Stability of elastoviscoplastic plane Couette flow

Several studies have investigated the turbulent flow of elastoviscoplastic (EVP) fluids, which exhibit yield stress in addition to viscoelasticity. The instabilities that could be responsible for the transition to turbulence in the EVP fluid flows remain unknown. Thus, the present explores the linear stability of EVP plane Couette flow (PCF) by employing the Saramito model. The eigenvalue problem is solved by using the pseudo-spectral method. In the limit of vanishing yield stress, EVP fluid behaves as Upper Convected Maxwell (UCM) fluid. The creeping flow of UCM fluid exhibits two stable Gorodotsov \& Leonov (GL) modes, thus a stable flow. As the Bingham number (i.e., yield stress) increases, the GL modes become unstable, implying an unstable flow. Additionally, there are new unstable modes with phase speed equalling the average velocity of the fluid. The analysis reveals an extra tangential stress term, arising due to yield stress, is responsible for the predicted instabilities. Also, the Saramito model exhibits weak Hadamard instability, i.e., unstable perturbations of arbitrarily small wavelengths. The present study demonstrates the removal of the Hadamard instability by adding a stress diffusion term in the Saramito constitutive equation. To conclude, the PCF of an EVP fluid is linearly unstable.