Dipartimento di Biotecnologie Mediche e Medicina Traslazionale, Università degli Studi di Milano, Via Fratelli Cervi 93, 20090 Segrate, Italy.
Soft Matter. 2016 Aug 21;12(31):6588-600. doi: 10.1039/c6sm00935b. Epub 2016 Jul 18.
Linearised fluctuating hydrodynamics describes effectively the concentration non-equilibrium fluctuations (NEF) arising during a diffusion process driven by a small concentration gradient. However, fluctuations in the presence of large gradients are not yet fully understood. Here we study the giant concentration NEF arising when a dense aqueous colloidal suspension is allowed to diffuse into an overlying layer of pure water. We use differential dynamic microscopy to determine both the statics and the dynamics of the fluctuations for several values of the wave-vector q. At small q, NEF are quenched by buoyancy, which prevents their full development and sets an upper timescale to their temporal relaxation. At intermediate q, the mean squared amplitude of NEF is characterised by a power law exponent -4, and fluctuations relax diffusively with diffusion coefficient D1. At large q, the amplitude of NEF vanishes and equilibrium concentration fluctuations are recovered, enabling a straightforward determination of the osmotic compressibility of the suspension during diffusion. In this q-range we also find that the relaxation of the fluctuations occurs with a diffusion coefficient D2 significantly different from D1. Both diffusion coefficients exhibit time-dependence with D1 increasing monotonically (by about 15%) and D2 showing the opposite behaviour (about 17% decrease). At equilibrium, the two coefficients coincide as expected. While the decrease of D2 is compatible with a diffusive evolution of the concentration profile, the increase of D1 is still not fully understood and may require considering nonlinearities that are neglected in current theories for highly stressed colloids.
线性化涨落流体力学有效地描述了在由小浓度梯度驱动的扩散过程中出现的浓度非平衡涨落 (NEF)。然而，对于大梯度下的涨落，我们还没有完全理解。在这里，我们研究了当密集的水溶胶悬浮液被允许扩散到纯水的上层时出现的巨大浓度 NEF。我们使用差分动态显微镜来确定波动矢量 q 的几个值的涨落的静态和动态。在小 q 时，浮力会猝灭 NEF，从而阻止它们的充分发展并设置它们的时间松弛的上限时间尺度。在中间 q 时，NEF 的均方幅度由幂律指数 -4 来描述，并且涨落以扩散系数 D1 扩散性地松弛。在大 q 时，NEF 的幅度消失并恢复平衡浓度涨落，从而能够在扩散过程中直接确定悬浮液的渗透压。在这个 q 范围内，我们还发现涨落的松弛具有与 D1 明显不同的扩散系数 D2。两个扩散系数都表现出时间依赖性，D1 单调增加（约 15%），D2 表现出相反的行为（约 17%减少）。在平衡时，两个系数如预期的那样重合。虽然 D2 的减少与浓度分布的扩散演化兼容，但 D1 的增加仍然没有得到充分的理解，可能需要考虑当前高度应力胶体理论中忽略的非线性。
