JPH02226043A - Reaction measuring apparatus - Google Patents
Reaction measuring apparatusInfo
- Publication number
- JPH02226043A JPH02226043A JP4613789A JP4613789A JPH02226043A JP H02226043 A JPH02226043 A JP H02226043A JP 4613789 A JP4613789 A JP 4613789A JP 4613789 A JP4613789 A JP 4613789A JP H02226043 A JPH02226043 A JP H02226043A
- Authority
- JP
- Japan
- Prior art keywords
- frequency
- reaction
- relays
- oscillating
- measurement
- 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.)
- Pending
Links
- 238000006243 chemical reaction Methods 0.000 title claims description 33
- 238000005259 measurement Methods 0.000 claims abstract description 15
- 230000010355 oscillation Effects 0.000 claims description 20
- 239000013078 crystal Substances 0.000 claims description 14
- 238000012545 processing Methods 0.000 claims description 5
- 239000007788 liquid Substances 0.000 abstract description 11
- 239000010453 quartz Substances 0.000 abstract description 5
- VYPSYNLAJGMNEJ-UHFFFAOYSA-N silicon dioxide Inorganic materials O=[Si]=O VYPSYNLAJGMNEJ-UHFFFAOYSA-N 0.000 abstract description 5
- 238000001879 gelation Methods 0.000 description 12
- 238000000034 method Methods 0.000 description 9
- 238000004062 sedimentation Methods 0.000 description 9
- 239000000523 sample Substances 0.000 description 8
- 210000004027 cell Anatomy 0.000 description 6
- 238000001179 sorption measurement Methods 0.000 description 6
- 239000002245 particle Substances 0.000 description 5
- 238000010586 diagram Methods 0.000 description 4
- 239000002158 endotoxin Substances 0.000 description 4
- 239000000126 substance Substances 0.000 description 4
- 239000004793 Polystyrene Substances 0.000 description 3
- 238000000691 measurement method Methods 0.000 description 3
- 229920002223 polystyrene Polymers 0.000 description 3
- 230000004520 agglutination Effects 0.000 description 2
- 239000000427 antigen Substances 0.000 description 2
- 102000036639 antigens Human genes 0.000 description 2
- 108091007433 antigens Proteins 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 230000003287 optical effect Effects 0.000 description 2
- 229920005989 resin Polymers 0.000 description 2
- 239000011347 resin Substances 0.000 description 2
- 239000012488 sample solution Substances 0.000 description 2
- 239000000725 suspension Substances 0.000 description 2
- 102000009027 Albumins Human genes 0.000 description 1
- 108010088751 Albumins Proteins 0.000 description 1
- 241001529572 Chaceon affinis Species 0.000 description 1
- 238000009825 accumulation Methods 0.000 description 1
- 239000003918 blood extract Substances 0.000 description 1
- 239000000919 ceramic Substances 0.000 description 1
- 238000007796 conventional method Methods 0.000 description 1
- 210000002858 crystal cell Anatomy 0.000 description 1
- 238000001514 detection method Methods 0.000 description 1
- 239000003814 drug Substances 0.000 description 1
- 239000012525 endotoxin sample Substances 0.000 description 1
- 239000003822 epoxy resin Substances 0.000 description 1
- 239000010419 fine particle Substances 0.000 description 1
- 239000002184 metal Substances 0.000 description 1
- 239000000203 mixture Substances 0.000 description 1
- 238000012544 monitoring process Methods 0.000 description 1
- 239000003027 oil sand Substances 0.000 description 1
- 229920000647 polyepoxide Polymers 0.000 description 1
- 230000035484 reaction time Effects 0.000 description 1
- 238000005185 salting out Methods 0.000 description 1
Landscapes
- Investigating Or Analyzing Materials Using Thermal Means (AREA)
Abstract
Description
【発明の詳細な説明】
〔産業上の利用分野）
この発明は、化学、物理化学、生化学および食品、医療
、化学工業分野における反応計測を行う装置に関する。DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to an apparatus for measuring reactions in the fields of chemistry, physical chemistry, biochemistry, food, medicine, and chemical industry.
