Hütter Markus, Kröger Martin
Polymer Physics, ETH Zürich, Department of Materials, Wolfgang-Pauli-Strasse 10, CH-8093 Zürich, Switzerland.
J Chem Phys. 2006 Jan 28;124(4):044511. doi: 10.1063/1.2161214.
In this article we derive the phoretic forces acting on a tracer particle, which is assumed to be small compared to the mean free path of the surrounding nonequilibrium gas, but large compared to the size of the surrounding gas molecules. First, we review and extend the calculations of Waldmann [Z. Naturforsch. A 14A, 589 (1959)] using half-sphere integrations and an accommodation coefficient characterizing the collision process. The presented methodology is applied to a gas subject to temperature, pressure, and velocity gradients. Corresponding thermophoretic, barophoretic, and rheophoretic forces are derived, and explicit expressions for spherical particles are compared to known results. Second, nonequilibrium thermodynamics is used to join the diffusion equation for the tracer particle with the continuum equations of nonisothermal hydrodynamics of the solvent. So doing, the distinct origin of the thermophoretic and barophoretic forces is demonstrated. While the latter enters similarly to an interaction potential, the former is given by flux-flux correlations in terms of a Green-Kubo relation, as shown in detail.
在本文中，我们推导了作用于示踪粒子上的泳动力，该示踪粒子与周围非平衡气体的平均自由程相比假定为小尺寸，但与周围气体分子的尺寸相比假定为大尺寸。首先，我们回顾并扩展了瓦尔德曼[《自然科学研究》A辑14A卷，589页（1959年）]的计算，采用半球积分法以及一个表征碰撞过程的适应系数。所提出的方法应用于受温度、压力和速度梯度作用的气体。推导了相应的热泳力、压泳力和流泳力，并将球形粒子的显式表达式与已知结果进行了比较。其次，利用非平衡热力学将示踪粒子的扩散方程与溶剂的非等温流体动力学连续方程相结合。这样做，证明了热泳力和压泳力的不同起源。如详细所示，后者类似于相互作用势那样进入，而前者由格林 - 久保关系中的通量 - 通量关联给出。
