Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Phys Rev E. 2018 Jan;97(1-1):012608. doi: 10.1103/PhysRevE.97.012608.
The normal modes and relaxation rates of weak colloidal gels are investigated in calculations using different models of the hydrodynamic interactions between suspended particles. The relaxation spectrum is computed for freely draining, Rotne-Prager-Yamakawa, and accelerated Stokesian dynamics approximations of the hydrodynamic mobility in a normal mode analysis of a harmonic network representing several colloidal gels. We find that the density of states and spatial structure of the normal modes are fundamentally altered by long-ranged hydrodynamic coupling among the particles. Short-ranged coupling due to hydrodynamic lubrication affects only the relaxation rates of short-wavelength modes. Hydrodynamic models accounting for long-ranged coupling exhibit a microscopic relaxation rate for each normal mode, λ that scales as l^{-2}, where l is the spatial correlation length of the normal mode. For the freely draining approximation, which neglects long-ranged coupling, the microscopic relaxation rate scales as l^{-γ}, where γ varies between three and two with increasing particle volume fraction. A simple phenomenological model of the internal elastic response to normal mode fluctuations is developed, which shows that long-ranged hydrodynamic interactions play a central role in the viscoelasticity of the gel network. Dynamic simulations of hard spheres that gel in response to short-ranged depletion attractions are used to test the applicability of the density of states predictions. For particle concentrations up to 30% by volume, the power law decay of the relaxation modulus in simulations accounting for long-ranged hydrodynamic interactions agrees with predictions generated by the density of states of the corresponding harmonic networks as well as experimental measurements. For higher volume fractions, excluded volume interactions dominate the stress response, and the prediction from the harmonic network density of states fails. Analogous to the Zimm model in polymer physics, our results indicate that long-ranged hydrodynamic interactions play a crucial role in determining the microscopic dynamics and macroscopic properties of weak colloidal gels.
采用不同悬浮颗粒间流体力学相互作用模型对弱胶体凝胶的本征模和弛豫率进行了研究。在对代表几个胶体凝胶的谐和网络本征模分析中，利用自由排水、Rotne-Prager-Yamakawa 和加速Stokesian 动力学对流体力学迁移率的近似，计算了弛豫谱。研究发现，颗粒间长程流体力学耦合从根本上改变了态密度和本征模的空间结构。由于流体动力润滑产生的短程耦合仅影响短波长模的弛豫率。考虑长程耦合的流体动力学模型表现出各本征模的微观弛豫率λ，它与空间相关长度 l 呈 l^{-2}的标度关系。对于忽略长程耦合的自由排水近似，微观弛豫率λ与 l^{-γ}呈标度关系，其中 γ随颗粒体积分数增加在 3 到 2 之间变化。提出了一种关于本征模涨落对内禀弹性响应的简单唯象模型，它表明长程流体力学相互作用在凝胶网络粘弹性中起着核心作用。利用对短程耗散吸引力响应而凝胶化的硬球动力学模拟对态密度预测的适用性进行了检验。对于模拟中考虑长程流体力学相互作用时达到 30%体积分数的颗粒浓度，弛豫模量的幂律衰减与密度态的对应谐和网络以及实验测量结果生成的预测相符。对于更高的体积分数，排除体积相互作用主导了应力响应，谐和网络密度态的预测失效。与高分子物理中的 Zimm 模型类似，我们的结果表明，长程流体力学相互作用在决定弱胶体凝胶的微观动力学和宏观性质方面起着至关重要的作用。
