Effects of relaxation time on start-up time for starting flow of Maxwell fluid in a pipe

Although the analytical solution of the starting flow of Maxwell fluid in a pipe has been derived for a long time, the effect of relaxation time lambda on start-up time t (s) of this flow is still not well understood. Especially, there exist a series of jumps on the t (s)-lambda curve. In this paper we introduce a normalized mechanical energy by mode decomposition and mathematical analogy to describe the start-up process. An improved definition of start-up time is presented based on the normalized mechanical energy. It is proved that the t (s)-lambda curve contains a series of jumps if lambda is larger than a critical value. The exact positions of the jumps are determined and the physical reason of the jumps is discussed.