JPH0263181B2 - - Google Patents
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- Publication number
- JPH0263181B2 JPH0263181B2 JP59135978A JP13597884A JPH0263181B2 JP H0263181 B2 JPH0263181 B2 JP H0263181B2 JP 59135978 A JP59135978 A JP 59135978A JP 13597884 A JP13597884 A JP 13597884A JP H0263181 B2 JPH0263181 B2 JP H0263181B2
- Authority
- JP
- Japan
- Prior art keywords
- particle size
- scattered light
- measured
- light intensity
- size distribution
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired
Links
- 239000002245 particle Substances 0.000 claims description 105
- 238000006243 chemical reaction Methods 0.000 claims description 22
- 238000000034 method Methods 0.000 claims description 14
- 238000005259 measurement Methods 0.000 claims description 13
- 238000004364 calculation method Methods 0.000 claims description 11
- 230000001678 irradiating effect Effects 0.000 claims description 3
- 241001274197 Scatophagus argus Species 0.000 description 8
- 239000004793 Polystyrene Substances 0.000 description 7
- 238000005315 distribution function Methods 0.000 description 7
- 229920002223 polystyrene Polymers 0.000 description 7
- 239000013307 optical fiber Substances 0.000 description 5
- 238000010586 diagram Methods 0.000 description 4
- 239000007788 liquid Substances 0.000 description 3
- 230000000694 effects Effects 0.000 description 2
- 239000011521 glass Substances 0.000 description 2
- 230000003287 optical effect Effects 0.000 description 2
- 239000000725 suspension Substances 0.000 description 2
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 2
- 230000003321 amplification Effects 0.000 description 1
- QXJJQWWVWRCVQT-UHFFFAOYSA-K calcium;sodium;phosphate Chemical compound [Na+].[Ca+2].[O-]P([O-])([O-])=O QXJJQWWVWRCVQT-UHFFFAOYSA-K 0.000 description 1
- 238000007796 conventional method Methods 0.000 description 1
- 239000000284 extract Substances 0.000 description 1
- RVRCFVVLDHTFFA-UHFFFAOYSA-N heptasodium;tungsten;nonatriacontahydrate Chemical compound O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.[Na+].[Na+].[Na+].[Na+].[Na+].[Na+].[Na+].[W].[W].[W].[W].[W].[W].[W].[W].[W].[W].[W] RVRCFVVLDHTFFA-UHFFFAOYSA-N 0.000 description 1
- 230000010354 integration Effects 0.000 description 1
- 239000011159 matrix material Substances 0.000 description 1
- 239000011859 microparticle Substances 0.000 description 1
- 239000000203 mixture Substances 0.000 description 1
- 238000012544 monitoring process Methods 0.000 description 1
- 238000003199 nucleic acid amplification method Methods 0.000 description 1
- 229920006395 saturated elastomer Polymers 0.000 description 1
- 239000012798 spherical particle Substances 0.000 description 1
- 230000009466 transformation Effects 0.000 description 1
- 238000002834 transmittance Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N15/00—Investigating characteristics of particles; Investigating permeability, pore-volume or surface-area of porous materials
- G01N15/02—Investigating particle size or size distribution
- G01N15/0205—Investigating particle size or size distribution by optical means
- G01N15/0211—Investigating a scatter or diffraction pattern
Landscapes
- Chemical & Material Sciences (AREA)
- Dispersion Chemistry (AREA)
- Physics & Mathematics (AREA)
- Health & Medical Sciences (AREA)
- Life Sciences & Earth Sciences (AREA)
- Analytical Chemistry (AREA)
- Biochemistry (AREA)
- General Health & Medical Sciences (AREA)
- General Physics & Mathematics (AREA)
- Immunology (AREA)
- Pathology (AREA)
- Length Measuring Devices By Optical Means (AREA)
Description
【発明の詳細な説明】
〔発明の技術分野〕
本発明は、微小粒子の径を測定する粒径測定装
置に関する。DETAILED DESCRIPTION OF THE INVENTION [Technical Field of the Invention] The present invention relates to a particle size measuring device for measuring the diameter of microparticles.
粒径Ｄの球状粒子にレーザ光等の平行な単色光
を照射したとき、角度θ方向に生じる散乱光強度
ｉ（Ｄ、θ）はミー（Mie）散乱理論によつて正
確に計算することができる。
When a spherical particle with a particle size D is irradiated with parallel monochromatic light such as a laser beam, the scattered light intensity i (D, θ) generated in the direction of angle θ can be accurately calculated using Mie scattering theory. can.
そこで本発明者は、被測定粒子群に照射したレ
ーザ光の散乱理論に基づいて求めた１粒子による
散乱光強度ｉ（Ｄ、θ）と、粒径分布nr(D)との間
に
Ｉ（θ）∫i（Ｄ、θ）nr(D)dD ……(1)
なる関係が成立することに基づいて、その粒径分
布nr(D)を求める粒径測定装置を提唱した。 Therefore, the present inventor has determined that there is a difference between the scattered light intensity i (D, θ) by one particle, which is determined based on the scattering theory of laser light irradiated onto a group of particles to be measured, and the particle size distribution n r (D). (θ)∫i(D, θ)n r (D)dD ...(1) Based on the following relationship, we proposed a particle size measuring device that determines the particle size distribution n r (D).
