Geometric shapes of the interface surface of bicomponent flows between two concentric rotating cylinders  

作　　者：李开泰 史峰 

机构地区：[1]College of Science,Xi’an Jiaotong University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2008年第10期1363-1376,共14页应用数学和力学（英文版）

基　　金：the National Natural Science Foundation of China(Nos.10571142,10771167)

摘　　要：In this paper, the shape problem of interface of bicomponent flows between two concentric rotating cylinders is investigated. With tensor analysis, the problem is reduced to an energy functional isoperimetric problem when neglecting the effects of the dissipative energy caused by viscosity. We derive the associated Euler-Lagrangian equation, which is a nonlinear elliptic boundary value problem of the second order. Moreover, by considering the effects of the dissipative energy, we propose another total energy functional to characterize the geometric shape of the interface, and obtain the corresponding Euler-Lagrangian equation, which is also a nonlinear elliptic boundary value problem of the second order. Thus, the problem of the geometric shape is converted into a nonlinear boundary value problem of the second order in both cases.In this paper, the shape problem of interface of bicomponent flows between two concentric rotating cylinders is investigated. With tensor analysis, the problem is reduced to an energy functional isoperimetric problem when neglecting the effects of the dissipative energy caused by viscosity. We derive the associated Euler-Lagrangian equation, which is a nonlinear elliptic boundary value problem of the second order. Moreover, by considering the effects of the dissipative energy, we propose another total energy functional to characterize the geometric shape of the interface, and obtain the corresponding Euler-Lagrangian equation, which is also a nonlinear elliptic boundary value problem of the second order. Thus, the problem of the geometric shape is converted into a nonlinear boundary value problem of the second order in both cases.

关 键 词：bicomponent flow interface surface Navier-Stokes equations concentric rotating cylinders 

分 类 号：O35[理学—流体力学]