JP6730860B2 - Evaluation method of skin condition - Google Patents
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Description
本発明は、乾燥状態等の皮膚の状態を評価する方法に関する。 The present invention relates to a method for evaluating skin condition such as dry condition.
皮膚の乾燥状態等を測定する方法としては、角層の水分量を測定する方法、皮脂量を測定する方法が知られている。水分量の測定法としては、肌の電気伝導度や電気容量を測定する方法等が知られている（特許文献１）。また、皮脂量の測定法としては、反射光の屈折率で油分の割合を推定する方法等が知られている（特許文献２）。
一方、環境の肌に与える影響を観察するために、皮膚表面の平板に対する摩擦係数を測定することが試みられている（非特許文献１）
Known methods for measuring the dry state of the skin include a method for measuring the amount of water in the stratum corneum and a method for measuring the amount of sebum. As a method of measuring the amount of water, a method of measuring electric conductivity or electric capacity of skin is known (Patent Document 1). In addition, as a method for measuring the amount of sebum, a method of estimating the proportion of oil by the refractive index of reflected light is known (Patent Document 2).
On the other hand, in order to observe the influence of the environment on the skin, it has been attempted to measure the friction coefficient of the skin surface against a flat plate (Non-Patent Document 1).
しかしながら、前記の角層の水分量の測定法や皮脂の測定法は、原理が複雑なので高価な機器が必要になる、発汗や乾燥など経時的に変化する皮膚の状態を正確に評価できない等の問題がある。
一方、環境の肌に対する影響を板などとの摩擦力を計測することで観察することは試みられているが、その場合、各人の肌の違いは平均値として取り扱われており、個人差を調べる検討は行われていない。
本発明は、各個人の肌の状態を、簡便に評価する手段を提供することを課題とする。
However, the above-mentioned method for measuring the amount of water in the stratum corneum and the method for measuring sebum require complicated and expensive equipment, and it is not possible to accurately evaluate the state of the skin that changes over time such as perspiration and dryness. There's a problem.
On the other hand, it has been attempted to observe the effect of the environment on the skin by measuring the frictional force with a plate, but in that case, the difference in the skin of each person is treated as an average value, and the individual difference is treated. No investigation is under way.
An object of the present invention is to provide means for easily evaluating the skin condition of each individual.
本発明者は、皮膚の状態と平板上での摩擦との関係を検討してきたところ、全く意外にも、特定の平板上における皮膚の摩擦だけで皮膚状態を評価するのではなく、表面粗さの異なる複数の平板を用意して、それらの平板上における皮膚の摩擦係数をそれぞれ測定し、測定された複数の摩擦係数相互の関係を指標とすることにより、皮膚の乾燥状態等を簡便かつ正確に評価できることを見出した。
より詳細には、以下のとおりである。すなわち、皮膚の評価に好適な平板がどのようなものであるかの探索を行っていく中で、表面粗さの違いによる摩擦係数の測定を行っていたところ、柔らかな肌では表面粗さが小さくなるにしたがって、摩擦係数が大きくなるのに対し、固い、あるいは潤いのない肌ではそのようなことはなく、表面粗さに依らず摩擦係数がほぼ一定であるということを見出した（図１）。本発明者は、この表面粗さと摩擦係数の関係を用いれば、皮膚の状態を評価できるのではとの着想に至り、本発明を完成した。
The present inventor has studied the relationship between the state of the skin and the friction on the flat plate, and, quite unexpectedly, does not evaluate the skin state only by the friction of the skin on a specific flat plate, but the surface roughness. By preparing multiple flat plates with different values, measuring the coefficient of friction of the skin on each of these flat plates, and using the relationship between the measured multiple friction coefficients as an index, the dry state of the skin can be easily and accurately measured. It was found that can be evaluated.
More details are as follows. That is, while conducting a search for what kind of flat plate is suitable for skin evaluation, we measured the coefficient of friction due to the difference in surface roughness. It has been found that the coefficient of friction increases as it decreases, but that does not occur with hard or moist skin, and that the coefficient of friction is almost constant regardless of the surface roughness (Fig. 1). ). The present inventor has arrived at the idea that the skin condition can be evaluated by using the relationship between the surface roughness and the friction coefficient, and completed the present invention.
