Purely pulsating flow of a viscoelastic fluid in a pipe revisited: The limit of large Womersley number

• The pulsating flow in a wide pipe of a viscoelastic fluid is considered.
• Simple approximate solution using the method of two scales is obtained.
• Flow structure is easily described by two algebraic functions of the Deborah number.

The flow of a Maxwell fluid in a pipe generated by a pulsating pressure gradient is considered. The problem is governed by two non-dimensional parameters, the Womersley number αα and a Deborah parameter γγ. We obtain a simple approximate solution in the limit of large αα (pipe diameter much larger than the viscous penetration depth) by solving the resulting boundary-layer problem through a two scales perturbation technique, which also helps to understand qualitatively the structure of the flow as γγ increases. This limit is of interest, for instance, for the blood flow in arteries. The main qualitative differences between the Newtonian fluid flow (γ=0γ=0) and the highly elastic fluid with γ=O(1)γ=O(1) or larger are easily discussed from the found solution in terms of just two algebraic functions of γγ.