Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany.
Soft Matter. 2017 May 14;13(18):3373-3384. doi: 10.1039/c7sm00459a. Epub 2017 Apr 21.
We consider a soft elastic matrix that contains particulate inclusions and is bounded by a rigid wall, e.g., the substrate. Such a situation arises in elastic composite materials. They may serve as soft actuators when forces are imposed on or induced between the embedded particles. We investigate how the presence of the rigid wall affects the interactions between the inclusions. First, for no-slip boundary conditions, we transfer Blake's derivation of a corresponding Green's function from low-Reynolds-number hydrodynamics to the linearly elastic case. Then, we list the general expressions to describe the situation for point-like particles in the presence of no-slip and free-slip surface conditions. To compare the effect of the different surface conditions to each other and to the bulk behavior, we address the example situation of pairwise interactions between two embedded particles. The axis through both particle centers is either aligned parallel or perpendicular to the surface. Our results suggest that walls with free-slip surface conditions are preferred when they serve as substrates for soft actuators made from elastic composite materials. As we further demonstrate, the presence of a rigid wall can qualitatively change the interactions between the inclusions. In effect, it can switch attractive interactions into repulsive ones (and vice versa). It should be straightforward to observe the effects in future experiments and to combine our results, e.g., with the modeling of biological cells and tissue on rigid surfaces.
我们考虑一个含有颗粒夹杂的软弹性基体，基体被一个刚性壁（例如，基底）所包围。这种情况会出现在弹性复合材料中。当力施加在嵌入的颗粒上或在它们之间产生时，它们可以作为软致动器。我们研究了刚性壁的存在如何影响夹杂之间的相互作用。首先，对于无滑移边界条件，我们将 Blake 从低雷诺数流体动力学推导出的相应格林函数转换到线性弹性情况。然后，我们列出了描述存在无滑移和自由滑移表面条件下点状颗粒情况的一般表达式。为了比较不同表面条件之间以及与整体行为之间的相互作用，我们考虑了两个嵌入颗粒之间的成对相互作用的示例情况。通过两个颗粒中心的轴要么与表面平行对齐，要么垂直对齐。我们的结果表明，当作为由弹性复合材料制成的软致动器的基底时，具有自由滑移表面条件的壁是优选的。正如我们进一步证明的那样，刚性壁的存在可以定性地改变夹杂之间的相互作用。实际上，它可以将吸引力相互作用转换为排斥力相互作用（反之亦然）。在未来的实验中观察这些效果，以及将我们的结果与刚性表面上生物细胞和组织的建模相结合，应该是很直接的。