この装置は、第６図にその概略構成を示すよう
に、レーザ装置１が発振出力したレーザ光をコリ
メータ系２を介して所定断面積の平行レーザビー
ムとし、これを被測定粒子群６に照射する。そし
て、上記被測定粒子群３の位置から等距離で、且
つ散乱角θに応じて微小角度Δθ毎に配置された
受光部にて前記レーザ光の被測定粒子群３による
散乱光をその散乱角θに応じてそれぞれ検知し、
その散乱光強度分布を求めている。尚、ここでは
光フアイバ４1〜４oの一端を前散乱角θに応じた
受光部に配置し、これらの光フアイバ４1〜４oを
介して導かれた各散乱光をフオトデテクタ５1〜
５oにて受光検知し、この検出したフオトデテク
タからの電流を電圧に変換し増幅する増幅器６1
〜６oを介して計算機システム７に入力するよう
に構成されている。この計算機システム７で、光
フアイバ４1〜４oが配置された散乱角θ1〜θoにお
ける散乱光強度I1、I2、…、Ioから散乱光強度分
布Ｉ（θ）＝（I1、I2、…、Io）が求められ、前記(1)
式に基づいて対数束縛積分方程式法または対数分
布関数近似法で粒径分布nr(D)が算出される。この
結果がデイスプレイ８を介し表示される。 As shown in FIG. 6, this device converts a laser beam oscillated by a laser device 1 into a parallel laser beam with a predetermined cross-sectional area via a collimator system 2, and irradiates this onto a particle group 6 to be measured. do. Then, the scattered light of the laser beam by the particle group 3 to be measured is detected at the scattering angle of the laser beam by the light-receiving section which is arranged equidistantly from the position of the particle group 3 to be measured and at every minute angle Δθ according to the scattering angle θ. Detect each according to θ,
The scattered light intensity distribution is being determined. Here, one end of the optical fibers 4 1 to 4 o is placed in a light receiving section corresponding to the forward scattering angle θ, and each scattered light guided through these optical fibers 4 1 to 4 o is sent to a photodetector 5 1 to 4 o.
An amplifier 6 which detects light reception at 5 o and converts the detected current from the photodetector into voltage and amplifies it.
~ 6o is configured to be input to the computer system 7 via. This computer system 7 calculates the scattered light intensity distribution I ( θ ) =( I 1 , I 2 , ..., I o ) are calculated, and the above (1)
Based on the formula, the particle size distribution n r (D) is calculated by the logarithmic bound integral equation method or the logarithmic distribution function approximation method. This result is displayed on the display 8.
ところが、このような装置にあつては、測定さ
れる散乱光強度分布が相対値であるため、これか
ら求められる粒径分布も相対的な値しかとり得な
いという不都合があつた。これ故、装置の適用分
野を拡大するために、粒径分布の絶対値をも測定
できる装置が要望されてきた。 However, in the case of such an apparatus, since the scattered light intensity distribution measured is a relative value, there is a disadvantage that the particle size distribution determined from this can only take a relative value. Therefore, in order to expand the field of application of the device, there has been a demand for a device that can also measure the absolute value of the particle size distribution.
〔発明の目的〕
本発明は、かかる要望に鑑みなされたものであ
り、その目的とするところは、粒径分布の絶対的
な量を測定できる実用性の高い粒径測定装置を提
供することにある。[Object of the Invention] The present invention has been made in view of such a need, and its purpose is to provide a highly practical particle size measuring device that can measure the absolute amount of particle size distribution. be.
本発明は、以下のような理論的根拠に着目して
なされたものである。
The present invention was made based on the following theoretical basis.
すなわち、第２図に示すように、通常、光路長
Ｌの測定空間に存在する数密度Npの被測定粒子
群に、半径Ｂのレーザビームを照射した場合、光
路における入射光の減衰を考慮した散乱光強度分
布Ｉ（θ）は次式に示される。 In other words, as shown in Fig. 2, when a laser beam of radius B is irradiated onto a group of particles to be measured with a number density N p existing in a measurement space with an optical path length L, the attenuation of the incident light in the optical path is considered. The scattered light intensity distribution I(θ) is expressed by the following equation.
Ｉ（θ）＝∫L p｛Iioexp〔−xNp∫c(D)nr(D)dD〕・∫i
（Ｄ、θ）・πB2Npnr(D)dD｝dx……(2)
ここに
Iio：入射光強度
ｅ(D)：散乱断面積
である。I(θ)=∫ L p {I io exp [−xN p ∫c(D)n r (D)dD]・∫i
(D, θ)·πB 2 N p n r (D)dD}dx (2) where I io : Incident light intensity e(D) : Scattering cross section.
いま、
Ｘ＝∫c(D)nr(D)dD ……(3)
Ａ＝IioπB2 ……(4)
とおくと、(1)式は
Ｉ（θ）＝Ａ〔∫L Oexp（−xNpＸ）dx〕・∫i（Ｄ、θ
）
nr(D)dD ……(5)
となり、ｘの積分を実行すると、
Ｉ（θ）＝Ａ〔１−exp（−LNpＸ）〕／Ｘ∫i（Ｄ、θ
）nr
(D)dD ……(6)
を得る。ここでＡ、数密度Np、散乱断面積ｃ(D)
および１粒子による散乱光強度ｉ（Ｄ、θ）は、
いずれも既知あるいはMie散乱理論に基づき導び
かれる値である。また、相対的な粒径分布nr(D)
は、散乱光強度分布の測定値In（θ）から前述の
方法に基づいて求め得る値である。したがつて、
いま散乱光強度分布の理論値Ｉ（θ）をなんらか
の方法によつて求めることができれば、上記(6)式
から被測定粒子群の数密度Np一義的に求まるこ
とになる。 Now , by setting _ exp(−xN pX )dx〕・∫i(D, θ
)
n r (D)dD ...(5), and when we perform the integration of x, I(θ)=A[1-exp(-LN p X)]/X∫i(D, θ
) n r (D)dD ……(6) is obtained. Here, A, number density N p , scattering cross section c(D)
And the scattered light intensity i (D, θ) by one particle is
All values are known or derived based on Mie scattering theory. Also, the relative particle size distribution n r (D)
is a value that can be determined from the measured value I n (θ) of the scattered light intensity distribution based on the method described above. Therefore,
If the theoretical value I(θ) of the scattered light intensity distribution can now be determined by some method, the number density N p of the particle group to be measured can be uniquely determined from the above equation (6).
