血流中の血球粒子の回転モーメントと粘性抵抗

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  • Rotational Moment and Viscous Resistance of Blood Cell Particles in Moving Liquid

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Abstract

血流中を運動する血球が受ける回転モーメントと粘性抵抗をBrenner(1958)の理論に基ずいて解析した. 低レイノルズ数におけるストークスの方程式と連続の式に対してFaxen(1929)の反射法(Reflection Method)を用いて3次まで厳密解を導出した. 回転モーメントと粘性抵抗はベッセル関数を含む複雑な形式となり初等関数では表現できなかった. 流体の粘性で正規化された抵抗は粒子が大きいと増加したが血管壁近傍では減少した. この傾向はとくに大きな粒子で明らかであった. 回転モーメントは血管壁近傍で増加した. 圧降下は壁近傍で減少した. 両者とも粒子が大きいほど増加した. 本研究は血流中の血球粒子自体に作用する力学量を推定するのに有用と考えられる.
We analyzed rotational moment and viscous drag force acting on a moving sphere in moving fluid. The analysis was confined on the slow Poiseuille flow which Reynolds number is lower than 1.0. The stoke's differential equation in combination with the continuity law were solved by rigorous mathematical expansion. We have used the Reflection method proposed by Faxen (1929). The rotational moment and viscous drag force were expressed by complex Bessel functions. The normalized viscous force increased with particle radius and decreased at near the wall. The rotational moment increased at near the wall. The pressure drop due to the particle decreased at near the wall. The moment and pressure drop increased with particle radius. The present analysis will be available for estimating the rotational moment and viscous drag force on the moving blood cell.

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