperture size to obtain a flow (Dmin) (for theoretical background, user can refer to Appendix 1). The whole measurement is performed easily, fastly and precisely.

GranuFlow是一种简单明了的粉末流动性测量装置，它由一个不同孔径的筒仓和一个专用的电子天平组成。这种流量是根据用天平测量的流速质量随时间演化的比率（斜率）自动计算出来的。利用原有的旋转系统，可以快速、方便地调整孔径大小。软件辅助测量和结果分析。通过测量一组孔径尺寸来获得流量曲线。后,整个流动曲线是配备Beverloo理论模型获得流动性指数(Cb、粉末流动性相关)和小孔径大小获得流(Dmin)(为理论背景,用户可以参考附录1)。整个测量容易执行,快速准确。

In this paper, we used a complete set of hole diameters: 4, 6, 8, 10, 12, 14mm and 16mm.

在本文中，我们使用了一套完整的孔径:4、6、8、10、12、14和16毫米。

The main purpose of this application note is to provide information about the measurements reproducibility with the GranuFlow and to show some examples about what is it able to offer. In a second part, a comparison between Hall Flowmeter and GranuFlow is presented in order to show the advantage of using GranuFlow.

本应用说明的主要目的是为医药领域提供有关乳糖分析的信息。

1. Experimental setup

实验方法

1. Material

材料

The product FlowLac 100 provided by Meggle Pharma is used in this application note. It is produced by spray-drying a suspension of fine milled alpha-lactose monohydrate crystals in a solution of lactose. When lactose in solution is spray-dried, a rapid removal of water is taking place, whereby amorphous, non-crystalline lactose is formed in addition to crystalline lactose.

Meggle Pharma提供的产品FlowLac 100用于本案例。它是通过喷雾干燥悬浮液的精细研磨阿尔法乳糖一水晶体在乳糖的解决方案。当溶液中的乳糖被喷雾干燥时，水的快速去除就发生了，因此除了结晶乳糖外，无定形的、非晶状的乳糖也形成了。

Due to the spray-drying process, this powder has a spherical shape, consisting of small alphalactose monohydrate crystals bound by amorphous lactose.

由于喷雾干燥过程，这种粉末有一个球形的形状，由无定形乳糖结合的小无定型乳糖晶体组成。

Figure 1: FlowLac 100, SEM Picture and particle size distribution (manufacturer data).

图1:FlowLac 100, SEM图片和粒度分布(生产商数据)。

1. Experimental protocol

实验方案

1. GranuFlow

粉体流动性分析仪

GranuFlow analysis were performed at 20.6°C and 34.6%RH. Mass Flowrate was investigated for different hole size (from 4mm to 16mm). Measurements were repeated three times

在20.6℃和34.6%RH下使用GranuFlow分析。研究了不同孔径(4mm ~ 16mm)下的质量流量。测量重复三次

F is the powder flowrate (in g/s) and Cb the Beverloo parameter (in g/cm3). Dmin is the minimum aperture size to obtain a flow (for more information about the Beverloo model, please refer to Appendix 1).

F为粉末流量(单位为g/s)， Cb为Beverloo参数(单位为g/cm3)。Dmin是获得流的小孔径大小(有关Beverloo模型的更多信息，请参见附录1)。

5 min are needed to run one complete measurements (with every hole size, cleaning and with Beverloo’s Law calculation).

需要5分钟来完成一次完整的测量(每个孔的大小，清洗和贝弗罗定律计算)。

1. Flodex

Flodex analysis were performed at 21.2°C and 34.3%RH. Mass flowrate was measured for the same aperture size than those used with the GranuFlow (from 4 to 16mm). Measurements were repeated two times.

在21.2℃和34.3%RH下使用Flodex进行分析。在孔径尺寸相同(4 - 16mm)的情况下测量质量流量。测量重复两次。

30 min are needed to run all measurements (with every hole size, cleaning, but without plotting the Beverloo’s Law).

