关键词: 黏度, 流体动力学, 数值分析, 同轴圆筒流变仪, Couette流动, 动边界函数, 特征函数法

Abstract:

During the initial testing stage with controlled stress or controlled shear rate, apparent viscosity is much higher than its true value because of factors such as transient flow process. Most existing researches about Couette flow in the measuring gap of coaxial cylinder rotational rheometer focus on constant boundary or time-dependent boundary in special form, which may has a gap with the actual changing boundary condition within rheometer. Thus, the arbitrary moving boundary condition was taken as f(t), and the transient flow was simplified in coaxial cylinder for Couette flow into two infinite parallel plates. The exact solutions of apparent viscosity and velocity under controlled stress boundary and controlled shear rate boundary were derived through eigenfunction method and Laplace transform. Meanwhile, the numerical calculations of apparent viscosity under six boundary conditions were made according to two kinds of gap size and different viscosity (2—200000 mm²·s^-1). It showed that when the viscosity of newton fluid was below 20 mm²·s^-1, the equilibrium of flow and apparent viscosity under controlled shear rate boundary cost less time. When the viscosity was among 20—20000 mm²·s^-1, the equilibrium under controlled stress boundary cost less time. However, the equilibrium time under two kinds of boundary was nearly the same when the viscosity was over 20000 mm²·s^-1.

Key words: viscosity, hydrodynamics, numerical analysis, coaxial cylinder rotational rheometer, Couette, moving boundary condition, eigenfunction method