〔発明の概要Ｊ
この発明の反応計測装置は、片面に液体が接するように
した圧電振動子、特に水晶振動子を複数同時に使用し、
複数の液体の反応を同時に計測する装置である。この装
置は、圧電振動子を配置した複数個のセルと、これと同
数の発振回路と高周波リレー、および、周波数測定回路
、データ処理料（Ｉｔ表装置よび恒温槽より構成されて
いる。[Summary of the Invention J The reaction measuring device of the present invention simultaneously uses a plurality of piezoelectric vibrators, particularly crystal vibrators, each of which is in contact with a liquid on one side,
This is a device that measures reactions of multiple liquids simultaneously. This device consists of a plurality of cells in which piezoelectric vibrators are arranged, the same number of oscillation circuits and high-frequency relays, a frequency measurement circuit, a data processing device (It table device, and a constant temperature oven).
この反応計測装置は、圧電振動子の発振周波数変化から
、液体の粘性変化や圧電振動子表面への吸着反応、沈降
反応などを計測するものである。This reaction measuring device measures changes in the viscosity of a liquid, adsorption reactions on the surface of a piezoelectric vibrator, sedimentation reactions, etc. from changes in the oscillation frequency of the piezoelectric vibrator.
本装置において、複数の圧電振動子それぞれに発振回路
が接続されており、その出力信号は、高周波リレーを介
し、そのうち１つの信号が選択され、周波数カウンター
で発振周波数が測定される。そして、リレーを順次切り
替えることによって、複数の試料の測定を同時に行なえ
るようにしたものである。In this device, an oscillation circuit is connected to each of the plurality of piezoelectric vibrators, and the output signals thereof are sent through a high frequency relay, one of the signals is selected, and the oscillation frequency is measured by a frequency counter. By sequentially switching the relays, multiple samples can be measured simultaneously.
本発明の反応計測の対象としては、粘度変化が最も重要
である。従来、粘度測定には、細管法、回転法などが用
いられてきた。細管法は、試料液体が細管を落下する速
度から粘度を求めるものである。また、回転法は、試料
液中で円筒状の金属棒を回転させ、せん断応力を求める
ことによって、粘度を求めるものである。また、この反
応がゲル化反応である場合には、試料の濁度を光学的に
測定する方法、機械的な振動を与えゲル化による粘性変
化を検知する方法が取られていた。The most important target for reaction measurement in the present invention is viscosity change. Conventionally, the capillary method, the rotation method, etc. have been used to measure viscosity. The capillary method determines the viscosity from the rate at which a sample liquid falls through a capillary. In addition, the rotation method is a method for determining viscosity by rotating a cylindrical metal rod in a sample liquid and determining shear stress. If this reaction is a gelation reaction, methods have been used to optically measure the turbidity of the sample, or to apply mechanical vibrations to detect changes in viscosity due to gelation.
【発明が解決しようとする課題］
従来の粘度測定法では、少量の試料では測定できないと
いう問題があり、測定に時間がかかり。[Problems to be Solved by the Invention] Conventional viscosity measurement methods have the problem of not being able to measure a small amount of sample, and the measurement takes time.
反応に伴う変化を測定することは不可能であった。また
２ゲル化反応の測定では、従来の濁度を測定する方法の
場合１着色試料の測定には不向きであり、塩析によって
大きな誤差を生じるという問題点と光学的測定系を含む
ためにシステムが複雑になるという問題点があった。さ
らに、光学的な方法は、直接ゲル化を測定するものでな
いため、正確な測定法とはい人なかった。また、機械的
な振動を与える方法では、機械部分があるため小型軽量
化が雑しいという問題があった。これらの点に加え、い
ずれの方法も、最低０．２ｍｌ程度の試料を必要とする
という問題があった。It was not possible to measure changes associated with the response. In addition, when measuring gelation reactions, the conventional method for measuring turbidity is unsuitable for measuring colored samples, and the problem is that large errors occur due to salting out, and the system requires an optical measurement system. The problem was that it became complicated. Furthermore, since the optical method does not directly measure gelation, it has not been considered an accurate measurement method. Furthermore, the method of applying mechanical vibrations has the problem that it is difficult to reduce the size and weight of the device due to the presence of mechanical parts. In addition to these points, each method has the problem of requiring a sample of at least about 0.2 ml.