ここでは、上述の散乱光強度分布の理論値Ｉ
（θ）を次のようにして求めている。 Here, the theoretical value I of the above-mentioned scattered light intensity distribution
(θ) is obtained as follows.
すなわち、まず粒径Ｄおよび粒子の数密度Np
が既知である基準粒群にレーザビームを照射し
て、散乱光強度Ipn（θ）を測定する。このとき測
定系の効果がη（θ）であれば、測定値Ipn（θ）
は、
Ipn（θ）＝η（θ）・Ip（θ） ……(7)
で示される。なお、ここにIp（θ）は、測定系に
入射される入射散乱光強度分布（理論値と一致す
る値）である。例えば第６図の構成の場合、散乱
角θiに配置された光フアイバ４ｉの受交効率を
ηRi、伝播の透過率をηpi、フオトデテクタ５ｉの
変換効率ををηTi、増幅器６ｉの増幅度をηAiとす
ると、測定系の効率η（θi）は、
η（θi）＝ηRiηPiηTiηAi ……(8)
で示される。 That is, first, the particle size D and the particle number density N p
A laser beam is irradiated onto a reference particle group whose particle size is known, and the scattered light intensity I pn (θ) is measured. At this time, if the effect of the measurement system is η(θ), then the measured value I pn (θ)
is expressed as I pn (θ)=η(θ)・I p (θ) ……(7). Note that I p (θ) here is the intensity distribution of incident scattered light incident on the measurement system (a value that matches the theoretical value). For example, in the case of the configuration shown in FIG. 6, the exchange efficiency of the optical fiber 4i arranged at the scattering angle θi is η Ri , the propagation transmittance is η pi , the conversion efficiency of the photodetector 5i is η Ti , and the amplification degree of the amplifier 6i is Letting η Ai be, the efficiency η (θi) of the measurement system is expressed as η (θi) = η Ri η Pi η Ti η Ai (8).
一方、基準粒子群は、その粒子Ｄ、粒子密度
Npが既知である。したがつて、単位面積、単位
エネルギ密度のレーザービームを照射した場合、
つまり(4)式のＡ＝１と置いた場合の散乱光強度分
布の散乱角θiにおける理論値Ip（θi）は、(6)式によ
つて求めることができる。 On the other hand, the reference particle group has its particle D, particle density
N p is known. Therefore, when irradiating a laser beam of unit area and unit energy density,
In other words, when A=1 in equation (4), the theoretical value I p (θi) of the scattered light intensity distribution at the scattering angle θi can be obtained from equation (6).
そこで、(6)式によつて求めた理論値Ip（θi）と、
測定値Ipn（θi）とから、この場合の換算係数Ｔ
（θi）を、
Ｔ（θi）＝１／η（θi）＝Ip（θi）／Ipn（θi
）……(9)
なる演算で求めることができる。この換算係数を
すべての散乱角について求め、これをＴ（θ）と
する。 Therefore, the theoretical value I p (θi) obtained by equation (6) is
From the measured value I pn (θi), the conversion factor T in this case is
(θi), T(θi)=1/η(θi)=I p (θi)/I pn (θi
)...(9) It can be obtained by the following calculation. This conversion factor is determined for all scattering angles and is designated as T(θ).
このようにして換算係数Ｔ（θ）が求まれば、
粒径Ｄおよび粒子密度Npが未知の被測定粒子群
による散乱光強度の測定値In（θ）から、入射散
乱光強度分布Ｉ（θ）を
Ｉ（θ）＝Ｔ（θ）・In（θ） ……(9)
なる式にて求めることができる。 If the conversion coefficient T(θ) is found in this way,
From the measured value I n (θ) of scattered light intensity by a group of particles to be measured whose particle size D and particle density N p are unknown, the incident scattered light intensity distribution I (θ) is calculated as I (θ) = T (θ)・I n (θ) ...(9) It can be obtained using the following formula.
なお、散乱光強度分布の理論値Ｉ（θ）が求ま
ると、次のようにして被測定粒子群の粒径分布の
絶対値ｎ(D)が求まる。 Note that once the theoretical value I(θ) of the scattered light intensity distribution is determined, the absolute value n(D) of the particle size distribution of the particle group to be measured is determined as follows.
