屈服应力流体液滴在垂直振荡下的铺展动力学
Spreading dynamics of a drop of yield-stress fluid subject to vertical oscillations
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- The University of Manchester（曼彻斯特大学）
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中文总结 AI 辅助
本研究通过实验与数值模拟对比，探究垂直振荡下屈服应力液滴的铺展动力学，发现SHB模型低估振荡响应，但可调整溶剂粘度捕捉铺展，并建立阈值加速度与屈服数的比例关系，为估算屈服应力提供新方法。
中文摘要 AI 辅助
从非理想化流动中测量流变性质是表征屈服应力材料的常规方法。我们扩展了经典的坍落度测试（该测试基于大液滴在重力作用下的铺展来评估屈服应力），通过使此类液滴的基底承受垂直振荡来实现。我们通过实验与数值模拟的直接对比来测试这种流动构型，数值模拟求解了与Saramito-Herschel-Bulkley (SHB)本构模型耦合的时间依赖柯西方程。这为SHB模型在接近屈服状态时提供了灵敏的测试，因为受振液滴可以通过随强制加速度增加而调整其形状来释放超过屈服应力的应力，从而在所有强制条件下都保持接近屈服阈值。我们发现SHB模型系统性地将液滴对强制的粘弹性振荡响应幅度低估了五倍。然而，通过选择代表材料适当屈服后流变特性的溶剂粘度，可以在牺牲匹配屈服前特性的代价下，数值上捕捉铺展行为。这凸显了模拟屈服与未屈服材料共存流动（如原型流变测试中遇到的流动）的根本性挑战。我们通过建立诱导铺展所需的阈值加速度（相对于重力）与屈服数（屈服应力与作用于液滴质心的重力应力之比）之间的比例关系，确立了受振液滴作为一种强大的原型流变构型，用于估算不同流变性、尺寸和形状液滴的屈服应力。
英文摘要
The measurement of rheological properties from non-idealised flows is routinely used to characterise yield-stress materials. We extend the canonical slump test, which evaluates yield stress based on the spread of a large drop under gravity, by subjecting such a drop to vertical oscillation of its substrate. We test this flow configuration by direct comparison between experiments and numerical simulations of the time-dependent Cauchy equations coupled to the Saramito-Herschel-Bulkley (SHB) constitutive model. This provides a sensitive test of the SHB model near yield because the vibrated drop can releases stress exceeding the yield stress by adjusting its shape as the forcing acceleration is increased, and thus, remains close to the yield threshold for all forcing. We find that the SHB model systematically underpredicts the amplitude of the viscoelastic oscillatory response of the drop to forcing by a factor of five. However, spreading can be captured numerically by selecting a solvent viscosity that represents the appropriate post-yield rheology of the material at the expense of matching sub-yield properties. This highlights a fundamental challenge in simulating flows in which yielded and unyielded material coexist, such as those encountered in proto-rheological tests. We establish the vibrated drop as a powerful proto-rheological configuration for estimating the yield stress across drops of different rheology, size and shape, by establishing a proportional relationship between the threshold acceleration required to induce spreading relative to gravity and the yield number, the ratio of yield stress to gravitational stress acting at the centre of mass of the drop.