本発明者らによって考案された水晶振動子による測定法
は、０．２ｍｌ以下の試料を測定することが可能であり
、システムの小型化も可能であるが、これまで、１つず
つ測定を行っているため、長い反応時間を要する試料で
は、処理能力の点で問題があった。The measurement method using a crystal oscillator devised by the present inventors is capable of measuring samples of 0.2 ml or less, and it is also possible to downsize the system. Therefore, there was a problem in terms of throughput for samples that required a long reaction time.
［課題を解決するための手段）
上記課題を解決するために、本発明は、圧電振動子を検
出素子とする反応計測装置に複数の水晶振動子を用い、
同時に複数の反応計測を行う装置を考案した。この反応
計測装置は、片面に液体が接するようにした圧！振動子
、特に水晶振動子な？ｊｌ数同時に使用し、複数の液体
の反応を同時に計測する装置を考案した。この装置は、
圧電振動子を配置した複数のセルと、これと同数の発振
回路と高周波リレー、および、周波数測定回路、データ
処理制御装置および恒温槽より構成した。[Means for Solving the Problems] In order to solve the above problems, the present invention uses a plurality of crystal oscillators in a reaction measuring device using a piezoelectric oscillator as a detection element,
We devised a device that can measure multiple reactions simultaneously. This reaction measuring device measures pressure so that liquid is in contact with one side! A resonator, especially a crystal resonator? We devised a device that uses jl numbers simultaneously to measure the reactions of multiple liquids at the same time. This device is
It consists of multiple cells with piezoelectric vibrators arranged, the same number of oscillation circuits and high-frequency relays, a frequency measurement circuit, a data processing control device, and a constant temperature oven.
〔作用１
圧電振動子は、圧電効果を利用したデバイスであり、発
振回路と接続することによって、発振させることができ
る。この際、圧電振動子の表面は、微小な振動を起こす
、このため振動子は、表面に物質が接することによって
、この振動に影響が及び、発振周波数の変化として反映
されてくる。ゆ久に、液体の粘性変化、物質の吸着、沈
降による物質堆積の測定を行うことが可能である。[Operation 1 A piezoelectric vibrator is a device that utilizes the piezoelectric effect, and can be caused to oscillate by connecting it to an oscillation circuit. At this time, the surface of the piezoelectric vibrator generates minute vibrations, so when a substance comes into contact with the surface of the vibrator, this vibration is affected and reflected as a change in the oscillation frequency. For a long time, it has been possible to measure changes in the viscosity of liquids, adsorption of substances, and accumulation of substances due to sedimentation.
この圧電振動子と発振回路を複数個並べ５発振回路から
出力される発振周波数の信号をリレーで切り賛え１周波
数カウンターで測定することによって、複数の反応を同
時に測定することができる。By arranging a plurality of piezoelectric vibrators and oscillation circuits and using a relay to receive the oscillation frequency signals output from the five oscillation circuits and measuring them with one frequency counter, it is possible to simultaneously measure a plurality of reactions.
〔実施例ｊ
以下、この発明の実施例を図面に基づいて説明する。第
１図は、本発明の反応計測装置の一実施例を示す模式図
を示したものである。第１図において１両面に電極が形
成された水晶振動子１１２、・・・、１７は、一方の面
が液体に接するようにセル２＋、２＊、・・・、２．に
設置され、そのセル２３．２ｔ 、・・・、２．、は恒
温Ｉ１３内に固定され、この水晶振動子１＋−１ｇ、・
・・、１、の電極が発振回路４＋、４重、・・・、４７
に接続されている０発振回路４３．４□、・・・、４７
は、高周波リレー５８，５□、・・・、５１１を介し周
波数カウンター６に接続され、されにデータをモニター
するためのマイクロコンピュータ（入出力インタフェー
スを含む）７に接続され、マイクロコンピュータ７には
、記録装置８、表示装置９、キースイッチ１０、リレー
駆動回路１１が接続されている。[Embodiment j] Hereinafter, an embodiment of the present invention will be described based on the drawings. FIG. 1 shows a schematic diagram showing an embodiment of the reaction measuring device of the present invention. In FIG. 1, crystal oscillators 112, . The cells 23.2t, . . . , 2. , is fixed in a constant temperature I13, and this crystal oscillator 1+-1g, ・
..., 1, electrode is oscillation circuit 4+, quadruple, ..., 47
0 oscillation circuit connected to 43.4□,...,47
are connected to the frequency counter 6 via high frequency relays 58, 5□, ..., 511, and then to a microcomputer (including an input/output interface) 7 for monitoring data. , a recording device 8, a display device 9, a key switch 10, and a relay drive circuit 11 are connected.
