Linear stability of elastic and elasto-inertial pipe flows of viscoelastic fluids

Pipe flow is known to be linear stable at all Reynolds number when the fluid is Newtonian. However, when a dilute viscoelastic polymer is introduced, the flow can become linearly unstable. Prior linear stability analyses were carried out using the Oldroyd-B model [1,2]. These results suggest a critical Reynolds number of at least $\textrm{Re}_c \gtrsim 60$. Experiments show instability down to $\textrm{Re}_c \simeq 5$ in a shear-thinning viscoelastic polymer solutions [3]. Here, we include the effects of shear thinning in a linear stability calculation and find that instability persists to arbitrarily low $\textrm{Re}$. We will discuss the linear eigenfunctions and the effects of finite Schmidt number on the calculations.

[1] Garg et al., Phys. Rev. Lett. 121, 024502 (2018)

[2] Chaudhary et al., J. Fluid Mech. 908, A11 (2021)

[3] Choueiri et al., Proc. Natl. Acad. Sci. U.S.A., 118, e2102350118 (2021)