El-Sapa Shreen
Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt.
Department of Mathematics, Faculty of Science, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.
Eur Phys J E Soft Matter. 2019 Mar 20;42(3):32. doi: 10.1140/epje/i2019-11791-1.
The gravitational settling of small spherical particles in an unbounded micropolar fluid with slip surfaces is considered. The motion is studied under the assumption of low Reynolds number. The slip boundary conditions on velocity and microrotation at the surface of the spherical particle is used. The solution for the stream function of the fluid flow is obtained analytically. The settling velocity is obtained and is plotted against the Knudsen number for various values of the micropolarity parameter and constants depending on the material of the solid surface. The problem of rotational motion of a particle with slip surface is also solved and the torque coefficient acting on the spherical particle is obtained and is plotted against Knudsen number for different values of micropolarity parameter, spin parameter, and the material constants. The correction to the Basset equation for settling velocity under gravity for slip particle in micropolar fluids is discussed with the range of Knudsen number which has been proven with known results available in the literature.
考虑了具有滑移面的无界微极流体中小球形颗粒的重力沉降。在低雷诺数假设下研究该运动。使用了球形颗粒表面速度和微旋转的滑移边界条件。通过解析得到了流体流动的流函数解。获得了沉降速度，并针对不同微极参数值和取决于固体表面材料的常数，将其与克努森数作图。还解决了具有滑移面的颗粒的旋转运动问题，得到了作用在球形颗粒上的扭矩系数，并针对不同微极参数、自旋参数和材料常数的值，将其与克努森数作图。讨论了微极流体中滑移颗粒在重力作用下沉降速度的巴塞特方程的修正，以及克努森数的范围，该范围已通过文献中的已知结果得到验证。
