The classical oscillatory shear wave model of Ferry et al. [J. Polym. Sci. 2:593-611, (1947)] is extended for active linear and nonlinear microrheology. In the Ferry protocol, oscillation and attenuation lengths of the shear wave measured from strobe photographs determine storage and loss moduli at each frequency of plate oscillation. The microliter volumes typical in biology require modifications of experimental method and theory. Microbead tracking replaces strobe photographs. Reflection from the top boundary yields counterpropagating modes which are modeled here for linear and nonlinear viscoelastic constitutive laws. Furthermore, bulk imposed strain is easily controlled, and we explore the onset of normal stress generation and shear thinning using nonlinear viscoelastic models. For this paper, we present the theory, exact linear and nonlinear solutions where possible, and simulation tools more generally. We then illustrate errors in inverse characterization by application of the Ferry formulas, due to both suppression of wave reflection and nonlinearity, even if there were no experimental error. This shear wave method presents an active and nonlinear analog of the two-point microrheology of Crocker et al. [Phys. Rev. Lett. 85: 888 - 891 (2000)]. Nonlocal (spatially extended) deformations and stresses are propagated through a small volume sample, on wavelengths long relative to bead size. The setup is ideal for exploration of nonlinear threshold behavior.

中文翻译：

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用于活动线性和非线性微流变学的 Ferry 横波模型的扩展。

Ferry 等人的经典振荡横波模型。[J. 聚合物。科学。2:593-611, (1947)] 扩展到有源线性和非线性微流变学。在 Ferry 协议中，从频闪照片测量的剪切波的振荡和衰减长度确定了每个板块振荡频率下的存储和损耗模量。生物学中典型的微升体积需要修改实验方法和理论。微珠跟踪取代了频闪照片。来自顶部边界的反射产生反向传播模式，此处针对线性和非线性粘弹性本构定律进行建模。此外，体积施加的应变很容易控制，我们使用非线性粘弹性模型探索法向应力生成和剪切变稀的开始。对于本文，我们提出了理论，尽可能精确的线性和非线性解决方案，以及更通用的仿真工具。然后，我们通过应用 Ferry 公式来说明由于波反射和非线性的抑制，即使没有实验误差，逆表征中的误差。这种剪切波方法提供了 Crocker 等人的两点微流变学的主动非线性模拟。[物理。牧师莱特。85: 888 - 891 (2000)]。非局部（空间扩展）变形和应力通过小体积样品传播，波长相对于珠子尺寸长。该设置非常适合探索非线性阈值行为。由于波反射和非线性的抑制，即使没有实验误差。这种剪切波方法提供了 Crocker 等人的两点微流变学的主动非线性模拟。[物理。牧师莱特。85: 888 - 891 (2000)]。非局部（空间扩展）变形和应力通过小体积样品传播，波长相对于珠子尺寸长。该设置非常适合探索非线性阈值行为。由于波反射和非线性的抑制，即使没有实验误差。这种剪切波方法提供了 Crocker 等人的两点微流变学的主动非线性模拟。[物理。牧师莱特。85: 888 - 891 (2000)]。非局部（空间扩展）变形和应力通过小体积样品传播，波长相对于珠子尺寸长。该设置非常适合探索非线性阈值行为。