Fluid–structure interaction in deformable circular microtubes with Phan–Thien–Tanner viscoelastic fluids: Influence of Newtonian solvent contribution

We investigate the fluid–structure interaction (FSI) of a viscoelastic fluid flowing through a long, slender, axisymmetric tube with an elastic, deformable wall. The deformation is assumed to be purely radial, thereby preserving the axisymmetric configuration. The fluid is modeled as a solvent–polymer mixture, in which the solvent exhibits Newtonian behavior and the polymeric stresses are described by the simplified Phan–Thien–Tanner (sPTT) constitutive model. The governing equations are rendered dimensionless, introducing four key parameters: the wall-compliance parameter ( α ), the Weissenberg number ( W i ), the tube slenderness ratio ( δ ), and the viscosity ratio ( β s ). Under the lubrication approximation, the fluid and structural problems become fully coupled, leading to a nonlinear flow field in which the axial velocity depends implicitly on the local pressure gradient. The resulting governing equations are solved numerically. The analysis reveals the strong interplay between fluid viscoelasticity and wall deformability in determining the flow’s transport characteristics. Increasing wall compliance enlarges the channel cross-sectional area, thereby reducing hydraulic resistance and the pressure drop required to sustain a prescribed flow rate. Similarly, increasing the nonlinear polymeric contribution, either through larger ϵ W i 2 or smaller solvent viscosity ratios, reduces the apparent viscosity and the wall shear stress, thereby decreasing the pressure drop required to sustain the imposed flow rate.