In this paper I present a simple and self-consistent framework based on microrheology that allows one to obtain the mechanical response of viscoelastic fluids and gels from the motion of probe particles immersed on it. By considering a non-markovian Langevin equation, I obtain general expressions for the mean-squared displacement and the time-dependent diffusion coefficient that are directly related to the memory kernels and the response function, and which allow one to obtain estimates for the complex shear modulus and the complex viscosity of the material. The usefulness of such approach is demonstrated by applying it to describe experimental data on chemically cross-linked polyacrylamide through its sol-gel transition.

中文翻译：

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凝胶粘弹性响应的微流变学方法

在这篇论文中，我提出了一种基于微流变学的简单且自洽的框架，它允许人们从浸在其上的探针粒子的运动中获得粘弹性流体和凝胶的机械响应。通过考虑非马尔可夫朗之万方程，我获得了均方位移和瞬态扩散系数的一般表达式，它们与记忆核和响应函数直接相关，并允许获得复切变的估计模量和材料的复数粘度。这种方法的有效性通过将其应用于描述化学交联聚丙烯酰胺通过其溶胶-凝胶转变的实验数据来证明。