Slow Motion of a Slip Spherical Particle Parallel to One or Two Plane Walls

表面滑移球形粒子平行一或二平面之緩慢運動

陳柏源(Po Y. Chen) ； 葛煥彰(Huan J. Keh)

《Journal of the Chinese Institute of Chemical Engineers》 34卷1期 (2003/01) Pp. 123-133

https://doi.org/10.6967/JCICE.200301.0123

摘要

本文以半解析半數值的方法，研究一剛性球形粒子於兩平行平板間之黏性流體中之任意位置，進行平行平板之移動與轉動所造成的緩流運動。所考慮之流體可為稍微稀薄之氣體，並可以在粒子的表面產生滑移現象。為便於求解主導流場之Stokes方程式，需要建立其在直角座標及球座標系統中之通解。首先以Fourier轉換，使此通解滿足平板上的邊界條件，再以邊界取點法使通解滿足球形粒子上的邊界條件。對於粒子位於兩平板間各種不同之相對位置，與各種不同之粒子表面滑移係數情形，分別計算流體施於粒子之阻力與阻力矩，可得良好之收斂數值結果。針對粒子平行單一平板與兩平板之運動，在粒子表面為不滑移與完全滑移的情況下，所計算出的阻力與阻力矩值，皆與現有文獻中之數值相吻合。而在任何粒子與平面之幾何架構情況下，粒子所受之阻力與阻力矩值，大致隨著粒子表面滑移係數之增加而有逐漸遞減的情形。

並列摘要

A combined analytical-numerical study for the creeping flow caused by a rigid spherical particle translating and rotating in a viscous fluid parallel to two flat plates at an arbitrary position between them is presented. The fluid, which may be a slightly rarefied gas, is allowed to slip at the surface of the particle. To solve the Stokes equations for the fluid velocity field, a general solution is constructed from fundamental solutions in both rectangular and spherical coordinate systems. Boundary conditions are enforced first at the plane walls by the Fourier transforms and then on the particle surface by a collocation technique. Numerical results for the hydrodynamic drag force and torque acting on the particle are obtained with good convergence for various values of the slip coefficient of the particle and of the separation distances between the particle and the walls. For the motion of a no-slip sphere and a perfectly-slip sphere parallel to a single plane wall or to two walls, our drag and torque results are in good agreement with the available solutions in the literature for all particle-to-wall spacings. The boundary-corrected drag force and torque exerted on the particle in general decrease with an increase in the slip coefficient for any given geometry.

並列關鍵字

Creeping flow ； Aerosol sphere ； Slip-flow surface ； Drag force and torque ； Boundary effect