滑移流条件下纳米粒子布朗运动的Stokes-Einstein扩散关系

Stokes-Einstein Diffusion Relationship for Brownian Motion of Nano-Meter Particle under Slip Flow Regime

采用低雷诺数流理论中的奇点叠加法对做平移和旋转的纳米粒子运动规律进行了研究,推导出了适用于滑移流区域的Stokes阻力和旋转阻力矩公式,并在此基础上建立了平移和旋转运动的Stokes-Einstein扩散关系式.理论分析表明,滑移流条件下粒子运动的阻力和阻力矩小于经典式无滑移理论解,相应的粒子扩散系数高于无滑移问题的解,说明在滑移流条件下粒子扩散能力有所增强,且增强程度与努森数Kn直接相关,其值越大增强效果越显著.推导的关系式适用于描述低浓度无界液体或气体中的粒子运动,可应用于化工、环境、选矿和生物力学等领域.

The shift and rotational motions of nano-meter particle in unbounded flow region are analyzed by the singularity superposed method following low Reynolds number theory. The formulas of Stokes drag force and rotational drag torque under slip regime are derived, and accordingly Stokes-Einstein diffusion relationships are established. The theoretical analysis shows that the drag for shift motion and drag torque for rotational motion are less than both solutions under the condition of no-slip regime, and accordingly Stokes-Einstein diffusion coefficients are greater than the no-slip cases, which indicates that the diffusion capability increases for the particle motion at slip regime. The increasing diffusion capability is related to Knudsen number directly： the larger the Knudsen number, the greater the diffusion capability. The derived results can be used to describe particles motion in the unbounded liquid or gas flow with low concentration, and are applicable in the fields of chemical industry, environmental science, ore dressing, biomechanics, and so on.