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Dabade, Vivekanand Marath, Navaneeth K. and Subramanian, Ganesh 2016. The effect of inertia on the orientation dynamics of anisotropic particles in simple shear flow. Journal of Fluid Mechanics, Vol. 791, p. 631.
Mandal, Shubhadeep Ghosh, Uddipta and Chakraborty, Suman 2016. Effect of surfactant on motion and deformation of compound droplets in arbitrary unbounded Stokes flows. Journal of Fluid Mechanics, Vol. 803, p. 200.
Daghooghi, Mohsen and Borazjani, Iman 2015. The influence of inertia on the rheology of a periodic suspension of neutrally buoyant rigid ellipsoids. Journal of Fluid Mechanics, Vol. 781, p. 506.
Haddadi, Hamed and Morris, Jeffrey F. 2015. Topology of pairsphere trajectories in finite inertia suspension shear flow and its effects on microstructure and rheology. Physics of Fluids, Vol. 27, Issue. 4, p. 043302.
Li, Run Zhang, Jingsheng Yong, Yumei Wang, Yang and Yang, Chao 2015. Numerical simulation of steady flow past a liquid sphere immersed in simple shear flow at low and moderate Re. Chinese Journal of Chemical Engineering, Vol. 23, Issue. 1, p. 15.
Loisel, V. Abbas, M. Masbernat, O. and Climent, E. 2015. Inertiadriven particle migration and mixing in a wallbounded laminar suspension flow. Physics of Fluids, Vol. 27, Issue. 12, p. 123304.
Haddadi, Hamed and Morris, Jeffrey F. 2014. Microstructure and rheology of finite inertia neutrally buoyant suspensions. Journal of Fluid Mechanics, Vol. 749, p. 431.
Li, Run Zhang, Jingsheng Yang, Chao Mao, ZaiSha and Yin, Xiaolong 2014. Numerical study on steady and transient mass/heat transfer involving a liquid sphere in simple shear creeping flow. AIChE Journal, Vol. 60, Issue. 1, p. 343.
Prakash, Jai Lavrenteva, Olga M. Byk, Leonid and Nir, Avinoam 2013. Interaction of equalsize bubbles in shear flow. Physical Review E, Vol. 87, Issue. 4,
Yeo, Kyongmin and Maxey, Martin R. 2013. Dynamics and rheology of concentrated, finiteReynoldsnumber suspensions in a homogeneous shear flow. Physics of Fluids, Vol. 25, Issue. 5, p. 053303.
We calculate the rheological properties of a dilute emulsion of neutrally buoyant nearly spherical drops at O(φRe3/2) in a simple shear flow(u∞ =
Combining the results of our O(φRe3/2) analysis with the known rheology of a dilute emulsion to O(φRe) leads to the following expressions for the relative viscosity (μe), and the nondimensional first (N1) and second normal stress differences (N2) to O(φRe3/2): μe = 1 + φ[(5λ+2)/(2(λ+1))+0.024Re3/2(5λ+2)2/(λ+1)2]; N1=φ[−Re4(3λ2+3λ+1)/(9(λ+1)2)+0.066Re3/2(5λ+2)2/(λ+1)2] and N2 = φ[Re2(105λ2+96λ+35)/(315(λ+1)2)−0.085Re3/2(5λ+2)2/(λ+1)2].
Thus, for small but finite Re, inertia endows an emulsion with a nonNewtonian rheology even in the infinitely dilute limit, and in particular, our calculations show that, aside from normal stress differences, such an emulsion also exhibits a shearthickening behaviour. The results for a suspension of rigid spherical particles are obtained in the limit λ → ∞.
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