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Droplet deformation is the first stage of all aerodynamically induced-breakups, considerably affecting the characteristics of the atomization. In the present study, using an adaptive volume of fluid method, two and three-dimensional direct numerical simulations have been performed to understand droplet deformation. A high Reynolds number and a range of relatively high Weber numbers are chosen, addressing the shear breakup of droplets in a stream. The study is focused on the initiation and growth of instabilities over the droplet. The role of Kelvin-Helmholtz and Rayleigh-Taylor instabilities in wave formation and azimuthal transverse modulation are shown and the obtained results for the most amplified wave-numbers are compared with instability theories for zero and non-zero vorticity layers. The present results for the most amplified wave-numbers and deformation topologies are in good agreement with the previous experimental results. [ABSTRACT FROM AUTHOR]

Abstract: The characterization of the motion of immersed bodies in fluids is existent in several manufacturing operations. In the current study, the unsteady motion of a spherical particle rolling down an inclined tube submerged in an incompressible Newtonian environment has been studied using experimental data of Chhabra et al., for a wide range of Reynolds numbers. An analytical expression for instantaneous particle velocity was gained using a non-perturbation series based technique so-called homotopy perturbation method first proposed by J.H. He. Therefore, acceleration and position of the particle are derived simply. Equation of motion was solved generally and for some realistic combinations of solid–liquid. The rolling behavior of the particle was studied clearly with the analytical method and had shown for different physical conditions. The effects of particle diameter (size), continues phase viscosity and inclination angle was studied. As an important result it was found that the inclination angle does not affect the acceleration duration. Present research shows the capability and effectiveness of HPM and exhibits a new application of this method for non-linear problems. Moreover, the limited studies for particles motion in contact with a solid boundary are extended. [Copyright &y& Elsevier]

Abstract: The settling behavior of solid particles is of fundamental importance in natural and artificial applications. In current study, the unsteady motion of a spherical particle falling in a Newtonian fluid was analyzed using a drag of the form given by Oseen/Ferreira, for a range of Reynolds numbers. Particle equation of motion involved added-mass term and neglected the Basset term. Using the homotopy perturbation method (HPM) analytical expressions for the instantaneous velocity, acceleration and position of the particle were derived. The practical applications of the results were discussed. The presented investigation showed the effectiveness of HPM. [Copyright &y& Elsevier]

Abstract: The description of the motion of immersed bodies in fluids is present in several manufacturing processes. In the current study, the unsteady motion of a spherical particle rolling down an inclined plane submerged in a Newtonian environment has been studied using a drag of the form given by Chhabra and Ferreira, for wide range of Reynolds numbers. An analytical solution for velocity, acceleration and position of the particle is derived, using homotopy perturbation method. Equation of motion was solved generally and for some practical conditions. The present investigation shows the effectiveness of HPM and exhibits a new application of this method for nonlinear problems. [Copyright &y& Elsevier]