すなわち、変換係数Ｔ（θ）が、Ａ＝１となる
条件の下で得られたものである場合、
CSCAT＝１−exp（−LNpＸ）／Ｘ ……(10)
とおけば、(6)式は
Ｉ（θ）＝CSCAT∫i（Ｄ、θ）nr(D)dD ……(11)
と書き直すことがきる。したがつてCSCATは、
CSCAT＝Ｉ（θ）／∫i（Ｄ、θ）nr（θ）dD ……(12)
で表せる。そこで、(12)式右辺の分子に(9)式で求め
た値を代入し、同分母に測定値In（θ）から従来
と同様の方法で求めた相対的な粒径分布nr（θ）
と理論的に求まる１粒子による散乱光強度ｉ（Ｄ、
θ）とを代入すればCSCATが求まる。 That is, if the conversion coefficient T(θ) is obtained under the condition that A=1, then C SCAT =1−exp(−LN p X)/X ……(10), then Equation (6) can be rewritten as I(θ)=C SCAT ∫i(D, θ)n r (D)dD ……(11). Therefore, C SCAT can be expressed as C SCAT = I (θ)/∫i (D, θ) n r (θ) dD (12). Therefore, the value obtained by equation (9) is substituted into the numerator on the right side of equation (12), and the relative particle size distribution n r ( θ)
The scattered light intensity i(D,
C SCAT can be found by substituting θ).
したがつて、(10)式をNpについて解いた式、つ
まり
Np＝−１／LXln（１−CSCAT・Ｘ） ……（13）
によつて、被測定粒子群の数密度Npを求めるこ
とができるかくして、
ｎ(D)＝Npnr(D) ……（14）
なる式から絶対的な粒径分布ｎ(D)が算出される。 Therefore, by solving equation (10) for N p , that is, N p =-1/LXln(1-C SCAT・X) ... (13), the number density N p of the particle group to be measured is calculated. Thus, the absolute particle size distribution n(D) is calculated from the formula: n(D)=N p n r (D) (14).
以上の理論的根拠に立却し、本発明は、予め粒
径および粒径密度の既知な基準粒子群にレージビ
ームを照射して測定系を介して散乱光強度分布の
測定値を得、この測定値と同理論値との比率を各
散乱角について求めた算係数を記憶する換算テー
ブルを備えている。そして、被測定粒子群にレー
ザービームを照射して得た散乱光強度分布の測定
値を前記換算テーブルに基づいて換算し前記測定
系の入射部における入射散乱光強度分布を得る換
算手段を備えるとともに、相対粒径分布算出手段
と絶対粒径分布算書手段とを備え、絶対粒径分布
算出手段は、相対粒径分布算出手段で得た相対的
な粒径分布と、前記換算手段で得た入射散乱光強
度分布とから絶対的な粒径分布を得るようにした
ものである。 Based on the above theoretical basis, the present invention irradiates a reference particle group whose particle size and particle size density are known in advance with a laser beam and obtains a measured value of the scattered light intensity distribution via a measurement system. It is equipped with a conversion table that stores calculation coefficients obtained by calculating the ratio between the measured value and the theoretical value for each scattering angle. and a conversion means for converting the measured value of the scattered light intensity distribution obtained by irradiating the particle group to be measured with a laser beam based on the conversion table to obtain the incident scattered light intensity distribution at the entrance part of the measurement system; , comprising a relative particle size distribution calculation means and an absolute particle size distribution calculation means, and the absolute particle size distribution calculation means calculates the relative particle size distribution obtained by the relative particle size distribution calculation means and the calculation means obtained by the conversion means. The absolute particle size distribution is obtained from the incident scattered light intensity distribution.
〔発明の効果〕
本発明によれば、被測定粒子群の絶対的な粒径
分布を測定することができるので、従来に較べて
測定の適用分野を拡大させることができる。[Effects of the Invention] According to the present invention, it is possible to measure the absolute particle size distribution of a particle group to be measured, and therefore the field of application of measurement can be expanded compared to the conventional method.
たとえば、本発明によればタービン内の蒸気の
モニタリングを行うことができる。すなわち、一
般に蒸気湿り度Ｈは、
Ｈ＝WL／WB ……（15）
で示される。ここに、
WL：蒸気中の液体の重さ
WB：全蒸気の重さ
である。タービン内の圧力は容易に測定すること
ができ、圧力が求まれば飽和蒸気曲線から気体の
密度および液体の密度が求まり、全蒸気の重さ
WBが求まる。そして、本発明の粒径測定装置を
用いれば、絶対的な粒径分布を測定することがで
きるので、各粒径の粒子の個数が分り、結局、蒸
気中の液体の重さWLを知ることができる。 For example, the present invention allows monitoring of steam within a turbine. That is, the steam wetness H is generally expressed as: H=W L /W B (15). Here, W L : Weight of liquid in vapor W B : Weight of total vapor. The pressure inside the turbine can be easily measured, and once the pressure is determined, the density of the gas and the density of the liquid can be determined from the saturated steam curve, and the weight of the total steam can be determined.
Find W B. By using the particle size measuring device of the present invention, it is possible to measure the absolute particle size distribution, so the number of particles of each particle size can be determined, and ultimately, the weight of the liquid in the vapor, WL, can be determined. be able to.
このように、本発明によれば、その実用的メリ
ツトは極めて高いことは明らかである。 Thus, it is clear that the present invention has extremely high practical merits.
以下、図面を参照し、本発明の一実施例につい
て説明する。
Hereinafter, one embodiment of the present invention will be described with reference to the drawings.
第１図は本実施例に係る粒径測定装置の基本構
成を示す図であり、第６図と同一部分には同一符
号を付してある。したがつて重視する部分の詳し
い説明は省くことにする。 FIG. 1 is a diagram showing the basic configuration of a particle size measuring device according to this embodiment, and the same parts as in FIG. 6 are given the same reference numerals. Therefore, a detailed explanation of the important parts will be omitted.
