Highlighting reproducibility & Comparison vs Flodex
再現(xiàn)性&Flodex的比較
 

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)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)用說明中，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 Pharmacopeia (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,快速準確。
In this paper, we used a complete set of hole diameters: 4, 6, 8, 10, 12, 14mm 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 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. Experimental setup

實驗方法

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提供的產(chǎn)品FlowLac 100用于本案例。它是通過噴霧干燥懸浮液的精細研磨阿爾法乳糖一水晶體在乳糖的解決方案。當溶液中的乳糖被噴霧干燥時，水的快速去除就發(fā)生了，因此除了結(jié)晶乳糖外，無定形的、非晶狀的乳糖也形成了。
Due to the spray-drying process, this powder has a spherical shape, consisting of small alphalactose monohydrate crystals bound by amorphous lactose.
由于噴霧干燥過程，這種粉末有一個球形的形狀，由無定形乳糖結(jié)合的小無定型乳糖晶體組成。

Figure 1: FlowLac 100, SEM Picture and particle size distribution (manufacturer data).
圖1:FlowLac 100, SEM圖片和粒度分布(生產(chǎn)商數(shù)據(jù))。

1. Experimental protocol
   實驗方案
2. GranuFlow
   粉體流動性分析儀

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。研究了不同孔徑(4mm ~ 16mm)下的質(zhì)量流量。測量重復(fù)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為粉末流量(單位為g/s)， Cb為Beverloo參數(shù)(單位為g/cm3)。Dmin是獲得流的最小孔徑大小(有關(guān)Beverloo模型的更多信息，請參見附錄1)。
5 min are needed to run one complete measurements (with every hole size, cleaning and with Beverloo’s Law calculation).
需要5分鐘來完成一次完整的測量(每個孔的大小，清洗和貝弗羅定律計算)。

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進行分析。在孔徑尺寸相同(4 - 16mm)的情況下測量質(zhì)量流量。測量重復(fù)兩次。
30 min are needed to run all measurements (with every hole size, cleaning, but without plotting the Beverloo’s Law).
需要30分鐘來運行所有的測量(每個孔的大小，清潔，但不繪制貝弗里洛定律)。
 

1. GranuFlow versus Flodex
   GranuFlow對比Flodex
2. Experimental results
   實驗結(jié)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:
下圖比較了GranuFlow和Flodex。所有的誤差條都是用可重現(xiàn)性測量得到的標準偏差來計算的(S是殘差平方和的平均值，用實驗和貝弗盧質(zhì)量流量來計算)。對FlowLac 100粉體的流動性進行了3次GranuFlow實驗和2次Flodex實驗:
Figure 2: Mass flowrate versus aperture size - Comparison between GranuFlow and Flodex.
圖2:質(zhì)量流量與孔徑大小- GranuFlow對比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).
第一個觀察結(jié)果是與Flodex相比，GranuFlow更容易使用。事實上，在兩次實驗之間，許多時間被浪費在更換Flodex的轉(zhuǎn)盤和清洗上。此外，F(xiàn)lodex儀器不符合的測定(計算是在使用excel軟件進行實驗后進行的)。
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).
關(guān)于平均殘差平方和,可以得出這樣的結(jié)論: 對于貝弗盧定律計算，GranuFlow (S²= 2.70 g / S²)比Flodex儀器(S²= 9.99 g / S²)更準確。
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.
如果我們考慮誤差條(特別是孔徑為16mm的)，我們可以看到，GranuFlow的重現(xiàn)性比Flodex更好。這一事實是解釋了具備完整自動檢測程序的GranuFlow的優(yōu)勢，而Flodex則只能通過使用(精密計時器)實現(xiàn)手動計時。
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.
最后，GranuFlow和Flodex的結(jié)果略有不同，F(xiàn)lodex儀器的一些問題可以解釋這一事實:在測量過程中粉末的透氣/靜電荷和多孔介質(zhì)的高度相關(guān)性。

1. Flodex issues
   Flodex問題
2. Triboelectricity and powder aeration
   靜電和粉體透氣性
   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實驗中，粉末用于分析質(zhì)量流量與孔徑大小的關(guān)系。然而，盡管該方案允許使用少量粉末，但也會導(dǎo)致粉末內(nèi)部電荷積聚(cf.圖3)，因此，在實驗結(jié)束時，粉末的質(zhì)量流量將不穩(wěn)定。
Figure 3: Beaker photography after experiments with Flodex - Highlighting the electrostatic effect.
圖3:用Flodex做實驗后的燒杯照片——靜電效果。
Moreover, using the same powder will aerate it, and therefore, it will modify the powder flowing behaviour.
此外，使用相同的粉末會使空氣進入粉體，因此，它會改變粉末的流動行為。
Powder height dependency
粉體高度依賴性
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).
與流體相反，當筒倉在重力作用下排出時，其流速并不取決于顆粒層的高度。實際上，當該值大于筒倉直徑的1.2倍時，筒倉底部的壓力由于Janssen效應(yīng)而飽和，因此流量保持不變(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儀器的高度較小(7.5cm)，在其容器排放結(jié)束時仍能觀察到粉末高度依賴性。因此，這個儀器只有在知道粉末流動的最小孔徑時才有用。

1. Conclusions
   結(jié)論

✓ An experiment with the GranuFlow is extremely faster than Flodex (5min with GranuFlow and 30min with Flodex).
使用GranuFlow的實驗速度比Flodex快得多(5分鐘使用顆粒劑，30分鐘使用Flodex)。
✓ GranuFlow allows to plot the full Beverloo mass flowrate curve, while Flodex only allow experimental data measurements.
GranuFlow能夠繪制完整的Beverloo質(zhì)量流量曲線，而Flodex只能夠給出實驗數(shù)據(jù)。
✓ 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使用貝弗羅定律(即Cb系數(shù)，誤差接近2.4%)對粉末流動性進行測量，并使用Dmin參數(shù)(粉末在筒倉結(jié)構(gòu)中流動的最小直徑)估計粘性指數(shù)。
✓ 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，F(xiàn)lodex提供的粉末流動性準確性稍差(3.1%)，而且沒有給出貝弗里洛定律(Beverloo law)的信息(需要用excel進行計算)。
Bibliography
參考文獻
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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 , 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)量流量表達式為:
 
𝐹 =
𝜌 √2 𝛽 𝜋 4
 √𝑔 (𝐷 − 𝐷𝑚𝑖𝑛)2,5 = 𝐶𝑏 √𝑔 (𝐷 − 𝐷𝑚𝑖𝑛)2,5