すなわち、本発明は、表面粗さが相違する複数の平板上に皮膚を接触させて平板表面に対して平行に動かしたときの摩擦係数をそれぞれ測定し、測定された摩擦係数相互の関係を皮膚状態の指標とすることを特徴とする皮膚状態の評価方法を提供するものである。
また、本発明は、肌に適用される剤を、肌に適用する前と適用した後との各々において評価した皮膚状態により、肌に適用される剤が肌に与える効果を評価する方法であって、前記の皮膚状態の評価方法により皮膚状態の評価を行う、肌に適用される剤が肌に与える効果を評価する方法を提供するものである。
That is, the present invention measures the friction coefficient when the skin is brought into contact with a plurality of flat plates having different surface roughness and moved in parallel to the flat plate surface, and the measured mutual relations of the friction coefficients are determined by the skin. It is intended to provide a method for evaluating a skin condition, which is characterized by using it as a condition index.
Further, the present invention is a method for evaluating the effect of an agent applied to the skin on the skin, based on the skin condition evaluated before and after the application of the agent applied to the skin. Thus, the present invention provides a method for evaluating the effect of an agent applied to the skin on the skin, in which the skin condition is evaluated by the method for evaluating the skin condition.
指等を、表面粗さが相違する複数の平板上を擦過させるだけで、簡便かつ正確に、皮膚がどの程度乾燥しているか、しっとりしているか、皮脂が過剰に分泌されているか等の皮膚の状態が評価できる。 Simply by rubbing your fingers on multiple flat plates with different surface roughness, you can easily and accurately determine how dry the skin is, how moist it is, and whether skin oil is excessively secreted. The state of can be evaluated.
本発明の皮膚状態の評価方法は、表面粗さが相違する複数の平板上に皮膚を接触させて平板表面に対して平行に動かしたときの摩擦係数をそれぞれ測定し、測定された複数の摩擦係数相互の関係を指標とすることを特徴とする。 The evaluation method of the skin condition of the present invention is to measure the friction coefficient when the skin is brought into contact with a plurality of flat plates having different surface roughness and moved in parallel to the flat plate surface, and a plurality of measured frictions are measured. The feature is that the mutual relationship of the coefficients is used as an index.
本発明方法に用いる平板は、表面粗さが相違する複数の平板である。複数の平板の素材は、金属板、樹脂板、木板、石板、紙板等のいずれでもよいが、同一であるのが好ましい。また、平板の大きさは、指、手のひら、手の甲、顔などの皮膚の一部を接触させて動かすことができる大きさであれば、特に限定されない。表面粗さは、市販の表面粗さ計、例えば（株）東京精密SURFCOM FLEX-50Aにより測定できる。 The flat plates used in the method of the present invention are a plurality of flat plates having different surface roughnesses. The material of the plurality of flat plates may be a metal plate, a resin plate, a wood plate, a stone plate, a paper plate, or the like, but it is preferable that they are the same. Further, the size of the flat plate is not particularly limited as long as it can move by contacting a part of skin such as a finger, a palm, a back of a hand, or a face. The surface roughness can be measured by a commercially available surface roughness meter, for example, Tokyo Seimitsu SURFCOM FLEX-50A.
本発明で用いる複数の平板の表面粗さは、相互に相違しており、Ｒａ＝０．００１〜５μｍの範囲であるのが、皮膚状態の評価性能の点から好ましい。さらに、Ｒａ＝０．００１〜０．１０μｍの範囲から選択される１種以上の平板と、Ｒａ＝０．１０〜３μｍの範囲から選択される１種以上の平板とを組み合わせて用いるのがより好ましい。表面粗さが相違する平板の数は２以上であればよく、２〜１０が好ましく、３〜６がより好ましい。なお、平板は水平に設置されていてもよいが、垂直や斜めに設置されていてもよい。また、平板は、固定して設置されておらず、摩擦力を検出するための力覚センサと一体となって例えば把持具に取り付けられその全体が動かせるものでもあってもよい。
また、複数の平板の材質は同一であることが好ましい。すなわち、材質を一定とし、表面粗さのみ相互に異った複数の平板を用いるのが好ましい。
The surface roughness of the plurality of flat plates used in the present invention is different from each other, and it is preferable that Ra is in the range of 0.001 to 5 μm from the viewpoint of the evaluation performance of the skin condition. Further, it is more preferable to use one or more flat plates selected from the range of Ra=0.001 to 0.10 μm and one or more flat plates selected from the range of Ra=0.10 to 3 μm in combination. preferable. The number of flat plates having different surface roughness may be 2 or more, preferably 2 to 10, and more preferably 3 to 6. The flat plate may be installed horizontally, but may be installed vertically or obliquely. Further, the flat plate may not be fixedly installed, but may be integrally attached to a force sensor for detecting a frictional force, for example, attached to a gripping tool and movable in its entirety.