この実施例が先に説明した従来例と異なる点
は、被測定粒子群の散乱領域Ｐを、所定間隔Ｌで
対向する一対の透光性遮へい体、例えばガラス板
１０ａ，１０ｂで形成した点と、計算システム７
に新たに換算テーブル１１を付加した点にある。 This embodiment differs from the conventional example described above in that the scattering region P of the particle group to be measured is formed by a pair of light-transmitting shields, for example, glass plates 10a and 10b, which face each other at a predetermined distance L. , calculation system 7
The point is that a new conversion table 11 has been added to the above.
換算テーブル１１は、記憶装置から構成され、
内部に収容されるデータ、つまり換算係数Ｔ（θ）
は次のようにして求められたものである。 The conversion table 11 is composed of a storage device,
Data stored inside, that is, conversion coefficient T(θ)
was determined as follows.
まず粒径Ｄ、粒子の数密度Npが既知である基
準粒子群を用意する。このような粒子としては、
ポリスチレン粒子、ガラス球等があるが、ここで
はポリスチレン粒子を用いた場合について説明す
る。 First, a reference particle group whose particle diameter D and particle number density N p are known is prepared. Such particles are
Although there are polystyrene particles, glass spheres, etc., the case where polystyrene particles are used will be explained here.
ポリスチレン粒子および水の重さを電子天秤等
を用いて正確に測定混合する。ポリスチレン粒子
の重さをWp、同密度をσp、水の重さをWw、同密
度をσwとすると、混合された懸濁液の粒子密度np
は、
np＝Wp／σp／４／３πrp 3・１／Wp／σp＋Ww／σw
……（16）
で示される。ここでrpはポリスチレン粒子の半径
である。 Accurately measure the weight of polystyrene particles and water using an electronic balance and mix. If the weight of polystyrene particles is W p , the same density is σ p , the weight of water is W w , and the same density is σ w , the particle density of the mixed suspension is n p
is n p =W p /σ p /4/3πr p 3・1/W p /σ p +W w /σ w
...(16) is shown. Here r p is the radius of the polystyrene particle.
次に、このポリスチレン粒子の懸濁液を散乱領
域Ｐに導き、レーザ装置１を動作させてレーザビ
ームを照射する。ポリスチレン粒子による散乱光
を、散乱角θi（ｉ＝１、２、…、ｎ）の位置にお
いた光フアイバ４1，４2，…，４oを介してフオ
トデテクタ５1，５2，…，５oに導き、このフオ
トデクタ５1，５2，…，５oにて光電変換をした
後、増幅器６1，６2，…，６oによつて増幅する。 Next, this suspension of polystyrene particles is introduced into the scattering region P, and the laser device 1 is operated to irradiate it with a laser beam. The light scattered by the polystyrene particles is transmitted to photodetectors 5 1 , 5 2 , . . . , 5 through optical fibers 4 1 , 4 2 , . After photoelectric conversion is performed by the photodetectors 5 1 , 5 2 , . . . , 5 o , the light is amplified by the amplifiers 6 1 , 6 2 , . . . , 6 o .
これによつて散乱光強度分布の測定値Ipn（θi）、
Ipn（θ2）、…、Ipn（θn）が得られる。 As a result, the measured value of the scattered light intensity distribution I pn (θi),
I pn (θ 2 ), ..., I pn (θn) are obtained.
一方、この場合には、粒子径Ｄおよび粒子密度
npが既知であるので、前記(2)式を用いて散乱光強
度分布の理論値Ｉ（θ）を求めておく。 On the other hand, in this case, the particle diameter D and the particle density
Since n p is known, the theoretical value I(θ) of the scattered light intensity distribution is determined using the above equation (2).
以上によつて得られたIpn（θ）とＩ（θ）とに
よつて各散乱角θi（ｉ＝１、２、…、ｎ）におけ
る換算係数Ｔ（θi）を
Ｔ（θi）＝Ip（θi）／Ipn（θi）……（17）
と求めることができる。したがつて、この換算係
数Ｔ（θ）が換算テーブル１１内に記憶される。 Using I pn (θ) and I(θ) obtained above, the conversion coefficient T(θi) at each scattering angle θi (i=1, 2,..., n) is calculated as T(θi)=I It can be found as p (θi)/I pn (θi)...(17). Therefore, this conversion coefficient T(θ) is stored in the conversion table 11.
次に粒径Ｄおよび粒子密度Npが未知である被
測定粒子群の絶対的な粒径分布ｎ(D)を求める場合
には、被測定粒子群を散乱領域Ｐに導く。この状
態でレーザ装置１を稼動させると、コリメータ系
２を通過した上述の測定と同一エネルギ、同一ビ
ーム径のレーザービームが被測定粒子群３に照射
される。この結果、計算機システム７には前述と
同様、散乱光強度分布の測定値In（θ）が、取り
込まれる。以下、計算機システム７における手順
を第３図乃至第５図のフローチヤートを用いて説
明する。 Next, when determining the absolute particle size distribution n(D) of a group of particles to be measured whose particle size D and particle density N p are unknown, the group of particles to be measured is guided to a scattering region P. When the laser device 1 is operated in this state, the particle group 3 to be measured is irradiated with a laser beam that has passed through the collimator system 2 and has the same energy and beam diameter as in the above-mentioned measurement. As a result, the measured value I n (θ) of the scattered light intensity distribution is loaded into the computer system 7 as described above. Hereinafter, the procedure in the computer system 7 will be explained using the flowcharts shown in FIGS. 3 to 5.
