使用Granutools粉体流动性分析仪进行乳糖粉体分析

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得到发展，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 Pharmacopea (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, 14 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 regarding lactose analysis for the Pharmaceutical field.

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. Lactose analysis

乳糖分析

1. Material

材料

The powders used in this application are provided by Meggle Pharma. All these samples are made of lactose. They are called by the manufacturer Tablettose 70, Tablettose 80, Flowlac 90 and Flowlac 100. According to supplier’s data, the physico-chemical properties of these powders are described by the following table:

本应用中使用的粉末由Meggle Pharma提供。所有这些样品都是乳糖。他们被制造商称为Tablettose 70, Tablettose 80, Flowlac 90和Flowlac 100。根据供应商的数据，这些粉末的理化性能描述如下表:

Table 1: Lactose physico-chemical properties

表1:乳糖理化性质

SEM pictures have been made in order to have an information of the particle size distribution and particles shape:

为了获得颗粒尺寸分布和颗粒形状的信息，通过扫描电镜获得如下图片：

The first observation concerns the particles shape, indeed, all Flowlac samples have spherical shape, while Tablettose samples have irregular one.

首先观察到的是颗粒的形状，所有的Flowlac样品都是球形的，而Tablettose样品是不规则的。

Then, with the help of ImageJ Software, the granulometric analysis of the four samples have been carried out (dpp is the mean primary particle diameter and σ the standard deviation):

mageJ软件的帮助下,四个样品进行了粒度分析(ddp是指初级粒子直径和标准差σ):

Table 2: Lactose granulometric analysis.

表2:乳糖颗粒分析。

1. GranuFlow analysis

使用GranuFlow进行分析

GranuFlow analysis were performed at 26°C and 40.0%RH (w = 8.5gH20/kgDryAir). Mass Flowrate was investigated for different hole size (from 4mm to 16mm). F is the powder flowrate (in g/s) and Cb the Beverloo parameter (in g/mm3). Dmin is the minimum aperture size to obtain a flow:

在26°C和40.00% RH下(w = 8.5gH20/kg干燥空气)进行颗粒流分析。研究了不同孔径(4mm ~ 16mm)下的质量流量。F为粉末流量(单位为g/s)， Cb为Beverloo参数(单位为g/mm3)。Dmin是获得流量的小孔径尺寸:

Table 3: Raw data obtained with the GranuFlow instrument for the four lactose samples.

表3:通过GranuFlow仪器获得的四个乳糖样品的原始数据。

These results are really interesting, indeed by the look of Hausner ratio (cf. Table 1), we can see that the classical tap density test (“Densitap”) is unable to make differentiation between one sample to another (despite the high heterogeneity in terms of samples physico-chemical composition). However, GranuFlow allows to its user to make powder classification with great accuracy (with the help of Cb and Dmin parameters). Although Flowlac 90 and Tablettose70 have the same Cb parameter, Dmin information allows us to affirm that Flowlac90 has the best flowability from all samples and its followed by Tablettose70. Flowlac100 comes in third position, while Tablettose80 has the lower flowability. To prove these assumptions the following figure shows the mass flowrate according to hole diameter:

这些结果确实很有趣，从豪斯纳比(cf. Table 1)可以看出，经典的振实密度测试(“Densitap”)无法区分样品之间的差异(尽管样品的物理化学成分具有高度异质性)。然而，GranuFlow满足用户对粉末进行非常的分类(借助Cb和Dmin参数)。虽然Flowlac90和Tablettose70具有相同的Cb参数，但Dmin信息可以让我们确认Flowlac90在所有样本中流动性好，其次是Tablettose70。Flowlac100排在第三位，而Tablettose80的流动性较差。为了证明这些假设，下图显示了根据孔直径的质量流量:

Figure 5: Mass flowrate versus aperture size for all lactose samples. Lines represent the Beverloo law.

图5:所有乳糖样品的质量流量与孔径大小。线条代表贝弗里洛定律。

This graph shows the good correlation between experimental data and modeled values (with Beverloo law). This fact is highly important, because with the Beverloo model, user can make data interpolation, and thus predicts the mass flowrate for different hole sizes.

这个图表显示了实验数据和模型值之间的良好相关性(用贝弗里洛定律)。这一事实是非常重要的，因为在贝弗卢模型中，用户可以进行数据补充，从而预测不同孔大小的质量流量。

Conclusions

总结

✓ GranuFlow allows to plot the full mass flowrate curve.

GranuFlow能够绘制完整的质量流量曲线

✓ GranuFlow gives information about the Beverloo law (i.e powder flowability and minimum diameter for the powder to flow in silo configuration).

GranuFlow给出了满足贝弗里洛定律计算需要的信息(如：在粉末在筒仓中，粉末的流动性和小流出孔径)

✓ GranuFlow allows to classify powders in terms of flowability, even if the classical tap density test is unable to see Hausner ratio difference.

即使经典的振实密度测试无法看出豪斯纳比值的差异，GranuFlow也能够根据流动性对粉末进行分类。

Bibliography

参考文献

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