未对齐平行板流变仪中的牛顿流体动力学
Newtonian fluid dynamics in a misaligned parallel-plate rheometer
AI总结：
本研究通过微扰展开建立理论模型并结合三维数值模拟，揭示了平行板流变仪的未对齐现象在小间隙高度下会产生额外二次速度和压力，导致主导力与力矩随倾斜角增大而增加，从而使流变仪低估牛顿流体粘度。
摘要：
平行板旋转流变仪通过使顶板相对于底板旋转以在流体中诱导剪切，并测量由此产生的扭矩和力作为诱导旋转速率的函数，从而测量流体的粘度。制造缺陷通常会导致流变仪的板发生无意未对齐，即顶板和底板不完全平行，这种未对齐会影响流变仪内部的流体动力学。本研究在小流变仪间隙高度的极限下，考察了未对齐对牛顿流体粘度测量的影响。使用微扰展开推导出了一般牛顿流体在具有小间隙高度的未对齐流变仪中行为的理论模型。理论结果表明，在小间隙高度下，未对齐会在流体中产生额外的二次速度分量和压力，从而影响流变仪中的力和力矩。在这种情况下，在小雷诺数下，作用在流变仪顶板上的主导力和力矩是平行于倾斜轴方向的粘性力、垂直于倾斜轴且在横截面内的压力力矩，以及沿流变仪高度方向的粘性力矩。发现顶板上的这些力和力矩随着未对齐倾斜角的增加而增大，导致流变仪以更大的幅度低估流体的粘度，且倾斜角越大低估越严重。三维数值模拟验证了理论预测。
英文摘要：
A parallel-plate rotational rheometer measures the viscosity of a fluid by rotating the top plate relative to the bottom plate in order to induce a shear on the fluid and measuring the torques and forces that result as a function of the induced rotation rate. Manufacturing imperfections can often lead to unintentional misalignment of the plates of the rheometer, where the top and bottom plates are not perfectly parallel, and this misalignment can affect the fluid dynamics inside the rheometer. This study examines the effect that misalignment has on the viscosity measurements of Newtonian fluids in the limit of small rheometer gap heights. A theoretical model for the behavior of a general Newtonian fluid in a misaligned rheometer with a small gap height is derived using perturbation expansions. The theoretical results show that at small gap heights, misalignment can produce additional secondary velocity components and pressures in the fluid, which affect the forces and moments in the rheometer. In such cases at small Reynolds numbers, the dominant forces and moments acting on the top plate of the rheometer are the viscous force in the direction parallel to the tilt axis, the pressure moment in the direction perpendicular to the tilt axis and in the cross-sectional plane, and the viscous moment in the direction along the height of the rheometer. These forces and moments on the top plate were found to increase as the misalignment tilt angle increases, leading to the rheometer underestimating the viscosity of the fluid by a greater magnitude with larger tilt angles. Three-dimensional numerical simulations validate the theoretical predictions.
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