Keh HJ, Kuo J
Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan, 106-17, Republic of China
J Colloid Interface Sci. 1997 Jan 15;185(2):411-23. doi: 10.1006/jcis.1996.4594.
An analytical study is presented for the quasisteady translation and steady rotation of a spherical particle covered by a layer of adsorbed polymers located at the center of a spherical cavity that may also have an adsorbed polymer layer on its inside wall. The Reynolds number is assumed to be small, and the surface polymer layers are assumed to be thin with respect to the particle radius and the spacing between solid surfaces. To solve the Stokes flow equations within and outside the polymer layers a method of matched asymptotic expansions in small parameters lambda1 and lambda2 is used, where lambda1 and lambda2 are the ratios of the polymer-layer length scale to the radius of curvature at the particle surface and at the cavity wall, respectively. The results for the hydrodynamic force and torque exerted on the particle are expressed as an effective hydrodynamic thickness (L) of the adsorbed polymer layer surrounding the particle, which are accurate to O(lambda21). The O(lambda1) term for L normalized by its value in the absence of the cavity is found to be independent of the polymer segment distribution, the hydrodynamic interactions among the segments, and the volume fraction of the segments. The O(lambda21) term for L, however, is a sensitive function of the polymer segment distribution and the volume fraction of the segments. In general, the boundary effects on the motion of a polymer-coated particle can be quite significant in appropriate situations.
本文针对位于球形腔中心的、覆盖有吸附聚合物层的球形颗粒的准稳态平移和稳态旋转进行了分析研究，该球形腔的内壁也可能有一层吸附聚合物层。假设雷诺数较小，且表面聚合物层相对于颗粒半径和固体表面之间的间距较薄。为求解聚合物层内外的斯托克斯流动方程，采用了在小参数λ1和λ2下的匹配渐近展开法，其中λ1和λ2分别是聚合物层长度尺度与颗粒表面和腔壁处曲率半径的比值。施加在颗粒上的流体动力和扭矩的结果表示为围绕颗粒的吸附聚合物层的有效流体动力学厚度（L），其精度为O(λ21)。发现L的O(λ1)项在无腔情况下按其值归一化后与聚合物链段分布、链段间的流体动力相互作用以及链段的体积分数无关。然而，L的O(λ21)项是聚合物链段分布和链段体积分数的敏感函数。一般来说，在适当情况下，边界对聚合物包覆颗粒运动的影响可能相当显著。
