使用Granutools粉體流動性分析儀進行乳糖粉體分析
 

1. Introduction

介紹

1. Theoretical Framework

理論概況
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. 
顆粒狀材料和精細(xì)粉體在工業(yè)上有著廣泛的應(yīng)用。為了控制和優(yōu)化加工方法，必須對這些材料進行精確的表征。表征方法既與顆粒的性質(zhì)(粒度、形態(tài)、化學(xué)成分等)有關(guān)，也與粉體的行為(流動性、密度、共混穩(wěn)定性、靜電性能等)有關(guān)。然而，關(guān)于散裝粉末的物理性能，大多數(shù)在研發(fā)或質(zhì)量控制實驗室使用的技術(shù)是基于舊的測量技術(shù)。在過去的十年中，我們更新了這些技術(shù)，以滿足研發(fā)實驗室和生產(chǎn)部門目前的要求。特別是，測量過程已經(jīng)自動化，并開發(fā)了嚴(yán)格的初始化方法，以獲得可重復(fù)和可解釋的結(jié)果。利用圖像分析技術(shù)提高了測量精度。
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.
一系列的測量方法已經(jīng)得到發(fā)展，以涵蓋所有的需要，工業(yè)加工粉末和顆粒材料。但是，在這個應(yīng)用中，我們將主要關(guān)注GranuFlow儀器。
 

1. GranuFlow

粉體流動性分析儀
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). 
與古老的霍爾流量計(ASTM B213, ISO4490) 或者與藥典(USP1174)中描述的“通過孔口的流動”方法相比，GranuFlow是一個先進的流速計。
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是一種簡單明了的粉末流動性測量裝置，它由一個不同孔徑的筒倉和一個專用的電子天平組成。這種流量是根據(jù)用天平測量的流速質(zhì)量隨時間演化的比率（斜率）自動計算出來的。利用原有的旋轉(zhuǎn)系統(tǒng)，可以快速、方便地調(diào)整孔徑大小。軟件輔助測量和結(jié)果分析。通過測量一組孔徑尺寸來獲得流量曲線。最后,整個流動曲線是配備知名Beverloo理論模型獲得流動性指數(shù)(Cb、粉末流動性相關(guān))和最小孔徑大小獲得流(Dmin)(為理論背景,用戶可以參考附錄1)。整個測量容易執(zhí)行,快速準(zhǔn)確。
In this paper, we used a complete set of hole diameters: 4, 6, 8, 10, 12, 14 and 16mm.
在本文中，我們使用了一套完整的孔徑: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.
本應(yīng)用說明的主要目的是為醫(yī)藥領(lǐng)域提供有關(guān)乳糖分析的信息。
 

1. Lactose analysis
   乳糖分析
2. 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:
本應(yīng)用中使用的粉末由Meggle Pharma提供。所有這些樣品都是乳糖。他們被制造商稱為Tablettose 70, Tablettose 80, Flowlac 90和Flowlac 100。根據(jù)供應(yīng)商的數(shù)據(jù)，這些粉末的理化性能描述如下表:
Table 1: Lactose physico-chemical properties
表1:乳糖理化性質(zhì)

	松裝密度(g/l)	振實密度	豪斯納比
Tablettose 70
Tablettose 80
Flowlac 90
Flowlac 100

 
SEM pictures have been made in order to have an information of the particle size distribution and particles shape:
為了獲得顆粒尺寸分布和顆粒形狀的信息，通過掃描電鏡獲得如下圖片：
The first observation concerns the particles shape, indeed, all Flowlac samples have spherical shape, while Tablettose samples have irregular one.
首先觀察到的是顆粒的形狀，所有的Flowlac樣品都是球形的，而Tablettose樣品是不規(guī)則的。
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軟件的幫助下,四個樣品進行了粒度分析(ddp是指初級粒子直徑和標(biāo)準(zhǔn)差σ):
Table 2: Lactose granulometric analysis.
表2:乳糖顆粒分析。