第３図に示すように、散乱光強度分布の測定値
In（θ）が計算機システム７内に取り込まれると、
計算機システム７は、換算テーブル１１内の換算
係数Ｔ（θ）を続み出して、前記(9)式に従つて測
定値In（θ）を入射散乱光強度Ｉ（θ）に変換す
る。 As shown in Figure 3, the measured value of the scattered light intensity distribution
When I n (θ) is imported into the computer system 7,
The computer system 7 extracts the conversion coefficient T(θ) from the conversion table 11 and converts the measured value I n (θ) into the incident scattered light intensity I(θ) according to equation (9).
次に、この得られた入射散乱光分布Ｉ（θ）か
ら前記(1)式に基づいて相対的な粒径分布nr(D)が求
められる。この粒径分布nr(D)の算出法として具体
的には(i)対数束縛積分方程式法、あるいは(ii)対数
分布関数近似法が用いられる。しかるのち、これ
らの手段によつて求められた粒径分布の絶対値化
処理が行われる。 Next, the relative particle size distribution n r (D) is determined from the obtained incident scattered light distribution I(θ) based on the above equation (1). Specifically, as a method for calculating this particle size distribution n r (D), (i) a logarithmic bound integral equation method or (ii) a logarithmic distribution function approximation method is used. Thereafter, the particle size distribution determined by these means is converted into an absolute value.
上記対数束縛積分方程式法は、粒径がとり得る
範囲を細分化し、連立方程式によつて近似し乍ら
粒径分布を求めるものであり、その処理の流れは
例えば第４図の如く示される。即ち、粒径範囲を
〔Dnio、Dnax〕とし、この区間をＮ分割して前記
第(1)式を次のように近似する。 The logarithm-bound integral equation method subdivides the possible particle size range and approximates it using simultaneous equations to obtain the particle size distribution, and the process flow is shown, for example, in FIG. 4. That is, the particle size range is set to [D nio , D nax ], this interval is divided into N, and the above equation (1) is approximated as follows.
Ｉ（θ）＝N
〓j=1
∫Dj Dj-1ｉ（Ｄ、θ）nr(D)dD
そして、〔Gj、Dj-1〕なる範囲では粒径分布nr
(D)が一定であると仮定し、
∫Dj Dj-1ｉ（Ｄ、θ）nr(D)dD〔∫Dj Dj-1ｉ（Ｄ、
θ）dD〕nr（Dj）
と近似する。このとき、
is（Dj、θ）＝∫Dj Dj-1ｉ（Ｄ、θ）dD
と置くと、前式を次のように整理することができ
る。I(θ)= N 〓 j=1 ∫ Dj Dj-1 i(D, θ)n r (D)dD Then, in the range [G j , D j-1 ], the particle size distribution n r
Assuming that (D) is constant, ∫ Dj Dj-1 i(D, θ)n r (D)dD[∫ Dj Dj-1 i(D,
Approximate it as θ)dD〕n r (Dj). At this time, by setting i s (Dj, θ)=∫ Dj Dj-1 i (D, θ) dD, the above equation can be rearranged as follows.
Ｉ（θ）＝N
〓j=1
is（Dj、θ）nr（Dj）
しかして、前記散乱光強度分布の測定点をθ1、
θ2〜θnとすると、
Ｉ（θi）＝N
〓j=1
is（Dj、θi）ｎ（Dj）
として表わすことができ、
is（Dj、θi）＝iij
Ｉ（θi）＝Ii
nr（Dj）＝nj
とおいて、
Ｉ＝I1
I2
：
Io、Ｇ＝i11i12…i1N
i21i22…i2N
： ： ：
io1io2…ioN、
ｎ＝n1
n2
：
nN
とすると、前式を次のように表現できる。 I(θ)= N 〓 j=1 i s (Dj, θ)n r (Dj) Therefore, the measurement point of the scattered light intensity distribution is θ 1 ,
When θ 2 ~ θn, it can be expressed as I(θi)= N 〓 j=1 i s (Dj, θi)n(Dj), and i s (Dj, θi)=i ij I(θi)=I Letting i n r (Dj)=n j , I=I 1 I 2 : I o , G=i 11 i 12 ...i 1N i 21 i 22 ...i 2N : : : i o1 i o2 ...i oN , n =n 1 n 2 : n N , the previous equation can be expressed as follows.
I〓＝G〓・ｎ
そして、これを対数変換したものを
I〓＝G〓・ｎ
で表わし、粒径分布が滑らかであると云う条件、
即ちnjの３次の差分の２乗和を小さな値に抑える
べくn*Hnを付加したとき、その最小２乗解はラ
グランジ（Lagrange）の未定乗数法により
ｎ＝（G〓*G〓＋γH）-1G〓*I〓
として求めることができる。但し、G〓*はG〓の転
置行列であり、γ未定乗数である。しかして、粒
径分布njが正または零であると云う条件の下で、
上式の解が最小２乗解である為の条件を満足する
ように、粒径分布njのうちの正なるものを選択す
れば、ここに前記散乱光強度分布Ｉ（θ）からそ
の粒径分布nr(D)を求めることが可能となる。つま
り、前式の解が最小２乗解である為の条件（カー
ン・タツカー（Kuhn−Tucker）の定理）
ｙ＝G〓*（G〓n−I〓＋γHn
なるｙが
(a) nj＝０なるｉに対してyj０
(b) nj＞０なるｊに対してy1＝０
を満足するようにすれば、（ｎ０）なる条件の
下での最小２乗解を得ることが可能となる。 I〓=G〓・n Then, the logarithmic transformation of this is expressed as I〓=G〓・n, and the condition that the particle size distribution is smooth,
In other words, when n * Hn is added to suppress the sum of squares of the cubic differences of n j to a small value, the least squares solution is n = (G〓 * G〓 + γH using Lagrange's undetermined multiplier method) ) -1 G〓 * I〓. However, G〓 * is a transposed matrix of G〓, and is a γ undetermined multiplier. Therefore, under the condition that the particle size distribution n j is positive or zero,
If a positive particle size distribution n j is selected so that the solution of the above equation satisfies the condition for being a least squares solution, then the particle size can be calculated from the scattered light intensity distribution I(θ). It becomes possible to obtain the diameter distribution n r (D). In other words, the condition for the solution of the previous equation to be a least squares solution (Kuhn-Tucker theorem) is that y=G〓 * (G〓n−I〓+γHn) (a) n j = If y j 0 (b) n j >0 satisfies y1=0 for i which is 0, it is possible to obtain the least squares solution under the condition (n0). becomes.
