The steady rotational motion of a spherical particle with frictionally slip surface about a diameter in a quiescent unbounded fluid is studied analytically for a small but finite Reynolds number $Re$. The Navier–Stokes equation governing the axisymmetric fluid flow around the particle is solved by using a regular perturbation method. The expansion expression for the retarding torque exerted by the fluid on the particle good to $\mathrm{O}\left(R{e}^3\right)$ is obtained as a function of the scaled slip coefficient of the particle in closed form. This perturbation analysis shows that the perturbed fluid velocity field is of $\mathrm{O}\left(Re\right)$, the same as that for the translation of the particle, but the first correction to the hydrodynamic torque occurs at $\mathrm{O}\left(R{e}^2\right)$, much weaker than that to the hydrodynamic drag force acting on a translating particle which is still of $\mathrm{O}\left(Re\right)$. The hydrodynamic torque is found to be a monotonic increasing function of the Reynolds number and a monotonic decreasing function of the scaled slip coefficient, similar to the effect of fluid inertia on the hydrodynamic force on a slip particle undergoing translation. The inertial effect on the hydrodynamic torque, which can be a sensitive function of the slip coefficient and vanishes as the particle surface is fully slip, is generally negligible for the case of $Re<3$ but significant as $Re$ is greater than about 10.

对于较小但有限的雷诺数，分析性地研究了具有摩擦滑动面的球形颗粒在静态无界流体中的直径的稳态旋转运动。 $\mathrm{[R}Ë$。通过使用常规的扰动方法可以解决控制粒子周围轴对称流体流动的Navier–Stokes方程。流体施加在颗粒上的阻滞扭矩的膨胀表达式好于$\mathrm{Ø}（\mathrm{[R}{Ë}^3）$作为闭合形式的颗粒的比例滑移系数的函数，获得Δε。这种扰动分析表明，扰动的流体速度场是$\mathrm{Ø}（\mathrm{[R}Ë）$，与粒子平移的相同，但是对流体动力扭矩的第一次校正发生在 $\mathrm{Ø}（\mathrm{[R}{Ë}^{\mathrm{2个}}）$，远比作用在平移粒子上的流体动力阻力要弱得多，而平移粒子仍然是 $\mathrm{Ø}（\mathrm{[R}Ë）$。发现流体动力扭矩是雷诺数的单调增加函数和缩放的滑移系数的单调减小函数，类似于流体惯性对经历平移的滑移颗粒上的流体动力的影响。对于流体动力转矩的惯性作用，可能是滑移系数的敏感函数，并随着颗粒表面完全滑移而消失，对于以下情况，通常可以忽略不计。$\mathrm{[R}Ë<3$ 但作为 $\mathrm{[R}Ë$ 大于约10