Further, it is preferable that the materials of the plurality of flat plates are the same. That is, it is preferable to use a plurality of flat plates having the same material and different surface roughnesses.
前記複数の平板上に皮膚を接触させて皮膚表面と平板表面とが平行な状態を維持して皮膚（体）もしくは平板を動かしたときの摩擦係数をそれぞれ測定する。すなわち、複数の平板の表面で皮膚を擦過させて摩擦係数を測定する。この際の垂直応力は、一定とするのが好ましく、例えば０．１〜５Ｎの範囲内で所定の垂直応力とするのが好ましい。皮膚もしくは平板を動かす速度は、０．１〜２０ｃｍ／ｓｅｃが好ましい。皮膚を動かす場合は、垂直応力を一定とする、すなわち加える力を加減するために、力覚センサによって検出される力をリアルタイムでモニタするのが好ましい。固定して設置されていない平板を用いる場合も、同様にリアルタイムでモニタするのが好ましい。あるいは、例えばばねを用いて押しつけ力を一定にするなど、周知の手段を用いて、平板に加わる垂直応力を一定に維持することができる。 The skin is brought into contact with the plurality of flat plates to maintain the parallel state of the skin surface and the flat plate surface, and the friction coefficient when the skin (body) or the flat plate is moved is measured. That is, the coefficient of friction is measured by rubbing the skin on the surfaces of a plurality of flat plates. The vertical stress at this time is preferably constant, and for example, a predetermined vertical stress within the range of 0.1 to 5 N is preferable. The speed of moving the skin or the flat plate is preferably 0.1 to 20 cm/sec. When moving the skin, it is preferable to monitor the force detected by the force sensor in real time in order to make the vertical stress constant, that is, to adjust the applied force. Similarly, when using a flat plate that is not fixedly installed, it is preferable to monitor in real time. Alternatively, the vertical stress applied to the flat plate can be kept constant by using a well-known means, for example, a pressing force is kept constant by using a spring.
摩擦係数は、前記平板に設けられた垂直応力と水平応力の計測が可能な周知の力覚センサを用いて測定することができる。 The friction coefficient can be measured by using a well-known force sensor which is provided on the flat plate and can measure vertical stress and horizontal stress.
得られる複数の摩擦係数相互の関係、すなわち変化の向きや大小を皮膚状態の指標とすれば、皮膚状態が評価できる。例えば、乾燥状態にある皮膚においては、表面粗さの小さい平板の摩擦係数が低く、表面粗さの大きい平板においても摩擦係数が低いままである。一方、しっとり、柔らかい皮膚においては、表面粗さの小さい平板での摩擦係数が高く、表面粗さの大きい平板での摩擦係数が低くなる（図１）。これは、化粧料が潤いや柔軟性を肌に与える性能の評価に用いることができる。すなわち、潤いや柔軟性を肌に与える性能が高い化粧料を皮膚に塗布すると表面粗さの小さい平板での摩擦係数が高く、表面粗さの大きい平板での摩擦係数が低くなることを利用して、表面粗さの小さい平板での摩擦係数と表面粗さの大きい平板での摩擦係数の差を、潤いや柔軟性を肌に与える性能の指標とすることができる（図２）。 The skin condition can be evaluated by using the relationship among the obtained plurality of friction coefficients, that is, the direction and magnitude of the change as an index of the skin condition. For example, on dry skin, a flat plate having a small surface roughness has a low coefficient of friction, and a flat plate having a large surface roughness has a low coefficient of friction. On the other hand, in moist and soft skin, a flat plate having a small surface roughness has a high friction coefficient and a flat plate having a large surface roughness has a low friction coefficient (FIG. 1). This can be used for evaluation of the performance of the cosmetic to impart moisture and flexibility to the skin. That is, by applying to the skin a cosmetic having a high ability to impart moisture and flexibility to the skin, the coefficient of friction of a flat plate having a small surface roughness is high, and the coefficient of friction of a flat plate having a large surface roughness is low. Thus, the difference between the friction coefficient of a flat plate having a small surface roughness and the friction coefficient of a flat plate having a large surface roughness can be used as an index of the performance of imparting moisture and flexibility to the skin (FIG. 2).