需要30分钟来运行所有的测量(每个孔的大小，清洁，但不绘制贝弗里洛定律)。

1. GranuFlow versus Flodex

GranuFlow对比Flodex

1. Experimental results

实验结果

The following figure allows comparison between GranuFlow and Flodex. All error bars are calculated using the standard deviation obtained for reproducibility measurements (S is the average sum of squared residuals, calculated with the experimental and Beverloo mass flowrates). The flowability of FlowLac 100 powder was investigated three times with the GranuFlow and two times with the Flodex:

下图比较了GranuFlow和Flodex。所有的误差条都是用可重现性测量得到的标准偏差来计算的(S是残差平方和的平均值，用实验和贝弗卢质量流量来计算)。对FlowLac 100粉体的流动性进行了3次GranuFlow实验和2次Flodex实验:

Figure 2: Mass flowrate versus aperture size - Comparison between GranuFlow and Flodex.

图2:质量流量与孔径大小- GranuFlow对比Flodex

The first observation is related to the ease of use of the GranuFlow in comparison with Flodex. Indeed, many time is wasted to change Flodex’s disks and to clean all the workplan between two experiments. Moreover, Flodex instrument does not allow the Beverloo law determination (calculations were done after experiment using the excel software).

个观察结果是与Flodex相比，GranuFlow更容易使用。事实上，在两次实验之间，许多时间被浪费在更换Flodex的转盘和清洗上。此外，Flodex仪器不符合的测定(计算是在使用excel软件进行实验后进行的)。

Regarding the average sum of squared residuals, it is possible to conclude that the Beverloo law regression is more accurate with the GranuFlow (S = 2.70g²/s²) than the Flodex instrument (S = 9.99g²/s²).

关于平均残差平方和,可以得出这样的结论: 对于贝弗卢定律计算，GranuFlow (S²= 2.70 g / S²)比Flodex仪器(S²= 9.99 g / S²)更准确。

If we consider the error bars (especially with an aperture of 16mm), we can see that the reproducibility is better with GranuFlow than Flodex. This fact is explained by the complete automatic procedure for the GranuFlow, while the time measurement is achieved manually (chronometer) with the Flodex instrument.

如果我们考虑误差条(特别是孔径为16mm的)，我们可以看到，GranuFlow的重现性比Flodex更好。这一事实是解释了具备完整自动检测程序的GranuFlow的优势，而Flodex则只能通过使用(精密计时器)实现手动计时。

Finally, GranuFlow and Flodex result are slightly different, some issues with the Flodex instrument may explain this fact: powder aeration/electrostatic charges during measurement and porous medium height dependency.

后，GranuFlow和Flodex的结果略有不同，Flodex仪器的一些问题可以解释这一事实:在测量过程中粉末的透气/静电荷和多孔介质的高度相关性。

1. Flodex issues

Flodex问题

1. Triboelectricity and powder aeration

静电和粉体透气性

For the Flodex experiment, the powder is used to analyse mass flowrate versus aperture size. However, despite this protocol allows to use a small powder quantity, it also leads to electrical charges build up inside the powder (cf. Figure 3). Therefore, at the end of experiment the powder mass flowrate will be erratic.

在Flodex实验中，粉末用于分析质量流量与孔径大小的关系。然而，尽管该方案允许使用少量粉末，但也会导致粉末内部电荷积聚(cf.图3)，因此，在实验结束时，粉末的质量流量将不稳定。

Figure 3: Beaker photography after experiments with Flodex - Highlighting the electrostatic effect.

图3:用Flodex做实验后的烧杯照片——静电效果。

Moreover, using the same powder will aerate it, and therefore, it will modify the powder flowing behaviour.

此外，使用相同的粉末会使空气进入粉体，因此，它会改变粉末的流动行为。

Powder height dependency

粉体高度依赖性

Contrary to the fluids, when a silo is discharged by gravity, the flow rate does not depend on the height of the granular layer. Indeed, when this value is greater than 1.2 times the diameter of the silo, the pressure at the bottom of the silo saturates due to the Janssen effect and hence, the flow rate remains constant (Mankoc et al., 2007).

