Analytical study on wall friction in a pipe induced by oscillatory Maxwell flows

The wall friction induced by oscillatory Maxwell flow in a pipeline was studied. The oscillation of velocity was controlled by Bessel equations,and the analytical solution was obtained using the variable separation method.The effect of oscillatory frequency on the wall friction was analyzed.The results show that the resonance-like characteristic of wall friction is revealed.For some critical values of oscillatory frequency,the wall friction increased dramatically.The effects of the elastic parameters of Maxwell fluids,pipe diameter and oscillatory frequency on the wall friction can be expressed by two dimensionless parameters (ω and R).In a certain region of parameter ω, there are less numbers of resonance peaks for smaller parameter R in the correlative curve of wall friction with ω.With the increase of R,the positions of resonance peaks move towards left,the number of peaks increased,and the amplitude of peak decreased.When the value of R is over 12,the curve becomes a monotone decreasing curve without any peaks and just like that of Newtonian fluids.This resonance-like characteristic of the wall friction is very useful for increasing the efficiency of oil displacement in the cores.