このような評価は、化粧料に限られるものではなく、他にも医薬品外用剤などについても行うことができる。すなわち、化粧料や医薬品外用剤などの肌に適用（塗布のみならずパップ剤などによる場合も含む）する剤を、肌に適用する前と適用した後との各々において、表面粗さが相違する複数の平板上に皮膚を接触させて平板表面に対して平行に動かしたときの摩擦係数をそれぞれ測定し、測定された複数の摩擦係数相互の関係の変化から化粧料や医薬品が肌に与える効果を評価することができる。 Such an evaluation is not limited to cosmetics, but can also be applied to other pharmaceutical external preparations and the like. That is, the surface roughness of an agent such as a cosmetic or an external preparation for pharmaceuticals (including not only the application but also the case of using a poultice) is different before and after the application to the skin. The effect of cosmetics or pharmaceuticals on the skin is measured by measuring the coefficient of friction when the skin is brought into contact with multiple flat plates and moving parallel to the flat plate surface, and the change in the relationship between the measured multiple friction coefficients. Can be evaluated.
また、油性感のある皮膚においては、表面粗さの小さい平板の測定１回目の摩擦係数が低いものの、皮膚の同じ位置を同一の表面粗さの平板で繰り返し測定すると徐々に摩擦係数が上昇する（図３）。これは表面にある油性成分が除去されるためであり、摩擦係数が一定になったところが肌本来の性質となる。摩擦係数が一定になった後で表面粗さの異なる平板で計測すると肌本来の状態を評価できる。濡れた状態や、クリームなどの剤が付着した皮膚も、同様に皮膚の同じ位置を常に同一の表面粗さの平板で繰り返し測定すると、当初は変動している摩擦係数が一定になるので、そのあとで、表面粗さの異なる平板で計測することで、肌本来の状態を評価できる。
このように、平板の表面粗さと摩擦係数の変化との相関関係から、皮膚状態を評価することができる。
In addition, in oily skin, although the coefficient of friction of the first measurement of a flat plate having a small surface roughness is low, the friction coefficient gradually increases when the same position of the skin is repeatedly measured with a flat plate having the same surface roughness. (Figure 3). This is because the oily component on the surface is removed, and the place where the coefficient of friction becomes constant is the original property of the skin. After the friction coefficient becomes constant, the original condition of the skin can be evaluated by measuring with flat plates having different surface roughness. In the wet state or on the skin to which agents such as cream adhere, if the same position of the skin is constantly repeatedly measured with a flat plate having the same surface roughness, the initially varying friction coefficient becomes constant, so Later, by measuring with flat plates having different surface roughness, the original condition of the skin can be evaluated.
Thus, the skin condition can be evaluated from the correlation between the surface roughness of the flat plate and the change in the friction coefficient.
表面粗さの相違する平板を２枚だけでなく、３枚〜８枚と増加させることにより、さらに詳細な皮膚状態を評価することができる。例えば、Ｒａ＝０．０１〜０．１（０．０２５）の平板を基準とし、Ｒａ＝０．１〜０．３（０．２５４）の平板、Ｒａ＝０．３〜０．５（０．３４１）の平板、Ｒａ＝０．５〜０．６（０．５６）の平板、Ｒａ＝０．６〜０．７（０．６４５）の平板、Ｒａ＝０．７〜０．８（０．７３８）の平板、及びＲａ＝０．８〜１．０（０．８１７）の平板を用いて、摩擦係数の変化を測定すれば、乾燥状態の度合、しっとり感の度合、油性感の度合も含めた多段階の皮膚状態が評価できる。 By increasing not only two flat plates having different surface roughness but three flat plates to three flat plates, more detailed skin condition can be evaluated. For example, with a flat plate having Ra=0.01 to 0.1 (0.025) as a reference, a flat plate having Ra=0.1 to 0.3 (0.254) and Ra=0.3 to 0.5 (0 .341) flat plate, Ra=0.5 to 0.6 (0.56) flat plate, Ra=0.6 to 0.7 (0.645) flat plate, Ra=0.7 to 0.8 ( 0.738) flat plate and Ra=0.8 to 1.0 (0.817) flat plate were used to measure the change in the friction coefficient, and the degree of dryness, the degree of moist feeling, and the oily feeling Multi-stage skin condition including degree can be evaluated.