以上を総括すれば
log〔Ｉ（θ）〕log〔∫i（Ｄ、θ）nr(D)dD〕
なる連立方程式にて前記第(1)式で示される関係を
近似し、次の２つの条件の下で最小２乗解を求め
ることにより粒径分布nr(D)が得られる。 To summarize the above, we approximate the relationship shown in the above equation (1) using the simultaneous equations log [I (θ)] log [∫i (D, θ) n r (D) dD], and form the following two equations. The particle size distribution n r (D) can be obtained by finding the least squares solution under two conditions.
条件１…粒径分布が滑らかである。Condition 1: Particle size distribution is smooth.
条件２…２０である。Condition 2...20.
これに対して対数分布関数近似法を用いる場合
には、
Ｅ＝｜log〔Ｉ（θ）〕−log（∫
i（Ｄ、θ）nr(D)dD〕｜2
が最小となるように、nr(D)の分布パラメータを決
定するようにすればよい。即ち、その処理の流れ
を第５図に示すようにnr(D)の分布関数を仮定し、
その仮定された分布関数をを修正し乍ら上記Ｅが
最小となるようにして行けばよい。この場合、上
記分布関数としては、例えば分布パラメータを
Ａ、Ｂとして
なる正規分布関数を初期値として仮定するように
すればよい。 On the other hand, when using the logarithmic distribution function approximation method, E=|log[I(θ)]−log(∫
The distribution parameter of n r (D) may be determined so that i(D, θ) n r (D) dD]| 2 is minimized. That is, the process flow is shown in Figure 5, assuming a distribution function of n r (D),
The assumed distribution function may be corrected so that E is minimized. In this case, the above distribution function is, for example, assuming the distribution parameters are A and B. It is sufficient to assume a normal distribution function as the initial value.
このようにして粒径分布（相対値）nr（θ）が
求められたならば、計算機システム７は、前記(12)
式に従つて、CSCATを算出する。また、計算機シ
ステム７は、前記(3)式に従つてＸを算出する。
CSCATとＸが決まつたら、次に前記（13）式に従
つて数密度Npが算出される。かくして、前記
（14）式から、計算機システムは、ｎ(D)を求め、
この結果をデイスプレイ８上に表示する。 Once the particle size distribution (relative value) n r (θ) is determined in this way, the computer system 7 calculates the above (12).
Calculate C SCAT according to the formula. Further, the computer system 7 calculates X according to equation (3) above.
Once C SCAT and X have been determined, the number density N p is then calculated according to equation (13) above. Thus, from the above equation (14), the computer system calculates n(D),
This result is displayed on the display 8.
以上のように本実施例によれば、絶対的な粒径
分布ｎ(D)を得ることができるので、前述したよう
に、測定の適用分野を拡げることができ、極めて
実用性の高い装置を提供することができる。 As described above, according to this example, it is possible to obtain the absolute particle size distribution n(D), so as mentioned above, the fields of application of measurement can be expanded, and an extremely practical device can be constructed. can be provided.
第１図は本発明の一実施例に係る粒径測定装置
の基本構成図、第２図は本発明の基本原理を説明
するための図、第３図乃至第５図は上記粒径測定
装置の作用を説明するための流れ図、第６図は従
来の粒径測定装置の基本構成図である。
１……レーザ装置、２……コリメータレンズ、
３……被測定粒子群、４1，４2〜４o……光フア
イバ、５1，５2〜５o……フオトデテクタ、６1，
６2〜６o……前置増幅器、７……計算機システ
ム、８……デイスプレイ、１０ａ，１０ｂ……ガ
ラス、１１……換算テーブル、Ｐ……散乱領域。
Fig. 1 is a basic configuration diagram of a particle size measuring device according to an embodiment of the present invention, Fig. 2 is a diagram for explaining the basic principle of the present invention, and Figs. 3 to 5 are the above-mentioned particle size measuring device. FIG. 6 is a basic configuration diagram of a conventional particle size measuring device. 1... Laser device, 2... Collimator lens,
3...Particle group to be measured, 41 , 42 to 4o ...Optical fiber, 51 , 52 to 5o ...Photodetector, 61 ,
6 2 - 6 o ... Preamplifier, 7... Computer system, 8... Display, 10a, 10b... Glass, 11... Conversion table, P... Scattering region.
