2019-11-01
Highlighting reproducibility & Comparison vs Flodex
再(zai)現性&Flodex的(de)比較
介紹
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(liao)和精細粉體在工業上有著廣泛(fan)的(de)應用。為了控制和優化加工方(fang)(fang)法，必須(xu)對(dui)這(zhe)些材料(liao)進行的(de)表征。表征方(fang)(fang)法既與顆粒的(de)性質(粒度(du)、形態、化學成分(fen)等)有(you)關，也與粉體的行為(wei)(流(liu)動性(xing)、密度(du)、共混穩定性(xing)、靜(jing)電性(xing)能等)有關。然而(er)，關于散(san)裝粉末的(de)(de)(de)物(wu)理性能(neng)，大(da)多數在(zai)研(yan)發(fa)或質量(liang)控制實驗(yan)室使用的(de)(de)(de)技術(shu)是(shi)基(ji)于舊的(de)(de)(de)測(ce)(ce)量(liang)技術(shu)。在(zai)過(guo)(guo)去的(de)(de)(de)十年中，我們更新了這(zhe)些技術(shu)，以(yi)滿足(zu)研(yan)發(fa)實驗(yan)室和生產(chan)部門目前的(de)(de)(de)要(yao)求。特(te)別是(shi)，測(ce)(ce)量(liang)過(guo)(guo)程已(yi)經自動化(hua)，并開發(fa)了嚴格的(de)(de)(de)初始化(hua)方(fang)法，以(yi)獲得可重(zhong)復和可解(jie)釋的(de)(de)(de)結果。利用圖像分析技術(shu)提高了測(ce)(ce)量(liang)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(ce)量方法(fa)已(yi)經發展，以涵蓋所有的需要(yao)，工業(ye)加工粉末和(he)顆粒(li)材料。但是，在這個應用(yong)說明(ming)中，我們(men)將(jiang)主要(yao)關注GranuFlow儀器。
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(de)(de)霍爾流(liu)量計(ASTM B213, ISO4490) 或者(zhe)與藥(yao)典(USP1174)中描(miao)述的(de)(de)“通過孔口的(de)(de)流(liu)動(dong)”方法(fa)相(xiang)比，GranuFlow是(shi)一個先進的(de)(de)流(liu)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(jian)單(dan)明了的(de)粉末流(liu)(liu)動性測(ce)量裝置，它由(you)一個不(bu)同(tong)孔(kong)徑的(de)筒倉和(he)一個專用的(de)電(dian)子天(tian)平組(zu)成。這種流(liu)(liu)量是根據用天(tian)平測(ce)量的(de)流(liu)(liu)速質量隨(sui)時間演(yan)化(hua)的(de)比(bi)率（斜率）自(zi)動計算出(chu)來的(de)。利用原(yuan)有的(de)旋轉系統，可以快速、方便(bian)地調整孔(kong)徑大小。軟件(jian)輔助測(ce)量和(he)結果分析。通過測(ce)量一組(zu)孔(kong)徑尺寸(cun)來獲得流(liu)(liu)量曲線。后(hou),整個(ge)流動曲線是配備Beverloo理論(lun)模型獲得流動性指數(Cb、粉末流動性(xing)相關)和(he)小孔徑大小獲得流(Dmin)(為理論背景,用戶可以參考附(fu)錄1)。整個(ge)測量容(rong)易執(zhi)行,快速準確(que)。
In this paper, we used a complete set of hole diameters: 4, 6, 8, 10, 12, 14mm and 16mm.
