The problem of flow past fluid spheres was first solved by Rybczynski and Hadmard where they had assumed both the flow field to be Newtonian. However, there are many practical cases where one or both of these immiscible fluids are non-Newtonian. One such case of importance is emulsions, where the non-Newtonian droplets are in the Newtonian liquid. To facilitate studies in this area, we present a systematic investigation on the motion of a Reiner–Rivlin fluid sphere(drop) contaminated with a monomolecular layer of surfactant film and dispersed in a spherical container having Newtonian fluid. The effect of surfactants is taken into account by the thermodynamic approach, which assumes a linear difference in the surface tension from the equilibrium value. The interfacial tension gradient caused by the surfactant adsorption at the drop surface generates surface forces exerted within the boundary region of the drop. The effect of the variable interfacial tension induces the Marangoni flow which causes the motion of the neighboring liquids by viscous traction and generates the Marangoni force which acts on the drop surface. The result shows that the drag force increases with the non-Newtonian cross-viscous parameter of the drop. The normalized force also increases with non-Newtonian cross-viscous parameter and when the Reiner–Rivlin viscous forces dominate the Newtonian viscous forces, which is offset in the presence of surface tension gradient forces. Further, as the surface tension gradient and non-Newtonian cross-viscous parameter of non-Newtonian fluid increases, the motion inside the drop slows down. The center of the internal circulation vortex migrates in Reiner–Rivlin fluid drop toward its center, when the Reiner–Rivlin viscous forces dominates the Newtonian viscous forces.

流过流体球的问题首先由 Rybczynski 和 Hadmard 解决，他们假设流场都是牛顿流场。然而，在许多实际情况下，这些不混溶流体中的一种或两种都是非牛顿流体。一种重要的情况是乳液，其中非牛顿液滴在牛顿液体中。为了促进该领域的研究，我们对 Reiner-Rivlin 流体球（液滴）的运动进行了系统研究，该球体被表面活性剂膜的单分子层污染并分散在具有牛顿流体的球形容器中。热力学方法考虑了表面活性剂的影响，该方法假设表面张力与平衡值之间存在线性差异。由液滴表面的表面活性剂吸附引起的界面张力梯度产生施加在液滴边界区域内的表面力。可变界面张力的影响引起马兰戈尼流动，通过粘性牵引引起相邻液体的运动，并产生作用于液滴表面的马兰戈尼力。结果表明，阻力随着液滴的非牛顿交叉粘性参数而增加。归一化力也随非牛顿交叉粘性参数而增加，并且当 Reiner-Rivlin 粘性力主导牛顿粘性力时，在存在表面张力梯度力的情况下会抵消这一点。此外，随着非牛顿流体的表面张力梯度和非牛顿交叉粘性参数的增加，水滴内部的运动减慢。当 Reiner-Rivlin 粘性力支配牛顿粘性力时，内环流涡的中心在 Reiner-Rivlin 流体滴中向其中心迁移。