また、上述したように、一般的な皮膚では、表面粗さの小さい平板での摩擦係数と表面粗さの大きい平板での摩擦係数の差を、潤いあるいは柔らかさの指標とすることができるが、３枚あるいはそれ以上の平板を用いると、皮膚の発汗の有無を容易に観察できる。すなわち、発汗状態の皮膚では、水分が供給されることで、摩擦係数が不安定となり、表面粗さの小さい平板での摩擦係数と表面粗さの大きい平板での摩擦係数の大小関係が逆転する。このことを利用して、測定した皮膚の発汗状態若しくは被験者の肌が発汗しやすいか否かを判定することができる（図４）。発汗のしやすさは摩擦係数の変動により判定できるが、その際の皮膚の柔軟性も同時に判別することができる。この判定は、測定を繰り返し行えば２枚の平板で行うことも可能だが、３枚以上が好ましく、５枚以上用いることが更に好ましい。測定の煩雑さを考えると１０枚以下が好ましい。 Further, as described above, in general skin, the difference between the friction coefficient of a flat plate having a small surface roughness and the friction coefficient of a flat plate having a large surface roughness can be used as an index of moisture or softness. If three or more flat plates are used, it is possible to easily observe the presence or absence of perspiration on the skin. That is, in the case of perspiring skin, the supply of water makes the friction coefficient unstable, and the magnitude relationship between the friction coefficient of a flat plate having a small surface roughness and the friction coefficient of a flat plate having a large surface roughness is reversed. .. By utilizing this, it is possible to determine whether or not the measured sweating state of the skin or the skin of the subject easily sweats (FIG. 4). The easiness of sweating can be determined by the change in the friction coefficient, and the flexibility of the skin at that time can be determined at the same time. This determination can be performed on two flat plates by repeating the measurement, but it is preferably 3 or more, and more preferably 5 or more. Considering the complexity of measurement, 10 or less sheets are preferable.
次に実施例を挙げて本発明を更に詳細に説明する。 Next, the present invention will be described in more detail with reference to examples.
実施例１
高密度ポリエチレン板（ＨＤＰＥ）（表面粗さＲａ＝０．０８）と同（表面粗さＲａ＝２．５）の平板の下部に摩擦係数測定装置を設置した。これらの平板上を垂直応力約０．５Ｎの力で手指の腹を擦過し、摩擦係数を測定した。
Example 1
A friction coefficient measuring device was installed below a flat plate of the same (surface roughness Ra=2.5) as the high density polyethylene plate (HDPE) (surface roughness Ra=0.08). The flats of the fingers were rubbed on these flat plates with a force of vertical stress of about 0.5 N, and the friction coefficient was measured.
それぞれ指の乾燥状態の異なる被験者５名（Ａ、Ｂ、Ｃ、Ｄ、Ｅ）の摩擦係数を図５に示す。
図５中、被験者Ｄは、指が乾燥しており、カサカサして硬い状態であった。この被験者Ｄは、表面粗さの小さいＨＤＰＥ板では摩擦係数が低く、一方表面粗さの大きい板でも摩擦係数は低かった。この結果から、乾燥状態の皮膚は、表面粗さの小さい平板では摩擦係数が低く、表面粗さの大きい平板も低いままであることがわかる。
FIG. 5 shows the friction coefficient of 5 subjects (A, B, C, D, E) each having a different finger dry state.
In FIG. 5, subject D had a dry finger and was in a dry and hard state. This test subject D had a low coefficient of friction with an HDPE plate having a small surface roughness, while having a low coefficient of friction even with a plate having a large surface roughness. From this result, it can be seen that the dry skin has a low friction coefficient with a flat plate having a small surface roughness, and the flat plate having a large surface roughness remains low.