在本文中，我(wo)們使用(yong)了一套完(wan)整(zheng)的孔徑(jing):4、6、8、10、12、14和16毫米(mi)。
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(ying)用說明的主要目(mu)的是為醫(yi)藥領(ling)域提(ti)供有關乳糖(tang)分(fen)析的信息。
實驗方法
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(gong)的產(chan)品(pin)FlowLac 100用于本案(an)例。它是通過噴(pen)霧(wu)干燥懸浮(fu)液的(de)(de)精(jing)細(xi)研磨阿爾(er)法乳糖(tang)(tang)一水晶(jing)體(ti)在乳糖(tang)(tang)的(de)(de)解(jie)決方案(an)。當溶液中的(de)(de)乳糖(tang)(tang)被(bei)噴(pen)霧(wu)干燥時，水的(de)(de)快速去除就(jiu)發生了，因此除了結晶(jing)乳糖(tang)(tang)外，無(wu)定形的(de)(de)、非晶(jing)狀的(de)(de)乳糖(tang)(tang)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(you)于噴(pen)霧干燥(zao)過程，這種(zhong)粉末有一個球形的形狀(zhuang)，由(you)無定形乳(ru)糖(tang)(tang)結合(he)的小無定型乳(ru)糖(tang)(tang)晶(jing)體(ti)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(生產商(shang)數據(ju))。
實驗方案
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(xia)使用GranuFlow分(fen)析(xi)。研(yan)究了不同孔徑(4mm ~ 16mm)下的質量(liang)流(liu)量(liang)。測(ce)量(liang)重復三次
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(liang)(單位為g/s)， Cb為Beverloo參數(單(dan)位為g/cm3)。Dmin是獲得流的小孔徑大小(有關(guan)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(zhong)來完(wan)成(cheng)一次(ci)完(wan)整的(de)測(ce)量(每(mei)個(ge)孔的大小，清洗(xi)和貝弗(fu)羅定律計算(suan))。
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(kuang)下測量質量流(liu)量。測量重復兩次。
30 min are needed to run all measurements (with every hole size, cleaning, but without plotting the Beverloo’s Law).
需(xu)要(yao)30分鐘來運行(xing)所(suo)有(you)的測量(每個孔的大(da)小(xiao)，清潔，但不繪制貝(bei)弗里(li)洛(luo)定律)。
GranuFlow對比Flodex
實驗結果
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(xia)圖比(bi)較(jiao)了GranuFlow和Flodex。所有的(de)誤差(cha)(cha)條都是(shi)用(yong)可重(zhong)現性測量(liang)得到的(de)標準(zhun)偏差(cha)(cha)來(lai)計算的(de)(S是(shi)殘差(cha)(cha)平方和的(de)平均值，用(yong)實驗(yan)和貝(bei)弗盧(lu)質量(liang)流量(liang)來(lai)計算)。對FlowLac 100粉(fen)體的(de)流動(dong)性進行(xing)了3次GranuFlow實驗(yan)和2次Flodex實驗(yan):
Figure 2: Mass flowrate versus aperture size - Comparison between GranuFlow and Flodex.
圖2:質量流量與孔徑大小- GranuFlow對(dui)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).
個觀察結果是與Flodex相比，GranuFlow更容(rong)易使用。事實(shi)(shi)上，在(zai)兩次(ci)實(shi)(shi)驗之間，許(xu)多時間被(bei)浪費在(zai)更換Flodex的轉盤(pan)和(he)清洗上。此外，Flodex儀器不符合的測定(計算是在(zai)使用excel軟件進(jin)行實驗后進(jin)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).
關于平(ping)均殘差平(ping)方(fang)和,可以(yi)得(de)出這樣的結論: 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(que)。
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(guo)我們考慮誤差條(特別是孔徑為16mm的)，我們(men)可以看到(dao)，GranuFlow的重現性比Flodex更好(hao)。這一事(shi)實(shi)是解釋了(le)具備(bei)完(wan)整(zheng)自動(dong)檢(jian)測(ce)程序(xu)的GranuFlow的(de)優勢，而Flodex則只能通過使用(精密計時器)實現手動計(ji)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.
