同轴圆筒流变仪初始瞬态黏度的解析与数值研究

同轴圆筒流变仪在恒剪速或恒应力测试初始过程中测试黏度远高于真实值的现象与流场非稳态作用等因素有关。测量间隙内的Couette流动研究主要集中在边界条件为恒值或某一具体时间函数下的理论推导,而测量间隙的边界条件实际为某一动边界。假设动边界为任意f(t),将同轴圆筒间Newtonian流体初始流变测试过程简化为无限大平板间Couette流动,采用特征函数法和Laplace变换推导应力和剪速边界下流场及表观黏度精确解,同时依据不同间隙尺寸和运动黏度对6种边界条件下的瞬态表观黏度进行数值计算。结果表明:当u <20 mm²·s^-1时,控制剪速边界下流场及表观黏度平衡时间更短;当20 mm²·s^-12·s^-1时,控制应力边界下流场及表观黏度平衡时间更短;当u >20000 mm²·s^-1时,两类边界条件下的平衡时间相近。

Analytical and numerical studies on apparent viscosity in coaxial cylinder rotational rheometer during initial unsteady stage

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.