与流体相反，当筒仓在重力作用下排出时，其流速并不取决于颗粒层的高度。实际上，当该值大于筒仓直径的1.2倍时，筒仓底部的压力由于Janssen效应而饱和，因此流量保持不变(Mankoc et al., 2007)。

However, due to the small height of the Flodex instrument (7.5cm), the powder height dependency is still observed at the end of its tank discharge. Thus, this instrument will be only useful to have an idea about the minimum aperture for the powder to flow.

然而，由于Flodex仪器的高度较小(7.5cm)，在其容器排放结束时仍能观察到粉末高度依赖性。因此，这个仪器只有在知道粉末流动的小孔径时才有用。

1. Conclusions
2.  

✓ An experiment with the GranuFlow is extremely faster than Flodex (5min with GranuFlow and 30min with Flodex).

使用GranuFlow的实验速度比Flodex快得多(5分钟使用颗粒剂，30分钟使用Flodex)。

✓ GranuFlow allows to plot the full Beverloo mass flowrate curve, while Flodex only allow experimental data measurements.

GranuFlow能够绘制完整的Beverloo质量流量曲线，而Flodex只能够给出实验数据。

✓ GranuFlow provides powder flowability measurements with Beverloo Law (i.e. Cb coefficient, with an error close to 2.4%) and an estimation of the Cohesive Index with Dmin parameter (minimum diameter for the powder to flow in silo configuration).

GranuFlow使用贝弗罗定律(即Cb系数，误差接近2.4%)对粉末流动性进行测量，并使用Dmin参数(粉末在筒仓结构中流动的小直径)估计粘性指数。

✓ However, Flodex provides powder flowability with a slightly worse accuracy (3.1%), and no information about the Beverloo law is given (calculation need to be carried out with excel).

但是，Flodex提供的粉末流动性准确性稍差(3.1%)，而且没有给出贝弗里洛定律(Beverloo law)的信息(需要用excel进行计算)。

Bibliography

参考文献

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Appendix 1: GranuFlow theoretical background

附录1：GranuFlow理论背景

The mass flowrate F through a circular orifice of diameter D is given by the product of the mean speed of the grains <vout>, the aperture area and the bulk density ρ. One has the general expression:

质量流率F通过圆孔的直径D的产物颗粒的平均速度<流出速度>、孔径面积和体积密度ρ。一个是一般表达式:

𝐹 = 𝜌 < 𝑣𝑜𝑢𝑡 >

𝜋 𝐷2 4

The Beverloo's law is based on two hypotheses:

贝弗里洛定律基于两个假设:

• The flow is blocked when the orifice diameter is below a threshold Dmin.

当孔板直径低于阈值Dmin时，阻挡流动。

• The grains experience a free fall before passing through the orifice, i.e. 𝑣𝑜𝑢𝑡 = √2 𝑔 𝛽 𝐷. This relation comes from the idea that the jamming mechanism is due to the formation of a semispherical arch before the orifice. If this arch has a typical size proportional to the aperture, we obtain 𝛽 = 0,5. To be more general, the parameter 𝛽 can be a free parameter.

Finally, the mass flowrate expression becomes:

颗粒自由落体,然后再通过孔,即𝑣𝑜𝑢𝑡=√2𝑔𝛽𝐷。这种关系来自于这样一种观点，即堵塞机构是由于在孔口前形成半球形的拱。如果这拱具有典型的孔径大小成正比的,我们获得𝛽= 0、5。通常来讲,参数𝛽可以自由参数。

后，质量流量表达式为:

𝐹 =

𝜌 √2 𝛽 𝜋 4

 √𝑔 (𝐷 − 𝐷𝑚𝑖𝑛)2,5 = 𝐶𝑏 √𝑔 (𝐷 − 𝐷𝑚𝑖𝑛)2,5