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.