1. GranuFlow analysis
   使用GranuFlow進行分析

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干燥空氣)進行顆粒流分析。研究了不同孔徑(4mm ~ 16mm)下的質(zhì)量流量。F為粉末流量(單位為g/s)， Cb為Beverloo參數(shù)(單位為g/mm3)。Dmin是獲得流量的最小孔徑尺寸:
Table 3: Raw data obtained with the GranuFlow instrument for the four lactose samples.
表3:通過GranuFlow儀器獲得的四個乳糖樣品的原始數(shù)據(jù)。
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:
這些結(jié)果確實很有趣，從豪斯納比(cf. Table 1)可以看出，經(jīng)典的振實密度測試(“Densitap”)無法區(qū)分樣品之間的差異(盡管樣品的物理化學(xué)成分具有高度異質(zhì)性)。然而，GranuFlow滿足用戶對粉末進行非常精確的分類(借助Cb和Dmin參數(shù))。雖然Flowlac90和Tablettose70具有相同的Cb參數(shù)，但Dmin信息可以讓我們確認(rèn)Flowlac90在所有樣本中流動性最好，其次是Tablettose70。Flowlac100排在第三位，而Tablettose80的流動性較差。為了證明這些假設(shè)，下圖顯示了根據(jù)孔直徑的質(zhì)量流量:
Figure 5: Mass flowrate versus aperture size for all lactose samples. Lines represent the Beverloo law.
圖5:所有乳糖樣品的質(zhì)量流量與孔徑大小。線條代表貝弗里洛定律。
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.
這個圖表顯示了實驗數(shù)據(jù)和模型值之間的良好相關(guān)性(用貝弗里洛定律)。這一事實是非常重要的，因為在貝弗盧模型中，用戶可以進行數(shù)據(jù)補充，從而預(yù)測不同孔大小的質(zhì)量流量。
Conclusions
總結(jié)
✓ GranuFlow allows to plot the full mass flowrate curve.
GranuFlow能夠繪制完整的質(zhì)量流量曲線
✓ GranuFlow gives information about the Beverloo law (i.e powder flowability and minimum diameter for the powder to flow in silo configuration).
GranuFlow給出了滿足貝弗里洛定律計算需要的信息(如：在粉末在筒倉中，粉末的流動性和最小流出孔徑)
✓ GranuFlow allows to classify powders in terms of flowability, even if the classical tap density test is unable to see Hausner ratio difference.
即使經(jīng)典的振實密度測試無法看出豪斯納比值的差異，GranuFlow也能夠根據(jù)流動性對粉末進行分類。
Bibliography
參考文獻(xiàn)
Appendix 1: GranuFlow theoretical background
附錄1：GranuFlow理論背景
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:
質(zhì)量流率F通過圓孔的直徑D的產(chǎn)物顆粒的平均速度<流出速度>、孔徑面積和體積密度ρ。一個是一般表達(dá)式:
𝐹 = 𝜌 < 𝑣𝑜𝑢𝑡 >
𝜋 𝐷2 4
 
The Beverloo's law is based on two hypotheses: 
貝弗里洛定律基于兩個假設(shè):
• The flow is blocked when the orifice diameter is below a threshold Dmin. 
當(dāng)孔板直徑低于閾值Dmin時，阻擋流動。 
• 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:
顆粒自由落體,然后再通過孔,即𝑣𝑜𝑢𝑡=√2𝑔𝛽𝐷。這種關(guān)系來自于這樣一種觀點，即堵塞機構(gòu)是由于在孔口前形成半球形的拱。如果這拱具有典型的孔徑大小成正比的,我們獲得𝛽= 0、5。通常來講,參數(shù)𝛽可以自由參數(shù)。 
最后，質(zhì)量流量表達(dá)式為:
 
𝐹 =
𝜌 √2 𝛽 𝜋 4
 √𝑔 (𝐷 − 𝐷𝑚𝑖𝑛)2,5 = 𝐶𝑏 √𝑔 (𝐷 − 𝐷𝑚𝑖𝑛)2,5