A semi-analytical study of the steady flow around a spherical particle rotating in an incompressible Newtonian fluid inside an eccentric spherical cavity with slip surfaces about their common diameter is presented at low Reynolds numbers. To solve the Stokes equation, a solution consisting of the general solutions in two systems of spherical coordinates is employed and the boundary conditions are fulfilled by a collocation method. Accurate results of the torque exerted by the fluid on the particle are obtained as a function of the dimensionless parameters $a∕b$, $d∕(b-a)$, $\beta a∕\eta$, and ${\beta }_{\mathrm{w}}b∕\eta$, where $a$ and $b$ are the radii and ${\beta }^{-1}$ and ${\beta }_{\mathrm{w}}^{-1}$ are the Navier slip coefficients of the particle and cavity, respectively, $d$ is the distance between the particle and cavity centers, and $\eta$ is the fluid viscosity. The boundary effect of the cavity with a slip wall on the rotation of the slip particle is quite significant and interesting. The torque normalized by that on the particle in an unbounded identical fluid vanishes as ${\beta }_{\mathrm{w}}b∕\eta =0$ (the cavity wall is fully slip), equals unity for a value of ${\beta }_{\mathrm{w}}b∕\eta$ very close to 3, and in general increases with an increase in ${\beta }_{\mathrm{w}}b∕\eta$ (or the stickiness of the cavity wall). When ${\beta }_{\mathrm{w}}b∕\eta >3$, the normalized torque is in general greater than unity, an increasing/decreasing function of the eccentricity parameter $d∕(b-a)$ if the value of $\beta a∕\eta$ (or the stickiness of the particle surface) is large/small, and an increasing function of $\beta a∕\eta$ and $a∕b$. When ${\beta }_{\mathrm{w}}b∕\eta <3$, conversely, the normalized torque is in general less than unity, a decreasing/increasing function of $d∕(b-a)$ if the value of $\beta a∕\eta$ is large/small, and a decreasing function of $\beta a∕\eta$ and $a∕b$. The cavity wall exerts less torque on the particle when it rotates about their common diameter than about an axis normal to it.

在低雷诺数下，对偏心球形腔内不可压缩的牛顿流体中旋转的球形粒子周围的稳态流动进行了半分析研究，该偏心球形腔的滑动面约为其共同直径。为了求解斯托克斯方程，采用了由两个球坐标系中的一般解组成的解，并通过搭配方法满足了边界条件。根据无因次参数获得流体施加在颗粒上的扭矩的准确结果$\mathrm{一种}∕b$， $d∕（b-\mathrm{一种}）$， $\beta \mathrm{一种}∕\eta$和 ${\beta }_{\mathrm{w}}b∕\eta$，在哪里 $\mathrm{一种}$ 和 $b$ 半径和 ${\beta }^{-\mathrm{1个}}$ 和 ${\beta }_{\mathrm{w}}^{-\mathrm{1个}}$ 分别是粒子和腔的Navier滑移系数， $d$ 是粒子和腔中心之间的距离，并且 $\eta$是流体粘度。具有滑动壁的空腔对滑动颗粒的旋转的边界影响是非常显着且有趣的。在无界的相同流体中，由粒子上的转矩归一化的转矩随着${\beta }_{\mathrm{w}}b∕\eta =0$ （型腔壁完全打滑），等于等于1的值 ${\beta }_{\mathrm{w}}b∕\eta$ 非常接近3，并且通常随着 ${\beta }_{\mathrm{w}}b∕\eta$（或腔壁的粘性）。什么时候${\beta }_{\mathrm{w}}b∕\eta >3$，归一化扭矩通常大于1，这是偏心率参数的增/减函数 $d∕（b-\mathrm{一种}）$ 如果值 $\beta \mathrm{一种}∕\eta$ （或粒子表面的粘性）大/小，并且增加功能 $\beta \mathrm{一种}∕\eta$ 和 $\mathrm{一种}∕b$。什么时候${\beta }_{\mathrm{w}}b∕\eta <3$相反，归一化扭矩通常小于1，减小/增大功能为 $d∕（b-\mathrm{一种}）$ 如果值 $\beta \mathrm{一种}∕\eta$ 是大/小，并且递减函数 $\beta \mathrm{一种}∕\eta$ 和 $\mathrm{一种}∕b$。当腔室壁绕其共同直径旋转时，比围绕其垂直轴旋转时，腔壁对粒子施加的扭矩较小。