Elastohydrodynamic theory for wet oblique collisions
Elastohydrodynamic theory for wet oblique collisions
复制标题
DOI：
10.1016/j.powtec.2006.07.006
复制
发表时间：
2006-10
影响因子：
5.2
通讯作者：
A. Kantak;Robert H. Davis
中科院分区：
文献类型：
--
作者：
A. Kantak;Robert H. Davis
本文提出了一个球形粒子与覆盖有薄液层的平面的斜碰撞模型。以前发展的完全浸入碰撞的弹性流体力学理论[Davis，Serayssol和Hinch 1986 JFM 63 479-497]被修正为法向运动分量，以考虑液层的有限厚度。然后将得到的油膜厚度分布的时间演变与滑动润滑一起使用，以确定运动的切向分量。临界斯托克斯数(粒子惯性和粘性力的无量纲比)是根据碰撞中涉及的材料的物理性质来预测的，低于该值时不会出现反弹，正如柔度参数所描述的那样，该柔度参数表示粘性力引起的弹性变形的无量纲度量。在临界Stokes数以外，正常恢复系数随Stokes数和柔度参数的增加而增大，在较高Stokes数时接近于干恢复系数。回弹时的润滑吸力受气蚀的限制。切向回复与冲击角度无关，除了取决于斯托克斯数和柔度参数外，还与流体层厚度与球体半径之比呈线性关系。发现切向恢复接近于1，并且柔顺参数的值越大，切向恢复通常越高。此外，在小柔度时，切向回复随Stokes数的增加而增加，在大柔度时随Stokes数的增加而减小。旋转速度的变化表现出与切向恢复相反的趋势。最后，给出了描述恢复系数和无量纲转速变化的闭合表达式。
This paper presents a model for oblique collisions of spherical particles with a plane surface covered with a thin liquid layer. Elastohydrodynamic theory developed previously for fully immersed collisions [Davis, Serayssol and Hinch 1986 JFM 63 479–497] is modified for the normal component of motion to account for the finite thickness of the liquid layer. The resulting time evolution of the film thickness profile is then used along with sliding lubrication to determine the tangential component of motion. The critical Stokes number (dimensionless ratio of particle inertia and viscous forces), below which no rebound is seen, is predicted in terms of the physical properties of the materials involved in the collision, as described by a compliance parameter representing a dimensionless measure of elastic deformation due to viscous forces. Beyond the critical Stokes number, the normal restitution coefficient is found to increase with the Stokes number and the compliance parameter, asymptoting to the dry restitution coefficient at high Stokes numbers. The lubrication suction resistance during rebound is limited by cavitation. The tangential restitution is independent of the impact angle and is linearly dependent on the ratio of the fluid layer thickness to the sphere radius, in addition to depending on the Stokes number and compliance parameter. The tangential restitution is found to be close to unity and is generally higher for a larger value of the compliance parameter. Moreover, the tangential restitution is seen to increase with the Stokes number at small compliance and decrease with the Stokes number at large compliance. The change in rotational velocity exhibits trends that are the reverse of the tangential restitution. Finally, closed-form expressions have been developed for describing the restitution coefficients and dimensionless change in rotational velocity.