測定は、試料液体をセル２．．２．、・・・、２１中に
入れ１発振周波数測定開始のスイッチを入れ、測定を開
始し、最初の発振周波数を基準としてこの後に求めた発
振周波数との差をΔＦとじて記録する。For measurement, sample liquid is placed in cell 2. ．． 2. . . 21, turn on the switch to start measuring the first oscillation frequency, start measurement, and record the difference between the first oscillation frequency as a reference and the oscillation frequency found thereafter as ΔF.
（エンドトキシン分析への応用）
９ＭＨ，−ＡＴカット水晶振動子を用い、恒温槽を３７
Ｃとした本装置に、エンドトキシン試料０．２ｍｌと
規定量のカブトガニ血液抽出物の凍結乾燥品とを混合し
、水晶振動子セル中に注入し１発振周波数の変化の測定
を行った。この操作を順次複数の水晶振動子について行
い同時にゲル化時間（周波数が変化しなくなるまでの時
間）の測定を行った。ゲル化時間の算出はデータ処理部
で行った。ゲル化時間はエンドトキシン濃度０゜１、−
１．０’ ｐｇ−ｍｌ−’の間で濃度に依存して変化し
た。また、試料量は、２０ｕｌでも測定が可能だった。(Application to endotoxin analysis) Using a 9MH, -AT cut crystal oscillator, a thermostatic chamber was heated to 37°C.
0.2 ml of the endotoxin sample and a specified amount of freeze-dried horseshoe crab blood extract were mixed into the apparatus designated as C, and the mixture was injected into a quartz crystal cell, and the change in one oscillation frequency was measured. This operation was performed sequentially for a plurality of crystal oscillators, and the gelation time (the time until the frequency stopped changing) was measured at the same time. The gelation time was calculated by the data processing section. Gelation time is endotoxin concentration 0゜1, -
It varied depending on the concentration between 1.0'pg-ml-'. Furthermore, measurement was possible even with a sample amount of 20 ul.
さらに、本装置は粘度変化の他、吸着反応の計測にも使
用が可能である。一つの例として、水晶振動子へのアル
ブミンの連続的な吸着を発振周波数の変化で追跡できる
ことがわかった。Furthermore, this device can be used to measure not only viscosity changes but also adsorption reactions. As an example, we found that the continuous adsorption of albumin to a quartz crystal can be tracked by changes in the oscillation frequency.
従って、吸着反応とゲル化反応が同時に起こる場合は、
ゲル化反応の速度をゲル化時間だけでなく、ゲル化終了
後の共振周波数変化の値から推定おいても同時に吸着反
応が進行し、エンドトキシン濃度に対するゲル化終了後
の発振周波数変化の値によってもエンドトキシン濃度の
計測が可能であった。Therefore, if the adsorption reaction and gelation reaction occur simultaneously,
If we estimate the speed of the gelation reaction not only from the gelation time but also from the value of the change in resonance frequency after the end of gelation, we can estimate that the adsorption reaction is proceeding at the same time, and also by the value of the change in oscillation frequency after the end of gelation with respect to the endotoxin concentration. It was possible to measure endotoxin concentration.