后，GranuFlow和Flodex的結(jie)果略(lve)有不同，Flodex儀器的一些問(wen)題可以解釋這一事實(shi):在測量(liang)過(guo)程中粉末的透氣/靜電(dian)荷(he)和多孔介(jie)質的高度相關性(xing)。
Flodex問題
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(mo)(mo)用(yong)于(yu)分析質量(liang)流量(liang)與孔徑大小的關系。然(ran)而，盡管該方案允許使用(yong)少量(liang)粉末(mo)(mo)，但也(ye)會導致粉末(mo)(mo)內部電荷積聚(cf.圖3)，因(yin)此，在(zai)實驗(yan)結束時，粉末(mo)的質(zhi)量流量將不穩定。
Figure 3: Beaker photography after experiments with Flodex - Highlighting the electrostatic effect.
圖3:用(yong)Flodex做(zuo)實(shi)驗(yan)后的燒杯照片(pian)——靜電(dian)效(xiao)果(guo)。
Moreover, using the same powder will aerate it, and therefore, it will modify the powder flowing behaviour.
此外(wai)，使用(yong)相同的(de)粉末(mo)會使空氣進入粉體，因此，它會改變(bian)粉末(mo)的(de)流(liu)動行為(wei)。
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(ti)相反(fan)，當筒(tong)倉在(zai)重力作(zuo)用(yong)下排(pai)出時，其流速并不取決于顆粒層的高度。實際(ji)上(shang)，當該值(zhi)大于筒(tong)倉直徑的1.2倍(bei)時，筒倉底部的壓力(li)由于Janssen效應而飽和，因此流(liu)量(liang)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(qi)容(rong)器排(pai)放(fang)結束時仍(reng)能觀(guan)察到粉末高度依(yi)賴性。因此，這個儀(yi)器只(zhi)有(you)在知道(dao)粉末流動的小(xiao)孔(kong)徑(jing)時才有(you)用。
? An experiment with the GranuFlow is extremely faster than Flodex (5min with GranuFlow and 30min with Flodex).
使用GranuFlow的實驗(yan)速度比Flodex快得多(5分鐘使用顆粒劑(ji)，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(hui)制完整的Beverloo質量流(liu)量曲線，而Flodex只能夠(gou)給出實驗數據。
? 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(ding)律(即Cb系數，誤差接近2.4%)對粉末流動性(xing)進行測(ce)量，并使用Dmin參(can)數(shu)(粉末(mo)在筒倉(cang)結構中流(liu)動(dong)的小(xiao)直徑)估(gu)計粘性指(zhi)數。
? 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(gong)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(xu)要用excel進行計(ji)算(suan))。
Bibliography
參考文獻
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Appendix 1: GranuFlow theoretical background
附(fu)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:
質量(liang)流率F通過圓(yuan)孔的(de)直徑D的(de)產物顆(ke)粒的(de)平均(jun)速度<流出(chu)速(su)度>、孔徑面積(ji)和體積(ji)密度ρ。一個是一般表達(da)式:
?? = ?? < ???????? >
?? ??2 4
The Beverloo's law is based on two hypotheses:
貝弗(fu)里洛(luo)定律基(ji)于(yu)兩個(ge)假(jia)設:
• The flow is blocked when the orifice diameter is below a threshold Dmin.
當(dang)孔板直徑低于閾值Dmin時，阻擋(dang)流動。
• The grains experience a free fall before passing through the orifice, i.e. ???????? = √2 ?? ?? ??. 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 ?? = 0,5. To be more general, the parameter ?? can be a free parameter.
Finally, the mass flowrate expression becomes:
顆粒自(zi)由(you)落體(ti),然(ran)后(hou)再通過孔(kong),即????????=√2??????。這(zhe)種關系來自于這(zhe)樣一種觀點(dian)，即堵(du)塞機構是由于在孔口前形(xing)成半球形(xing)的拱(gong)。如果這(zhe)拱(gong)具有典型的孔徑大小成正比的,我們獲得(de)??= 0、5。通常來講,參數??可以自(zi)由參數。
后，質(zhi)量(liang)流量(liang)表達式為:
?? =
?? √2 ?? ?? 4
√?? (?? − ????????)2,5 = ???? √?? (?? − ????????)2,5
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