一方、図５中、被験者Ｃは、指がしっとり、柔らかい状態であった。この被験者Ｃは、表面粗さの小さいＨＤＰＥ板では摩擦係数が高く、一方表面粗さの大きい板では摩擦係数が低くなった。この結果から、しっとりした状態の皮膚は、表面粗さの小さい平板では摩擦係数が高く、表面粗さの大きい平板では摩擦係数が低くなることがわかる。 On the other hand, in FIG. 5, the test subject C had a soft and soft finger. This test subject C had a high friction coefficient with the HDPE plate having a small surface roughness, while having a low friction coefficient with the plate having a large surface roughness. From these results, it can be seen that the moistened skin has a high friction coefficient on a flat plate having a small surface roughness and a low friction coefficient on a flat plate having a large surface roughness.
これらの結果に基づき、表面粗さと摩擦係数の変化と皮膚状態との相関性を予め求めておけば、皮膚状態の評価が可能になる。 Based on these results, the skin condition can be evaluated if the correlation between the surface roughness, the change in the friction coefficient, and the skin condition is obtained in advance.
実施例２
図６のような表面粗さを相互に異ならせたＳＵＳ板を７板配置した摩擦係数測定装置を作製した。図６中、中心は未加工ＳＵＳ板（Ｒａ＝０．０２５）であり、その周囲には、ブラスト処理により表面粗さを変化させた（Ｒａ＝０．２〜０．９）ＳＵＳ板を配置した。
被験者１１名が、指で未加工板を擦過（０．５Ｎ）したときの摩擦係数を図７に示す。実施例１の場合と同様に、皮膚の状態により摩擦係数は大きく変化した。なお、回数の変化により摩擦係数が変化するのは、発汗などにより皮膚状態が変化するからである。
Example 2
A friction coefficient measuring device in which seven SUS plates having mutually different surface roughness are arranged as shown in FIG. 6 was manufactured. In FIG. 6, the center is an unprocessed SUS plate (Ra=0.025), and the SUS plate whose surface roughness is changed by blasting (Ra=0.2 to 0.9) is arranged around it. did.
FIG. 7 shows the friction coefficient when 11 test subjects rubbed the unprocessed plate with their fingers (0.5 N). As in the case of Example 1, the friction coefficient greatly changed depending on the skin condition. The friction coefficient changes with the change in the number of times because the skin condition changes due to sweating or the like.
被験者１１名が、指でブラスト処理板を擦過（０．５Ｎ）したときの摩擦係数の変化を図８に示す。図８より、表面粗さが小さい場合は個人差が大きく、表面粗さが大きくなると個人差が縮小し、実施例１と同じ傾向があった。 FIG. 8 shows changes in the friction coefficient when 11 test subjects rub the blasted plate with their fingers (0.5 N). From FIG. 8, when the surface roughness is small, the individual difference is large, and when the surface roughness is large, the individual difference is reduced, and there is the same tendency as in Example 1.
Claims (4)
皮膚の乾燥状態、しっとり感又は柔軟性については、予め得られたこれらの皮膚状態に関する表面粗さと摩擦係数の変化との相関関係に基づいて評価し、
油性感については、表面粗さの小さい平板の摩擦係数を測定し、次いで皮膚の同じ位置を同一の表面粗さの平板で繰り返し摩擦係数を測定して、摩擦係数が徐々に上昇することで評価し、
汗のかきやすさについては、表面粗さの小さい平板での摩擦係数と表面粗さの大きい平板での摩擦係数の大小関係が逆転することで汗をかきやすいことを評価する、皮膚状態の評価方法。 It is necessary to measure the friction coefficient when the skin is brought into contact with a plurality of flat plates with different surface roughness and move in parallel to the flat plate surface, and to use the relationship between the measured multiple friction coefficients as an index. Characteristic, a dry state of the skin, a moist feeling, flexibility, a feeling of oiliness and a method for evaluating a skin condition selected from the ease of sweating,
For the dry state of the skin, moist feeling or flexibility, it is evaluated based on the correlation between the surface roughness and the change in the friction coefficient relating to these skin conditions obtained in advance,
Regarding the oily feeling, the friction coefficient of a flat plate with a small surface roughness was measured, and then the friction coefficient was repeatedly measured at the same position on the skin with a plate of the same surface roughness, and the friction coefficient was gradually increased. Then
Regarding the easiness of sweating, a method of evaluating the skin condition is evaluated by reversing the magnitude relationship between the friction coefficient of a flat plate with a small surface roughness and the friction coefficient of a flat plate with a large surface roughness. ..
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