جستجوی مقالات مرتبط با کلیدواژه « حساب اغتشاشات » در نشریات گروه « مکانیک »

In this paper, steady motion of non-Newtonian falling drop through a Newtonian fluid at low Reynolds number is investigated analytically. Here, the Upper Convected Maxwell model (UCM) is used for drop phase and Newtonian model is considered for external fluid. During the past few decades, studies relating to non-Newtonian instabilities especially those involving free surfaces are amongst the most striking. These types of studies can be used to optimize design processes in, for example, the petroleum and medicine related processes, metal extraction, and paint and power-plant related fields. Analytical solution is obtained using the perturbation method. Reynolds and Deborah numbers are used to linearize the equations governing the problem in analytical method. Deborah number indicates the elastic effect of drop. The drag force increases by the growth of the elastic effect of non-Newtonian Drop’s. The non-Newtonian drop loses its shape and exchanges to an oblate form. Increment in Deborah number enhances the dimple at the bottom of the drop and results in an increment in its drag force and as a consequence its terminal velocity decreases. A hole is created at the rear of the drop due to the presence of inertia force and focus of normal component of stress at the rear of the drop. The novelty of this study is to consider the convection (non-linear) term of the momentum equations which was neglected in the previous studies due to the creeping flow.

Motion and deformation of the drop falling in an immiscible fluid has become a benchmark problem in fluid mechanics and has a wide range of application in petroleum, medicine processing, metals extraction, power plant and heat exchanger. In this paper, an exact analytical solution of a falling viscous drop at low Reynolds number is investigated. Analytical solution for both internal and external flows is obtained using the perturbation method. The Reynolds numbers and capillary are considered as the perturbation parameters. Drop’s shape remains spherical for sufficient small ones. The falling drop’s shape at Newtonian phase, deforms from its spherical shape as its volume increases. Inertial forces, surface tension, normal components stresses have the most influence on the falling drop’s shape. Drop’s deformation is due to the forces at the interfaces acting between two fluids. By volume increase of the falling drop, normal components stresses overcome to the surface tension and cause a dimple at the bottom drops in addition to the inertial force enhancement. For small non-dimensional parameters (Reynolds number and capillary) drop’s deformation is exactly similar to a sphere and then by increase in Reynolds number and capillary, the drop’s shape alters and cause a dimple at the bottom drops. Analytical solution show suitable agreement in terminal velocity and drop shape estimation with experimental results.