Apparent viscosity is an important parameter for fundamental research and industrial applications of colloidal suspensions. Core–shell particles are generally applied to carry, transport and protect functional materials and ingredients. In the present study the apparent viscosity of the monodisperse core–shell particles in suspensions was analytically formulated by introducing the cell model based on the low Reynolds number hydrodynamics at steady states. Three cell models proposed by Simha, Happel and Kuwabara, respectively, were applied to explore the problems. The core–shell particles were generally considered to be composed of two immiscible concentric liquids, each of which can approach to the solid phase or gas phase in limiting situations. The factors influencing the apparent viscosity from the viscosity of the surrounding fluid were not only the volume fraction of particles in the suspension, but also the viscosity of the fluids constituting the particles. For a dilute multi-emulsion with $\phi$ < 0.1 and the core volume of 50 vol% the particle, the apparent viscosity of the suspension slightly increased by less than 1.25 times due to the changes in shell viscosity; however, the apparent viscosity increased significantly by 3.5–4.2 times in a concentration system with $\phi =0.5$. In addition, the apparent viscosity also increases monotonically with increasing the core viscosity; while, the influence of core viscosity on apparent viscosity was much less than that of the shell viscosity. Increasing the shell thickness can result in a decrease in the apparent viscosity of the multi-emulsion.

表观粘度是胶体悬浮液的基础研究和工业应用的重要参数。核壳颗粒通常用于携带，运输和保护功能性材料和成分。在本研究中，悬浮液中单分散核-壳颗粒的表观粘度是通过引入基于稳态下低雷诺数流体动力学的细胞模型来解析确定的。分别使用Simha，Happel和Kuwabara提出的三个单元模型来探讨这些问题。通常认为核-壳颗粒由两种不混溶的同心液体组成，在限制情况下，每种液体都可以接近固相或气相。由周围流体的粘度影响表观粘度的因素不仅是悬浮液中颗粒的体积分数，而且是构成颗粒的流体的粘度。对于具有稀释性的乳液$\phi$<0.1，且颗粒的芯体积为50 vol％，由于壳粘度的变化，悬浮液​​的表观粘度略微提高了不到1.25倍；但是，在浓缩系统中，表观粘度显着提高了3.5–4.2倍。$\phi =0。5$。另外，表观粘度也随着核心粘度的增加而单调增加。而核粘度对表观粘度的影响远小于壳粘度。壳厚度的增加可导致多乳液的表观粘度降低。