标题： 由于附近粒子引起的振荡板上的多余剪切力 显示英文标题

标题： Excess shear force exerted on oscillating plate due to a nearby particle

摘要： 在本文中，我们从理论上研究了在粘性液体上方悬浮有刚性粒子的情况下，无限水平平面在快速横向振荡时所受到的剪切力。 这项研究主要受到石英晶体微天平（QCM-D）技术的启发，该技术依赖于分析在液体介质中快速振荡（在兆赫兹范围内）的石英晶体盘由于其表面吸附的小物质而产生的响应（复阻抗）。 事实上，靠近振荡晶体的液体介质中悬浮的小物质也可能对阻抗产生贡献，因为它们会改变悬浮液体对石英晶体施加的局部剪切力。 对于稀释悬浮液，单个粒子的贡献是可叠加的，因此我们的分析仅限于位于平面任意距离上方的单个球形粒子引起的额外剪切力。 考虑了三种不同的情况：（i）高固体惯性极限情况，其中重粒子可以视为静止；（ii）任意质量的自由悬浮粒子，经历流体介导的周期性旋转和平移；（iii）与板整体一起移动而不旋转的吸附粒子。 对于小振幅平面振荡，非定常斯托克斯流动方程适用。 我们使用反射法构造这些方程的级数解，其各项被明确写出。 由于流动在远离振荡板处呈指数衰减，仅包含少量低阶项的截断级数在广泛的粒子尺寸和分离距离范围内与严格的数值结果表现出良好的一致性。 目前的结果支持这样一个观点，即悬浮小物质对测量阻抗的水动力贡献是不可忽略的，甚至是主导的。 显示英文摘要

摘要： In the present paper we theoretically study the shear force exerted on an infinite horizontal plane undergoing fast lateral oscillations in presence of a rigid particle suspended in the viscous liquid above the plate. The study is largely motivated by Quartz Crystal Microbalance (QCM-D) technique which relies on analyzing response (complex impedance) of fast oscillating (in MHz range) quartz crystal disk in the liquid medium due to small substances adsorbed at its surface. In fact, small substances suspended in the liquid medium in the vicinity of the oscillating crystal may also contribute to impedance, as they modify the local shear force the suspending liquid exerts on the quartz crystal. For a dilute suspension the contributions of individual particles are additive and, therefore, our analysis is restricted to the excess shear force due a single spherical particle located at arbitrary distance above the plane. Three distinct cases are considered: (i) limiting case of high solid inertia, whereas the heavy particle can be considered as stationary; (ii) a freely suspended particle of arbitrary mass, undergoing fluid-mediated time-periodic rotation and translation and (iii) an adsorbed particle moving with the plate as a whole without rotation. For small-amplitude plane oscillations the unsteady Stokes flow equations apply. We construct the series solution of these equations using the method of reflections, whereas its terms are written explicitly. Due to the exponential decay of the flow away from the oscillating plate, the truncated series containing only few low-order terms shows an excellent agreement with the rigorous numerical results for a wide range of particle sizes and separation distances. The present results support the notion that the hydrodynamic contribution of the suspended small substances to the measured impedance is non-negligible or even dominant.