Tarazona P, Marini Bettolo Marconi Umberto
Departamento de Física Teórica de la Materia Condensada, and Instituto de Ciencia de Materiales Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049 Madrid, Spain.
J Chem Phys. 2008 Apr 28;128(16):164704. doi: 10.1063/1.2904881.
Motivated by recent studies on the dynamics of colloidal solutions in narrow channels, we consider the steady state properties of an assembly of noninteracting particles subject to the action of a traveling potential moving at a constant speed, while the solvent is modeled by a heat bath at rest in the laboratory frame. Here, since the description we propose takes into account the inertia of the colloidal particles, it is necessary to consider the evolution of both positions and momenta and study the governing equation for the one-particle phase-space distribution. First, we derive the asymptotic form of its solutions as an expansion in Hermite polynomials and their generic properties, such as the force and energy balance, and then we particularize our study to the case of an inverted parabolic potential barrier. We numerically obtain the steady state density and temperature profile and show that the expansion is rapidly convergent for large values of the friction constant and small drifting velocities. On the one hand, the present results confirm the previous studies based on the dynamic density functional theory (DDFT): On the other hand, when the friction constant is large, it display effects such as the presence of a wake behind the barrier and a strong inhomogeneity in the temperature field which are beyond the DDFT description.
受近期关于窄通道中胶体溶液动力学研究的启发，我们考虑了一组非相互作用粒子在以恒定速度移动的行波势作用下的稳态性质，而溶剂在实验室坐标系中由静止的热浴来建模。在此，由于我们提出的描述考虑了胶体粒子的惯性，所以有必要考虑位置和动量的演化，并研究单粒子相空间分布的控制方程。首先，我们将其解的渐近形式推导为厄米多项式展开及其一般性质，如力和能量平衡，然后将研究具体到倒抛物线势垒的情况。我们通过数值方法得到稳态密度和温度分布，并表明对于大摩擦常数和小漂移速度，该展开迅速收敛。一方面，目前的结果证实了基于动态密度泛函理论（DDFT）的先前研究；另一方面，当摩擦常数很大时，它表现出诸如势垒后存在尾流以及温度场中强烈的不均匀性等效应，这些是DDFT描述所无法涵盖的。
