A theoretical bridge between linear and nonlinear microrheology
A theoretical bridge between linear and nonlinear microrheology
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DOI：
10.1063/1.3598322
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发表时间：
2011-06-01
影响因子：
4.6
通讯作者：
Squires, Todd M.
中科院分区：
文献类型：
--
作者：
DePuit, Ryan J.;Khair, Aditya S.;Squires, Todd M.
被动微流变学利用波动耗散定理，通过假设的广义斯托克斯-爱因斯坦关系（GSER）将胶体探针的热波动与材料的近平衡线性响应行为联系起来。另一方面，主动和非线性微流变学测量强驱动探针的非线性响应，波动耗散不适用于该非线性响应。这使得没有明确的方法从这样的测量中恢复宏观流变特性。虽然这两种技术有很多共同之处，但很少有人试图将对一种技术的理解与另一种技术联系起来。在被动微观流变学中，一般假设GSER成立，而不需要显式计算微观结构变形和应力，而在非线性微观流变学中，必须显式确定微观结构以获得拖曳力。在这里，我们试图弥合这两种技术之间的理解的差距差距，通过使用一个单一的模型系统，明确探索温和的强制限制，被动（Ω> 0）和主动（U > 0）微观流变学是相同的。具体来说，我们明确计算的微观结构的变形和应力的微流变探针内移动的稀胶体悬浮液。在温和的强制限制，我们发现在散装材料的微观结构应力成正比的局部应变张量，独立的详细的流量，与有效的剪切模量相关的前因子。一个直接的后果是，由于被动（线性响应）微观流变学的体应力的探针电阻定量恢复宏观振荡剪切流变学的结果。然而，直接探针浴相互作用，导致定量的差异是无关的宏观剪切流变学。然后，我们检查非线性微观流变学的微观结构方程，其U > 0极限降低到被动微观流变学中的Ω> 0极限。从被动微观流变学的结果的指导下，我们表明，直接探针材料的相互作用无关的宏观剪切流变学。此外，我们表明，体积微观结构变形（定量恢复宏观剪切流变学的线性极限）现在服从一个控制方程，定性不同于宏观流变学，由于空间相关的，拉格朗日不稳定的混合物的剪切和拉伸流。这必然使非线性微观流变学的任何定量解释复杂化。(C)2011年美国物理学会。[doi：10.1063/1.3598322]
Passive microrheology exploits the fluctuation-dissipation theorem to relate thermal fluctuations of a colloidal probe to the near-equilibrium linear response behavior of the material through an assumed generalized Stokes Einstein relation (GSER). Active and nonlinear microrheology, on the other hand, measures the nonlinear response of a strongly driven probe, for which fluctuation-dissipation does not hold. This leaves no clear method for recovering the macroscopic rheological properties from such measurements. Although the two techniques share much in common, there has been little attempt to relate the understanding of one to the other. In passive microrheology, the GSER is generally assumed to hold, without the need for explicit calculation of the microstructural deformation and stress, whereas in nonlinear microrheology, the microstructure must be explicitly determined to obtain the drag force. Here we seek to bridge the gap in understanding between these two techniques, by using a single model system to explicitly explore the gentle-forcing limit, where passive (omega > 0) and active (U > 0) microrheology are identical. Specifically, we explicitly calculate the microstructural deformations and stresses as a microrheological probe moves within a dilute colloidal suspension. In the gentle-forcing limit, we find the microstructural stresses in the bulk material to be directly proportional to the local strain tensor, independent of the detailed flow, with a prefactor related to the effective shear modulus. A direct consequence is that the probe resistance due to the bulk stresses in passive (linear response) microrheology quantitatively recovers the results of macroscopic oscillatory shear rheology. Direct probe-bath interactions, however, lead to quantitative discrepancies that are unrelated to macroscopic shear rheology. We then examine the microstructural equations for nonlinear microrheology, whose U > 0 limit reduces to the omega > 0 limit in passive microrheology. Guided by the results from passive microrheology, we show that direct probe-material interactions are unrelated to the macroscopic shear rheology. Moreover, we show that the bulk microstructural deformations (which quantitatively recover macroscopic shear rheology in the linear limit) now obey a governing equation that differs qualitatively from macroscopic rheology, due to the spatially dependent, Lagrangian unsteady mixture of shear and extensional flows. This inherently complicates any quantitative interpretation of nonlinear microrheology. (C) 2011 American Institute of Physics. [doi:10.1063/1.3598322]