A more fundamental understanding of non-equilibrium phenomena involving fluids confined to restricted geometries presents indeed a difficult challenge. Here we explore a novel approach to describe the collective diffusion of Brownian particles confined to a spherical surface by adapting the dynamic density functional theory (DDFT) to this geometry. The ensuing diffusion equation is then transformed into a system of coupled ordinary differential equations by implementing spherical harmonics expansions of the relevant functions. This study is complemented with Brownian dynamics (BD) simulations performed with an innovative extension of the Ermak–McCammon algorithm, while employing conditional ensemble averages over initial non-equilibrium states. In both cases the relaxations processes are analyzed through the decay modes obtained from the spectral method. The simple DDFT approach considered here provides a fairly good description of the BD results. In particular, the theoretical predictions for the initial progression rates of the local density modes turn out to be almost exact, and we found that this can be explained in terms of the eigenvalues and eigenvectors corresponding to an initial renormalized potential. As an illustration, the model system has been tailored to the experimental conditions of Pickering emulsions stabilized by functionalized gold nanoparticles.

对涉及受限于有限几何形状的流体的非平衡现象的更基本的理解确实提出了艰巨的挑战。在这里，我们探索一种新颖的方法，通过将动态密度泛函理论（DDFT）应用于这种几何形状，来描述局限于球形表面的布朗粒子的集体扩散。然后，通过实现相关函数的球谐展开，将随后的扩散方程转化为耦合的常微分方程组。这项研究通过对Ermak–McCammon算法的创新扩展而进行的布朗动力学（BD）模拟进行了补充，同时在初始非平衡状态上采用了条件集合平均。在这两种情况下，通过从光谱方法获得的衰减模式来分析弛豫过程。这里考虑的简单DDFT方法可以很好地描述BD结果。特别地，关于局部密度模式的初始进展速率的理论预测几乎是精确的，并且我们发现这可以用对应于初始重新归一化势能的特征值和特征向量来解释。作为说明，模型系统已针对由功能化金纳米粒子稳定的Pickering乳液的实验条件进行了定制。局部密度模式的初始发展速度的理论预测几乎是准确的，并且我们发现这可以用对应于初始重新归一化势能的特征值和特征向量来解释。作为说明，模型系统已针对由功能化金纳米粒子稳定的Pickering乳液的实验条件进行了定制。局部密度模式的初始发展速度的理论预测几乎是准确的，并且我们发现这可以用对应于初始重新归一化势能的特征值和特征向量来解释。作为说明，模型系统已针对由功能化金纳米粒子稳定的Pickering乳液的实验条件进行了定制。