（沈降反応測定への応用）
本発明の装置を用いて、０．０５−１００μｍの微粒子
の沈降現象の測定を行うことが可能である。抗体を固定
化したポリスチレン粒子の沈降現象の測定を行った。抗
体を固定化したポリスチレン粒子に抗原を加えると、粒
子の凝集反応を起こす、この凝集反応のため粒径が大き
くなり、沈降速度が速くなる。従って、懸濁液の平均沈
降時間を比較することによって、試料の抗原量を求める
ことができる。(Application to sedimentation reaction measurement) Using the apparatus of the present invention, it is possible to measure the sedimentation phenomenon of fine particles of 0.05 to 100 μm. The sedimentation phenomenon of polystyrene particles immobilized with antibodies was measured. When an antigen is added to polystyrene particles on which antibodies have been immobilized, the particles undergo an agglutination reaction. This agglutination reaction increases the particle size and increases the sedimentation rate. Therefore, by comparing the average sedimentation times of the suspensions, the amount of antigen in the sample can be determined.
抗ヒトＩｇＧを固定化した０、５μｍポリスチレン粒子
（１ｍｇ−ｍｌ−’）、０．２ｍｌと０．２ｍｌのヒト
ＩｇＧ試料液（１０−’−１０ｍｇ−ｍ１”ｌ）を混合
し、得られた懸濁液を水晶振動子セルに注入し、発振周
波数の測定を行った。0.2 ml of anti-human IgG-immobilized polystyrene particles (1 mg-ml-') and 0.2 ml of human IgG sample solution (10-'-10 mg-ml) were mixed to obtain the The suspension was injected into a crystal resonator cell, and the oscillation frequency was measured.
このとき全体の周波数変化の１／２に達したときの時間
を沈降時間として求めたところ、ヒトＩｇＧ試料液と沈
降時間の間に相関性が詔められた。この場合も本装置に
よって、同時に複数の測定を行うことができた。At this time, when the time taken to reach 1/2 of the total frequency change was determined as the sedimentation time, a correlation was found between the human IgG sample solution and the sedimentation time. In this case as well, the present device was able to perform multiple measurements simultaneously.
（樹脂の硬化の測定）
第２図は、本発明の反応計測装置の他の実施例を示す模
式図である。(Measurement of Curing of Resin) FIG. 2 is a schematic diagram showing another embodiment of the reaction measuring device of the present invention.
第２図において、水晶振動子Ｉ１．ｌｔ、・・・Ｉｎは
、水晶振動子の片面のみが試料に接するようにした構造
のセル２．．２．、・・・、２．１に設置されており、
硬化前の樹脂１２が入った容器１３の中に配置されてい
る。容器１３は恒温槽３の中に入れられ、温度がコント
ロールされる。エポキシ樹脂を使用し、測定を行ったと
ころ、ｐＡ脂砂硬化したがい周波数の現象が観測され、
水晶振動子の位置と周波数変化との対比から、硬化の進
行についての知見を得ることができた。In FIG. 2, crystal oscillator I1. lt, . ．． 2. , ..., is installed in 2.1,
It is placed in a container 13 containing resin 12 before hardening. The container 13 is placed in a constant temperature bath 3, and the temperature is controlled. When measuring using epoxy resin, a frequency phenomenon was observed as pA oil sand hardened.
By comparing the position of the crystal oscillator and frequency changes, we were able to obtain knowledge about the progress of hardening.
以上の実施例において、水晶振動子は１ＭＨｚ−２０Ｍ
Ｈｚまで使用可能であった。また、ｌＫＨｚ −１０Ｍ
Ｈｚの圧電セラミックス振動子も使用可能であった５ま
た、セル付き圧電振動子は容易に装置から着脱でき、使
い捨てにすることが可能である。In the above embodiments, the crystal resonator is 1MHz-20M
It was usable up to Hz. Also, lKHz -10M
Hz piezoelectric ceramic vibrators could also be used.5 Furthermore, piezoelectric vibrators with cells can be easily attached and removed from the device and can be disposable.
