This paper is concerned with the hydrodynamic instability of the developing two-phase mixing layers. The development of mixing layers downstream of a splitter plate is initially dominated by a linear stability mechanism, and the coherent structures originate as a result of instabilities of instantaneous disturbed flows. Thus from a fundamental point of view, one of the purpose of the hydrodynamic stability theory is to understand the transition from laminar to turbulent flows.The main objective of this study is to investigate the effects of particles on the spatially developing two-phase mixing layer. Linear stability of the two-phase mixing layers is formulated and solved by two-directional integration method. It is found that this matching method gives more accurate results than the one-directional integration method.The numerical calculations of the effects of particles on the viscous spatial stability of the mixing layers are presented. Considering the assumption that the mean velocity profile of the particulate two-phase flow is identical to that of the single-phase flow, the resulting Orr-Sommerfeld equation was sofved numerically.For the viscous spatial stability of the particulate two-phase mixing layers, it is found that the presence of particles attenuates the most amplified rates and stabilizes the flow caused by the mean velocity gradient in the mixing layer. As the nondimensional parameter, X, increases, the amplification rate decreases.The higher the X, the more deviation of the eigenfunctions is seen between the single and two-phase flows. As the X increases, the peak of the Reynolds stress decreases due to the Stokes drag on the particles.
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