Department of Mechanical Engineering, Texas Tech University, 7th and Boston, Lubbock, Texas 79409, USA.
J Chem Phys. 2010 Sep 21;133(11):114702. doi: 10.1063/1.3475197.
Hydrodynamic coupling of a spherical particle to an undeformable planar fluid-fluid interface under creeping-flow conditions is discussed. The interface can be either surfactant-free or covered with an incompressible surfactant monolayer. In the incompressible surfactant limit, a uniform surfactant concentration is maintained by Marangoni stresses associated with infinitesimal surfactant redistribution. Our detailed numerical calculations show that the effect of surface incompressibility on lateral particle motion is accurately accounted for by the first reflection of the flow from the interface. For small particle-interface distances, the remaining contributions are significant, but they are weakly affected by the surface incompressibility. We show that for small particle-wall gaps, the transverse and lateral particle resistance coefficients can be rescaled onto corresponding universal master curves. The scaling functions depend on a scaling variable that combines the particle-wall gap with the viscosity ratio between fluids on both sides of the interface. A logarithmic dependence of the contact value of the lateral resistance function on the viscosity ratio is derived. Accurate numerical calculations are performed using our Cartesian-representation method.
在蠕动流条件下，讨论了球形颗粒与不可变形的平面流体-流体界面的流体动力耦合。该界面可以是无表面活性剂的，也可以覆盖不可压缩的表面活性剂单层。在不可压缩表面活性剂极限下，通过与微小表面活性剂再分配相关的 Marangoni 应力来保持均匀的表面活性剂浓度。我们详细的数值计算表明，表面不可压缩性对颗粒横向运动的影响可以通过界面处的流动第一次反射准确地考虑到。对于小的颗粒-界面距离，剩余的贡献是显著的，但它们受表面不可压缩性的影响较弱。我们表明，对于小的颗粒-壁间隙，横向和侧向颗粒阻力系数可以重新缩放到相应的通用主曲线。缩放函数取决于一个缩放变量，该变量将颗粒-壁间隙与界面两侧流体之间的粘度比结合在一起。横向阻力函数的接触值与粘度比呈对数关系。使用我们的笛卡尔表示法进行了精确的数值计算。