〔発明の効果１
本発明の粘度測定装置によって、きわめて少量の液体試
料の反応の測定が同時に複数、また、容器中の変化を複
数の場所で測定することができるようになった。また、
本装置は機械的な部分がないので、振動などの影響を受
けず、高い精度で再現性良い測定が可能となるとともに
小型軽量化することが可能であった。[Effect of the Invention 1] The viscosity measuring device of the present invention makes it possible to simultaneously measure the reactions of extremely small amounts of liquid samples in multiple locations, and to measure changes in the container at multiple locations. Also,
Since this device does not have any mechanical parts, it is not affected by vibrations, allows for highly accurate and reproducible measurements, and is also able to be made smaller and lighter.
第１図は本発明の反応計測装置の一実施例を示す模式図
、第２図は本発明の反応計測装置に他の実施例を示す模
式図である。
以上
ネ光明の反兄訂」・１罠ｌの４仇の大徳例と示Ｔ楳式図
第
図FIG. 1 is a schematic diagram showing one embodiment of the reaction measuring device of the present invention, and FIG. 2 is a schematic diagram showing another embodiment of the reaction measuring device of the present invention. The above is an example of the great virtues of the 4 enemies of 1 trap 1
Claims (4)
数の発振回路と高周波リレー、および、周波数測定回路
、データ処理制御装置および恒温槽より構成される反応
計測装置。(1) A reaction measurement device consisting of a plurality of cells in which piezoelectric vibrators are arranged, the same number of oscillation circuits and high-frequency relays, a frequency measurement circuit, a data processing control device, and a constant temperature bath.
求項１記載の反応計測装置。(2) The reaction measuring device according to claim 1, wherein the piezoelectric vibrator is an AT-cut crystal vibrator.
ター、キー入力スイッチ、表示装置、記録装置、入出力
信号インターフェース、リレー駆動回路より構成される
請求項１記載の反応計測装置。(3) The reaction measuring device according to claim 1, wherein the data processing control device comprises a microcomputer, a key input switch, a display device, a recording device, an input/output signal interface, and a relay drive circuit.
造である請求項１記載の反応計測装置。(4) The reaction measuring device according to claim 1, wherein the piezoelectric vibrator has a structure to be used in the thermostatic oven.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP4613789A JPH02226043A (en) | 1989-02-27 | 1989-02-27 | Reaction measuring apparatus |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP4613789A JPH02226043A (en) | 1989-02-27 | 1989-02-27 | Reaction measuring apparatus |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| JPH02226043A true JPH02226043A (en) | 1990-09-07 |
Family
ID=12738591
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP4613789A Pending JPH02226043A (en) | 1989-02-27 | 1989-02-27 | Reaction measuring apparatus |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JPH02226043A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2018048865A (en) * | 2016-09-21 | 2018-03-29 | パナソニックＩｐマネジメント株式会社 | Resistance measurement device and method thereof |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS62288547A (en) * | 1986-06-06 | 1987-12-15 | Seiko Instr & Electronics Ltd | Apparatus for analyzing living body-related substance, bacterium and cell |
| JPS63171340A (en) * | 1987-01-09 | 1988-07-15 | Shimadzu Corp | Crystal oscillator type moisture meter |
| JPS6447932A (en) * | 1987-08-19 | 1989-02-22 | Seiko Instr & Electronics | Viscosity measuring apparatus |
-
1989
- 1989-02-27 JP JP4613789A patent/JPH02226043A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS62288547A (en) * | 1986-06-06 | 1987-12-15 | Seiko Instr & Electronics Ltd | Apparatus for analyzing living body-related substance, bacterium and cell |
| JPS63171340A (en) * | 1987-01-09 | 1988-07-15 | Shimadzu Corp | Crystal oscillator type moisture meter |
| JPS6447932A (en) * | 1987-08-19 | 1989-02-22 | Seiko Instr & Electronics | Viscosity measuring apparatus |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2018048865A (en) * | 2016-09-21 | 2018-03-29 | パナソニックＩｐマネジメント株式会社 | Resistance measurement device and method thereof |
| US10302582B2 (en) * | 2016-09-21 | 2019-05-28 | Panasonic Intellectual Property Management Co., Ltd. | Resistance-measurement apparatus and method for measuring resistance of powdery materials |
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