Claims (1)
ザ装置と、このレーザ装置から出射され上記被測
定粒子群によつて散乱された散乱光の散乱角毎の
強度を散乱光強度分布として測定する測定系と、
この測定系で得られた散乱光強度分布の測定値か
ら相対的な粒度分布を算出する相対粒径分布算出
手段と、予め粒径および粒径密度の既知な基準粒
子群に前記レーザビームを照射して得た散乱光強
度分布の測定値と同理論値との比率を各散乱角に
ついて求めた換算係数を記憶する換算テーブル
と、被測定粒子群に前記レーザビームを照射して
得た散乱光強度分布の測定値を前記換算テーブル
に基づいて換算し前記測定系の入射部における入
射散乱光強度分布を得る換算手段と、この換算手
段で得られた上記入射散乱強度分布と前記相対粒
径分布算出手段で得られた前記被測定粒子群の相
対的な粒径分布とから絶対的な粒径分布を算出す
る絶対粒径分布算出手段とを具備してなることを
特徴とする粒径測定装置。1. A laser device that irradiates a laser beam onto a group of particles to be measured, and a measurement system that measures the intensity of scattered light emitted from this laser device and scattered by the group of particles to be measured at each scattering angle as a scattered light intensity distribution. and,
Relative particle size distribution calculation means for calculating a relative particle size distribution from the measured value of the scattered light intensity distribution obtained by this measurement system, and a reference particle group whose particle size and particle size density are known in advance are irradiated with the laser beam. A conversion table that stores the conversion coefficient obtained by calculating the ratio between the measured value of the scattered light intensity distribution obtained by the method and the same theoretical value for each scattering angle, and the scattered light obtained by irradiating the particle group to be measured with the laser beam. a conversion means for converting the measured value of the intensity distribution based on the conversion table to obtain an incident scattered light intensity distribution at the entrance part of the measurement system; and the above-mentioned incident scattered light intensity distribution and the relative particle size distribution obtained by the conversion means. A particle size measuring device comprising absolute particle size distribution calculation means for calculating an absolute particle size distribution from the relative particle size distribution of the particle group to be measured obtained by the calculation means. .
Priority Applications (4)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP59135978A JPS6114543A (en) | 1984-06-30 | 1984-06-30 | Particle size maesuring instrument |
| US06/739,283 US4801205A (en) | 1984-06-30 | 1985-05-30 | Particle size measuring apparatus |
| DE8585303816T DE3581325D1 (en) | 1984-06-30 | 1985-05-30 | APPARATUS FOR MEASURING THE DIMENSIONS OF PARTICLES. |
| EP85303816A EP0167272B1 (en) | 1984-06-30 | 1985-05-30 | Particle size measuring apparatus |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP59135978A JPS6114543A (en) | 1984-06-30 | 1984-06-30 | Particle size maesuring instrument |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPS6114543A JPS6114543A (en) | 1986-01-22 |
| JPH0263181B2 true JPH0263181B2 (en) | 1990-12-27 |
Family
ID=15164322
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP59135978A Granted JPS6114543A (en) | 1984-06-30 | 1984-06-30 | Particle size maesuring instrument |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JPS6114543A (en) |
Cited By (2)
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|---|---|---|---|---|
| CN102353337A (en) * | 2011-09-19 | 2012-02-15 | 南京信息工程大学 | Method and device for detecting diameter of atmospheric black carbon aerosol particle |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS62222144A (en) * | 1986-03-25 | 1987-09-30 | Toshiba Corp | Apparatus for measuring particle size |
| JPH0264435A (en) * | 1988-08-31 | 1990-03-05 | Y D K:Kk | Measuring apparatus for particle size |
| JPH0643950B2 (en) * | 1989-09-29 | 1994-06-08 | 株式会社島津製作所 | Particle size distribution measuring device |
| JP3266107B2 (en) * | 1998-07-29 | 2002-03-18 | 株式会社島津製作所 | Particle counting method and particle measuring device |
| JP4132692B2 (en) * | 2001-02-20 | 2008-08-13 | 株式会社堀場製作所 | Particle size distribution measuring device |
| JP3814190B2 (en) | 2001-11-09 | 2006-08-23 | 株式会社堀場製作所 | Particle size distribution measuring device |
| GB2383127B (en) * | 2001-12-12 | 2004-10-20 | Proimmune Ltd | Device and method for investigating analytes in liquid suspension or solution |
| US6798508B2 (en) * | 2002-08-23 | 2004-09-28 | Coulter International Corp. | Fiber optic apparatus for detecting light scatter to differentiate blood cells and the like |
| JP4115313B2 (en) * | 2003-03-27 | 2008-07-09 | ダイセル化学工業株式会社 | Microcapsule wall membrane thickness calculator |
| JP4329555B2 (en) * | 2004-02-04 | 2009-09-09 | Ｔｏｔｏ株式会社 | Aerosol particle size measuring method, apparatus, and composite structure manufacturing apparatus including the same |
| WO2016067793A1 (en) * | 2014-10-29 | 2016-05-06 | 富士電機株式会社 | Particle analysis device |
| JP2017133925A (en) | 2016-01-27 | 2017-08-03 | 富士電機株式会社 | Particle analyzer |
| PL3521810T3 (en) * | 2018-01-31 | 2020-05-18 | Sick Engineering Gmbh | Analyser for the determination of fine dust |
-
1984
- 1984-06-30 JP JP59135978A patent/JPS6114543A/en active Granted
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102353337A (en) * | 2011-09-19 | 2012-02-15 | 南京信息工程大学 | Method and device for detecting diameter of atmospheric black carbon aerosol particle |
| WO2022270204A1 (en) | 2021-06-21 | 2022-12-29 | 富士フイルム株式会社 | Particle measurement device and particle measurement method |
Also Published As
| Publication number | Publication date |
|---|---|
| JPS6114543A (en) | 1986-01-22 |
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