填隙幂律流体下两刚性圆球错移时的黏性力

ON TANGENTIAL INTERACTION BETWEEN TWO RIGID SPHERES WITH INTERSTITIAL POWER-LAW FLUID

湿颗粒离散元模型以两球作用时填隙流体定常流动解为基础,其中切向作用是难点,国外仅有Goldman的牛顿流体渐近解.基于Reynolds润滑理论导出了两刚性球切向错动时填隙幂律流体的压力方程,并利用傅立叶级数展开简化,通过数值解法得到相应的压力分布、黏性阻力及阻力矩.该方程的解较之作者先前对速度场附加假定的结果精确,而当幂指数为1时等价于Goldman的牛顿流体渐近解.

Discrete Element Modeling for wet particle assembly is based on the interactions between two spheres with an interstitial fluid, when the fluid behaves as non-Newtonian, the analysis for the tangential interaction becomes much more complicated. Up-to-date there is only Goldman's asymptotic solution for Newtonian fluid. In the authors' previous study, an approximate approach for the tangential interaction with a Power-law fluid was proceeded with an additional assumption for velocity, correspondingly an pressure equation was obtained and then solved numerically to get the viscous force and moment. However, its validity has not yet been estimated. In order to get the more accurate expressions, a new approach was carried out based on Reynolds lubrication theory without the additional assumption. As a result a pressure equation was derived and then simplified by using Fourier-series expansion, after the pressure equation was solved, corresponding results for the viscous force and moment were obtained. The numerical results from the proposed equation were compared with those from the previous equation, showing that the additional assumption could be satisfied automatically for a Newtonian fluid, therefore the previous solutions can be applied to a Newtonian-like Power-law fluid, otherwise the proposed pressure equation is necessary. For a Power-law fluid, the power index is a key factor affecting the accuracy. The more deviation of the index from 1, the more errors produced. Generally the differences of viscous force and moment between the previous and the proposed schemes are significant less than those of the pressure distribution. Especially when the power index approaches or exceeds 0.8, the previous results are in good coincidence with the proposed ones, which suggest that the previous is valid with a satisfied accuracy, in this case, the additional assumption could be taken to simplify the derivation.